%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO879^1 : TPTP v9.2.1. Released v7.5.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n007.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 09:13:35 AM UTC 2026 % Result : Theorem 1.03s 1.24s % Output : Proof 1.03s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO879^1 : TPTP v9.2.1. Released v7.5.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n007.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Wed Jun 3 01:03:56 EDT 2026 % 0.17/0.34 % CPUTime : % 0.31/0.54 %----Proving TH0 % 1.03/1.24 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 1.03/1.24 % SZS status Theorem % 1.03/1.24 % SZS output start Proof % 1.03/1.24 ( % 1.03/1.24 (declare-sort $$unsorted 0) % 1.03/1.24 (declare-const tptp.c_False Bool) % 1.03/1.24 (declare-const tptp.c_In (-> $$unsorted $$unsorted Bool)) % 1.03/1.24 (declare-const tptp.c_Power (-> $$unsorted $$unsorted)) % 1.03/1.24 (declare-const tptp.c_Eps_i (-> (-> $$unsorted Bool) $$unsorted)) % 1.03/1.24 (declare-const tptp.c_Empty $$unsorted) % 1.03/1.24 (declare-const tptp.c_Repl (-> $$unsorted (-> $$unsorted $$unsorted) $$unsorted)) % 1.03/1.24 (declare-const tptp.c_Union (-> $$unsorted $$unsorted)) % 1.03/1.24 (declare-const tptp.c_Inj1 (-> $$unsorted $$unsorted)) % 1.03/1.24 (declare-const tptp.c_Unj (-> $$unsorted $$unsorted)) % 1.03/1.24 (declare-const tptp.c_V_ (-> $$unsorted $$unsorted)) % 1.03/1.24 (declare-const tptp.c_True Bool) % 1.03/1.24 (define tptp.c_not () (let ((_let_1 (@var "X0" Bool))) (lambda (@list _let_1) (=> _let_1 tptp.c_False)))) % 1.03/1.24 (define tptp.c_and () (let ((_let_1 (@var "X2" Bool))) (let ((_let_2 (@var "X1" Bool))) (let ((_let_3 (@var "X0" Bool))) (lambda (@list _let_3 _let_2) (forall (@list _let_1) (=> (=> _let_3 (=> _let_2 _let_1)) _let_1))))))) % 1.03/1.24 (define tptp.c_or () (let ((_let_1 (@var "X2" Bool))) (let ((_let_2 (@var "X1" Bool))) (let ((_let_3 (@var "X0" Bool))) (lambda (@list _let_3 _let_2) (forall (@list _let_1) (=> (=> _let_3 _let_1) (=> (=> _let_2 _let_1) _let_1)))))))) % 1.03/1.24 (define tptp.c_iff () (let ((_let_1 (@var "X0" Bool))) (let ((_let_2 (@var "X1" Bool))) (lambda (@list _let_1 _let_2) (_ (_ tptp.c_and (=> _let_1 _let_2)) (=> _let_2 _let_1)))))) % 1.03/1.24 (define tptp.c_Subq () (let ((_let_1 (@var "X1" $$unsorted))) (let ((_let_2 (@var "X2" $$unsorted))) (let ((_let_3 (_ tptp.c_In _let_2))) (let ((_let_4 (@var "X0" $$unsorted))) (lambda (@list _let_4 _let_1) (forall (@list _let_2) (=> (_ _let_3 _let_4) (_ _let_3 _let_1))))))))) % 1.03/1.24 (define tptp.c_TransSet () (let ((_let_1 (@var "X0" $$unsorted))) (let ((_let_2 (@var "X1" $$unsorted))) (lambda (@list _let_1) (forall (@list _let_2) (=> (_ (_ tptp.c_In _let_2) _let_1) (_ (_ tptp.c_Subq _let_2) _let_1))))))) % 1.03/1.24 (define tptp.c_atleast2 () (let ((_let_1 (@var "X1" $$unsorted))) (let ((_let_2 (@var "X0" $$unsorted))) (lambda (@list _let_2) (exists (@list _let_1) (_ (_ tptp.c_and (_ (_ tptp.c_In _let_1) _let_2)) (_ tptp.c_not (_ (_ tptp.c_Subq _let_2) (_ tptp.c_Power _let_1))))))))) % 1.03/1.24 (define tptp.c_atleast3 () (let ((_let_1 (@var "X1" $$unsorted))) (let ((_let_2 (@var "X0" $$unsorted))) (lambda (@list _let_2) (exists (@list _let_1) (_ (_ tptp.c_and (_ (_ tptp.c_Subq _let_1) _let_2)) (_ (_ tptp.c_and (_ tptp.c_not (_ (_ tptp.c_Subq _let_2) _let_1))) (_ tptp.c_atleast2 _let_1)))))))) % 1.03/1.24 (define tptp.c_atleast4 () (let ((_let_1 (@var "X1" $$unsorted))) (let ((_let_2 (@var "X0" $$unsorted))) (lambda (@list _let_2) (exists (@list _let_1) (_ (_ tptp.c_and (_ (_ tptp.c_Subq _let_1) _let_2)) (_ (_ tptp.c_and (_ tptp.c_not (_ (_ tptp.c_Subq _let_2) _let_1))) (_ tptp.c_atleast3 _let_1)))))))) % 1.03/1.24 (define tptp.c_atleast5 () (let ((_let_1 (@var "X1" $$unsorted))) (let ((_let_2 (@var "X0" $$unsorted))) (lambda (@list _let_2) (exists (@list _let_1) (_ (_ tptp.c_and (_ (_ tptp.c_Subq _let_1) _let_2)) (_ (_ tptp.c_and (_ tptp.c_not (_ (_ tptp.c_Subq _let_2) _let_1))) (_ tptp.c_atleast4 _let_1)))))))) % 1.03/1.24 (define tptp.c_atleast6 () (let ((_let_1 (@var "X1" $$unsorted))) (let ((_let_2 (@var "X0" $$unsorted))) (lambda (@list _let_2) (exists (@list _let_1) (_ (_ tptp.c_and (_ (_ tptp.c_Subq _let_1) _let_2)) (_ (_ tptp.c_and (_ tptp.c_not (_ (_ tptp.c_Subq _let_2) _let_1))) (_ tptp.c_atleast5 _let_1)))))))) % 1.03/1.24 (define tptp.c_exactly2 () (let ((_let_1 (@var "X0" $$unsorted))) (lambda (@list _let_1) (_ (_ tptp.c_and (_ tptp.c_atleast2 _let_1)) (_ tptp.c_not (_ tptp.c_atleast3 _let_1)))))) % 1.03/1.24 (define tptp.c_exactly3 () (let ((_let_1 (@var "X0" $$unsorted))) (lambda (@list _let_1) (_ (_ tptp.c_and (_ tptp.c_atleast3 _let_1)) (_ tptp.c_not (_ tptp.c_atleast4 _let_1)))))) % 1.03/1.24 (define tptp.c_exactly4 () (let ((_let_1 (@var "X0" $$unsorted))) (lambda (@list _let_1) (_ (_ tptp.c_and (_ tptp.c_atleast4 _let_1)) (_ tptp.c_not (_ tptp.c_atleast5 _let_1)))))) % 1.03/1.24 (define tptp.c_exactly5 () (let ((_let_1 (@var "X0" $$unsorted))) (lambda (@list _let_1) (_ (_ tptp.c_and (_ tptp.c_atleast5 _let_1)) (_ tptp.c_not (_ tptp.c_atleast6 _let_1)))))) % 1.03/1.24 (define tptp.c_exu_i () (let ((_let_1 (@var "X2" $$unsorted))) (let ((_let_2 (@var "X1" $$unsorted))) (let ((_let_3 (@var "X0" (-> $$unsorted Bool)))) (let ((_let_4 (_ _let_3 _let_2))) (lambda (@list _let_3) (_ (_ tptp.c_and (exists (@list _let_2) _let_4)) (forall (@list _let_2 _let_1) (=> _let_4 (=> (_ _let_3 _let_1) (= _let_2 _let_1))))))))))) % 1.03/1.24 (define tptp.c_reflexive_i () (let ((_let_1 (@var "X1" $$unsorted))) (let ((_let_2 (@var "X0" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 1.03/1.24 (define tptp.c_irreflexive_i () (let ((_let_1 (@var "X1" $$unsorted))) (let ((_let_2 (@var "X0" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ tptp.c_not (_ (_ _let_2 _let_1) _let_1))))))) % 1.03/1.24 (define tptp.c_symmetric_i () (let ((_let_1 (@var "X1" $$unsorted))) (let ((_let_2 (@var "X2" $$unsorted))) (let ((_let_3 (@var "X0" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 1.03/1.24 (define tptp.c_antisymmetric_i () (let ((_let_1 (@var "X2" $$unsorted))) (let ((_let_2 (@var "X1" $$unsorted))) (let ((_let_3 (@var "X0" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2 _let_1) (=> (_ (_ _let_3 _let_2) _let_1) (=> (_ (_ _let_3 _let_1) _let_2) (= _let_2 _let_1))))))))) % 1.03/1.24 (define tptp.c_transitive_i () (let ((_let_1 (@var "X3" $$unsorted))) (let ((_let_2 (@var "X1" $$unsorted))) (let ((_let_3 (@var "X0" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (_ _let_3 _let_2))) (let ((_let_5 (@var "X2" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_2 _let_5 _let_1) (=> (_ _let_4 _let_5) (=> (_ (_ _let_3 _let_5) _let_1) (_ _let_4 _let_1))))))))))) % 1.03/1.24 (define tptp.c_eqreln_i () (let ((_let_1 (@var "X0" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_1) (_ (_ tptp.c_and (_ (_ tptp.c_and (_ tptp.c_reflexive_i _let_1)) (_ tptp.c_symmetric_i _let_1))) (_ tptp.c_transitive_i _let_1))))) % 1.03/1.24 (define tptp.c_per_i () (let ((_let_1 (@var "X0" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_1) (_ (_ tptp.c_and (_ tptp.c_symmetric_i _let_1)) (_ tptp.c_transitive_i _let_1))))) % 1.03/1.24 (define tptp.c_linear_i () (let ((_let_1 (@var "X1" $$unsorted))) (let ((_let_2 (@var "X2" $$unsorted))) (let ((_let_3 (@var "X0" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (_ (_ tptp.c_or (_ (_ _let_3 _let_1) _let_2)) (_ (_ _let_3 _let_2) _let_1)))))))) % 1.03/1.24 (define tptp.c_trichotomous_or_i () (let ((_let_1 (@var "X1" $$unsorted))) (let ((_let_2 (@var "X2" $$unsorted))) (let ((_let_3 (@var "X0" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (_ (_ tptp.c_or (_ (_ tptp.c_or (_ (_ _let_3 _let_1) _let_2)) (= _let_1 _let_2))) (_ (_ _let_3 _let_2) _let_1)))))))) % 1.03/1.24 (define tptp.c_partialorder_i () (let ((_let_1 (@var "X0" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_1) (_ (_ tptp.c_and (_ (_ tptp.c_and (_ tptp.c_reflexive_i _let_1)) (_ tptp.c_antisymmetric_i _let_1))) (_ tptp.c_transitive_i _let_1))))) % 1.03/1.24 (define tptp.c_totalorder_i () (let ((_let_1 (@var "X0" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_1) (_ (_ tptp.c_and (_ tptp.c_partialorder_i _let_1)) (_ tptp.c_linear_i _let_1))))) % 1.03/1.24 (define tptp.c_strictpartialorder_i () (let ((_let_1 (@var "X0" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_1) (_ (_ tptp.c_and (_ tptp.c_irreflexive_i _let_1)) (_ tptp.c_transitive_i _let_1))))) % 1.03/1.24 (define tptp.c_stricttotalorder_i () (let ((_let_1 (@var "X0" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_1) (_ (_ tptp.c_and (_ tptp.c_strictpartialorder_i _let_1)) (_ tptp.c_trichotomous_or_i _let_1))))) % 1.03/1.24 (define tptp.c_If_i () (let ((_let_1 (@var "X2" $$unsorted))) (let ((_let_2 (@var "X3" $$unsorted))) (let ((_let_3 (@var "X0" Bool))) (let ((_let_4 (@var "X1" $$unsorted))) (lambda (@list _let_3 _let_4 _let_1) (_ tptp.c_Eps_i (lambda (@list _let_2) (_ (_ tptp.c_or (_ (_ tptp.c_and _let_3) (= _let_2 _let_4))) (_ (_ tptp.c_and (_ tptp.c_not _let_3)) (= _let_2 _let_1))))))))))) % 1.03/1.24 (define tptp.c_exactly1of2 () (let ((_let_1 (@var "X1" Bool))) (let ((_let_2 (@var "X0" Bool))) (lambda (@list _let_2 _let_1) (_ (_ tptp.c_or (_ (_ tptp.c_and _let_2) (_ tptp.c_not _let_1))) (_ (_ tptp.c_and (_ tptp.c_not _let_2)) _let_1)))))) % 1.03/1.24 (define tptp.c_exactly1of3 () (let ((_let_1 (@var "X2" Bool))) (let ((_let_2 (@var "X1" Bool))) (let ((_let_3 (@var "X0" Bool))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.c_or (_ (_ tptp.c_and (_ (_ tptp.c_exactly1of2 _let_3) _let_2)) (_ tptp.c_not _let_1))) (_ (_ tptp.c_and (_ (_ tptp.c_and (_ tptp.c_not _let_3)) (_ tptp.c_not _let_2))) _let_1))))))) % 1.03/1.24 (define tptp.c_nIn () (let ((_let_1 (@var "X1" $$unsorted))) (let ((_let_2 (@var "X0" $$unsorted))) (lambda (@list _let_2 _let_1) (_ tptp.c_not (_ (_ tptp.c_In _let_2) _let_1)))))) % 1.03/1.24 (define tptp.c_nSubq () (let ((_let_1 (@var "X1" $$unsorted))) (let ((_let_2 (@var "X0" $$unsorted))) (lambda (@list _let_2 _let_1) (_ tptp.c_not (_ (_ tptp.c_Subq _let_2) _let_1)))))) % 1.03/1.24 (define tptp.c_UPair () (let ((_let_1 (@var "X1" $$unsorted))) (let ((_let_2 (@var "X0" $$unsorted))) (let ((_let_3 (@var "X2" $$unsorted))) (lambda (@list _let_2 _let_1) (_ (_ tptp.c_Repl (_ tptp.c_Power (_ tptp.c_Power tptp.c_Empty))) (lambda (@list _let_3) (_ (_ (_ tptp.c_If_i (_ (_ tptp.c_In tptp.c_Empty) _let_3)) _let_2) _let_1)))))))) % 1.03/1.24 (define tptp.c_Sing () (let ((_let_1 (@var "X0" $$unsorted))) (lambda (@list _let_1) (_ (_ tptp.c_UPair _let_1) _let_1)))) % 1.03/1.24 (define tptp.c_binunion () (let ((_let_1 (@var "X1" $$unsorted))) (let ((_let_2 (@var "X0" $$unsorted))) (lambda (@list _let_2 _let_1) (_ tptp.c_Union (_ (_ tptp.c_UPair _let_2) _let_1)))))) % 1.03/1.24 (define tptp.c_SetAdjoin () (let ((_let_1 (@var "X1" $$unsorted))) (let ((_let_2 (@var "X0" $$unsorted))) (lambda (@list _let_2 _let_1) (_ (_ tptp.c_binunion _let_2) (_ tptp.c_Sing _let_1)))))) % 1.03/1.24 (define tptp.c_famunion () (let ((_let_1 (@var "X2" $$unsorted))) (let ((_let_2 (@var "X1" (-> $$unsorted $$unsorted)))) (let ((_let_3 (@var "X0" $$unsorted))) (lambda (@list _let_3 _let_2) (_ tptp.c_Union (_ (_ tptp.c_Repl _let_3) (lambda (@list _let_1) (_ _let_2 _let_1))))))))) % 1.03/1.24 (define tptp.c_Sep () (let ((_let_1 (@var "X2" $$unsorted))) (let ((_let_2 (@var "X4" $$unsorted))) (let ((_let_3 (@var "X1" (-> $$unsorted Bool)))) (let ((_let_4 (@var "X0" $$unsorted))) (let ((_let_5 (@var "X3" $$unsorted))) (let ((_let_6 (@list _let_1))) (lambda (@list _let_4 _let_3) (_ (_ (_ tptp.c_If_i (exists _let_6 (_ (_ tptp.c_and (_ (_ tptp.c_In _let_1) _let_4)) (_ _let_3 _let_1)))) (_ (_ tptp.c_Repl _let_4) (lambda _let_6 (_ (lambda (@list _let_5) (_ (_ (_ tptp.c_If_i (_ _let_3 _let_5)) _let_5) (_ tptp.c_Eps_i (lambda (@list _let_2) (_ (_ tptp.c_and (_ (_ tptp.c_In _let_2) _let_4)) (_ _let_3 _let_2)))))) _let_1)))) tptp.c_Empty))))))))) % 1.03/1.24 (define tptp.c_ReplSep () (let ((_let_1 (@var "X3" $$unsorted))) (let ((_let_2 (@var "X2" (-> $$unsorted $$unsorted)))) (let ((_let_3 (@list _let_1))) (let ((_let_4 (@var "X1" (-> $$unsorted Bool)))) (let ((_let_5 (@var "X0" $$unsorted))) (lambda (@list _let_5 _let_4 _let_2) (_ (_ tptp.c_Repl (_ (_ tptp.c_Sep _let_5) (lambda _let_3 (_ _let_4 _let_1)))) (lambda _let_3 (_ _let_2 _let_1)))))))))) % 1.03/1.24 (define tptp.c_binintersect () (let ((_let_1 (@var "X1" $$unsorted))) (let ((_let_2 (@var "X2" $$unsorted))) (let ((_let_3 (@var "X0" $$unsorted))) (lambda (@list _let_3 _let_1) (_ (_ tptp.c_Sep _let_3) (lambda (@list _let_2) (_ (_ tptp.c_In _let_2) _let_1)))))))) % 1.03/1.24 (define tptp.c_setminus () (let ((_let_1 (@var "X1" $$unsorted))) (let ((_let_2 (@var "X2" $$unsorted))) (let ((_let_3 (@var "X0" $$unsorted))) (lambda (@list _let_3 _let_1) (_ (_ tptp.c_Sep _let_3) (lambda (@list _let_2) (_ (_ tptp.c_nIn _let_2) _let_1)))))))) % 1.03/1.24 (define tptp.c_inj () (let ((_let_1 (@var "X4" $$unsorted))) (let ((_let_2 (@var "X3" $$unsorted))) (let ((_let_3 (@var "X2" (-> $$unsorted $$unsorted)))) (let ((_let_4 (_ _let_3 _let_2))) (let ((_let_5 (@var "X0" $$unsorted))) (let ((_let_6 (_ (_ tptp.c_In _let_2) _let_5))) (let ((_let_7 (@list _let_2))) (let ((_let_8 (@var "X1" $$unsorted))) (lambda (@list _let_5 _let_8 _let_3) (_ (_ tptp.c_and (forall _let_7 (=> _let_6 (_ (_ tptp.c_In _let_4) _let_8)))) (forall _let_7 (=> _let_6 (forall (@list _let_1) (=> (_ (_ tptp.c_In _let_1) _let_5) (=> (= _let_4 (_ _let_3 _let_1)) (= _let_2 _let_1))))))))))))))))) % 1.03/1.24 (define tptp.c_bij () (let ((_let_1 (@var "X3" $$unsorted))) (let ((_let_2 (@var "X4" $$unsorted))) (let ((_let_3 (@var "X2" (-> $$unsorted $$unsorted)))) (let ((_let_4 (@var "X0" $$unsorted))) (let ((_let_5 (@var "X1" $$unsorted))) (lambda (@list _let_4 _let_5 _let_3) (_ (_ tptp.c_and (_ (_ (_ tptp.c_inj _let_4) _let_5) _let_3)) (forall (@list _let_1) (=> (_ (_ tptp.c_In _let_1) _let_5) (exists (@list _let_2) (_ (_ tptp.c_and (_ (_ tptp.c_In _let_2) _let_4)) (= (_ _let_3 _let_2) _let_1))))))))))))) % 1.03/1.24 (define tptp.c_atleastp () (let ((_let_1 (@var "X2" (-> $$unsorted $$unsorted)))) (let ((_let_2 (@var "X1" $$unsorted))) (let ((_let_3 (@var "X0" $$unsorted))) (lambda (@list _let_3 _let_2) (exists (@list _let_1) (_ (_ (_ tptp.c_inj _let_3) _let_2) _let_1))))))) % 1.03/1.24 (define tptp.c_equip () (let ((_let_1 (@var "X2" (-> $$unsorted $$unsorted)))) (let ((_let_2 (@var "X1" $$unsorted))) (let ((_let_3 (@var "X0" $$unsorted))) (lambda (@list _let_3 _let_2) (exists (@list _let_1) (_ (_ (_ tptp.c_bij _let_3) _let_2) _let_1))))))) % 1.03/1.24 (define tptp.c_In_rec_poly_G_i () (let ((_let_1 (@var "X2" $$unsorted))) (let ((_let_2 (@var "X1" $$unsorted))) (let ((_let_3 (@var "X3" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "X5" (-> $$unsorted $$unsorted)))) (let ((_let_5 (@var "X4" $$unsorted))) (let ((_let_6 (@var "X0" (-> $$unsorted (-> $$unsorted $$unsorted) $$unsorted)))) (let ((_let_7 (@var "X6" $$unsorted))) (lambda (@list _let_6 _let_2 _let_1) (forall (@list _let_3) (=> (forall (@list _let_5 _let_4) (=> (forall (@list _let_7) (=> (_ (_ tptp.c_In _let_7) _let_5) (_ (_ _let_3 _let_7) (_ _let_4 _let_7)))) (_ (_ _let_3 _let_5) (_ (_ _let_6 _let_5) _let_4)))) (_ (_ _let_3 _let_2) _let_1)))))))))))) % 1.03/1.24 (define tptp.c_In_rec_poly_i () (let ((_let_1 (@var "X2" $$unsorted))) (let ((_let_2 (@var "X1" $$unsorted))) (let ((_let_3 (@var "X0" (-> $$unsorted (-> $$unsorted $$unsorted) $$unsorted)))) (lambda (@list _let_3 _let_2) (_ tptp.c_Eps_i (lambda (@list _let_1) (_ (_ (_ tptp.c_In_rec_poly_G_i _let_3) _let_2) _let_1)))))))) % 1.03/1.24 (define tptp.c_ordsucc () (let ((_let_1 (@var "X0" $$unsorted))) (lambda (@list _let_1) (_ (_ tptp.c_binunion _let_1) (_ tptp.c_Sing _let_1))))) % 1.03/1.24 (define tptp.c_nat_p () (let ((_let_1 (@var "X0" $$unsorted))) (let ((_let_2 (@var "X1" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X2" $$unsorted))) (lambda (@list _let_1) (forall (@list _let_2) (=> (_ _let_2 tptp.c_Empty) (=> (forall (@list _let_3) (=> (_ _let_2 _let_3) (_ _let_2 (_ tptp.c_ordsucc _let_3)))) (_ _let_2 _let_1))))))))) % 1.03/1.24 (define tptp.c_nat_primrec () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "X0" $$unsorted))) (let ((_let_3 (@var "X2" $$unsorted))) (let ((_let_4 (_ tptp.c_Union _let_3))) (let ((_let_5 (@var "X3" (-> $$unsorted $$unsorted)))) (let ((_let_6 (@var "X1" (-> $$unsorted $$unsorted $$unsorted)))) (lambda (@list _let_2 _let_6 _let_1) (_ (_ tptp.c_In_rec_poly_i (lambda (@list _let_3 _let_5) (_ (_ (_ tptp.c_If_i (_ (_ tptp.c_In _let_4) _let_3)) (_ (_ _let_6 _let_4) (_ _let_5 _let_4))) _let_2))) _let_1))))))))) % 1.03/1.24 (define tptp.c_add_nat () (let ((_let_1 (@var "X1" $$unsorted))) (let ((_let_2 (@var "X3" $$unsorted))) (let ((_let_3 (@var "X0" $$unsorted))) (lambda (@list _let_3 _let_1) (_ (_ (_ tptp.c_nat_primrec _let_3) (lambda (@list (@var "X2" $$unsorted) _let_2) (_ tptp.c_ordsucc _let_2))) _let_1)))))) % 1.03/1.24 (define tptp.c_mul_nat () (let ((_let_1 (@var "X1" $$unsorted))) (let ((_let_2 (@var "X3" $$unsorted))) (let ((_let_3 (@var "X0" $$unsorted))) (lambda (@list _let_3 _let_1) (_ (_ (_ tptp.c_nat_primrec tptp.c_Empty) (lambda (@list (@var "X2" $$unsorted) _let_2) (_ (_ tptp.c_add_nat _let_3) _let_2))) _let_1)))))) % 1.03/1.24 (define tptp.c_ordinal () (let ((_let_1 (@var "X1" $$unsorted))) (let ((_let_2 (@var "X0" $$unsorted))) (lambda (@list _let_2) (_ (_ tptp.c_and (_ tptp.c_TransSet _let_2)) (forall (@list _let_1) (=> (_ (_ tptp.c_In _let_1) _let_2) (_ tptp.c_TransSet _let_1)))))))) % 1.03/1.24 (define tptp.c_Inj0 () (let ((_let_1 (@var "X1" $$unsorted))) (let ((_let_2 (@var "X0" $$unsorted))) (lambda (@list _let_2) (_ (_ tptp.c_Repl _let_2) (lambda (@list _let_1) (_ tptp.c_Inj1 _let_1))))))) % 1.03/1.24 (define tptp.c_combine_funcs () (let ((_let_1 (@var "X4" $$unsorted))) (let ((_let_2 (_ tptp.c_Unj _let_1))) (let ((_let_3 (@var "X3" (-> $$unsorted $$unsorted)))) (let ((_let_4 (@var "X2" (-> $$unsorted $$unsorted)))) (lambda (@list (@var "X0" $$unsorted) (@var "X1" $$unsorted) _let_4 _let_3 _let_1) (_ (_ (_ tptp.c_If_i (= _let_1 (_ tptp.c_Inj0 _let_2))) (_ _let_4 _let_2)) (_ _let_3 _let_2)))))))) % 1.03/1.24 (define tptp.c_setsum () (let ((_let_1 (@var "X2" $$unsorted))) (let ((_let_2 (@list _let_1))) (let ((_let_3 (@var "X1" $$unsorted))) (let ((_let_4 (@var "X0" $$unsorted))) (lambda (@list _let_4 _let_3) (_ (_ tptp.c_binunion (_ (_ tptp.c_Repl _let_4) (lambda _let_2 (_ tptp.c_Inj0 _let_1)))) (_ (_ tptp.c_Repl _let_3) (lambda _let_2 (_ tptp.c_Inj1 _let_1)))))))))) % 1.03/1.24 (define tptp.c_proj0 () (let ((_let_1 (@var "X1" $$unsorted))) (let ((_let_2 (@list _let_1))) (let ((_let_3 (@var "X2" $$unsorted))) (let ((_let_4 (@var "X0" $$unsorted))) (lambda (@list _let_4) (_ (_ (_ tptp.c_ReplSep _let_4) (lambda _let_2 (exists (@list _let_3) (= (_ tptp.c_Inj0 _let_3) _let_1)))) (lambda _let_2 (_ tptp.c_Unj _let_1))))))))) % 1.03/1.24 (define tptp.c_proj1 () (let ((_let_1 (@var "X1" $$unsorted))) (let ((_let_2 (@list _let_1))) (let ((_let_3 (@var "X2" $$unsorted))) (let ((_let_4 (@var "X0" $$unsorted))) (lambda (@list _let_4) (_ (_ (_ tptp.c_ReplSep _let_4) (lambda _let_2 (exists (@list _let_3) (= (_ tptp.c_Inj1 _let_3) _let_1)))) (lambda _let_2 (_ tptp.c_Unj _let_1))))))))) % 1.03/1.24 (define tptp.c_binrep () (let ((_let_1 (@var "X1" $$unsorted))) (let ((_let_2 (@var "X0" $$unsorted))) (lambda (@list _let_2 _let_1) (_ (_ tptp.c_setsum _let_2) (_ tptp.c_Power _let_1)))))) % 1.03/1.24 (define tptp.c_lam () (let ((_let_1 (@var "X3" $$unsorted))) (let ((_let_2 (@var "X2" $$unsorted))) (let ((_let_3 (@var "X1" (-> $$unsorted $$unsorted)))) (let ((_let_4 (@var "X0" $$unsorted))) (lambda (@list _let_4 _let_3) (_ (_ tptp.c_famunion _let_4) (lambda (@list _let_2) (_ (_ tptp.c_Repl (_ _let_3 _let_2)) (lambda (@list _let_1) (_ (_ tptp.c_setsum _let_2) _let_1))))))))))) % 1.03/1.24 (define tptp.c_setprod () (let ((_let_1 (@var "X1" $$unsorted))) (let ((_let_2 (@var "X0" $$unsorted))) (lambda (@list _let_2 _let_1) (_ (_ tptp.c_lam _let_2) (lambda (@list (@var "X2" $$unsorted)) _let_1)))))) % 1.03/1.24 (define tptp.c_ap () (let ((_let_1 (@var "X2" $$unsorted))) (let ((_let_2 (@list _let_1))) (let ((_let_3 (@var "X3" $$unsorted))) (let ((_let_4 (@var "X1" $$unsorted))) (let ((_let_5 (@var "X0" $$unsorted))) (lambda (@list _let_5 _let_4) (_ (_ (_ tptp.c_ReplSep _let_5) (lambda _let_2 (exists (@list _let_3) (= _let_1 (_ (_ tptp.c_setsum _let_4) _let_3))))) (lambda _let_2 (_ tptp.c_proj1 _let_1)))))))))) % 1.03/1.24 (define tptp.c_setsum_p () (let ((_let_1 (@var "X0" $$unsorted))) (let ((_let_2 (_ tptp.c_ap _let_1))) (lambda (@list _let_1) (= (_ (_ tptp.c_setsum (_ _let_2 tptp.c_Empty)) (_ _let_2 (_ tptp.c_ordsucc tptp.c_Empty))) _let_1))))) % 1.03/1.24 (define tptp.c_tuple_p () (let ((_let_1 (@var "X4" $$unsorted))) (let ((_let_2 (@var "X3" $$unsorted))) (let ((_let_3 (@var "X2" $$unsorted))) (let ((_let_4 (@var "X0" $$unsorted))) (let ((_let_5 (@var "X1" $$unsorted))) (lambda (@list _let_4 _let_5) (forall (@list _let_3) (=> (_ (_ tptp.c_In _let_3) _let_5) (exists (@list _let_2) (_ (_ tptp.c_and (_ (_ tptp.c_In _let_2) _let_4)) (exists (@list _let_1) (= _let_3 (_ (_ tptp.c_setsum _let_2) _let_1)))))))))))))) % 1.03/1.24 (define tptp.c_Pi () (let ((_let_1 (@var "X3" $$unsorted))) (let ((_let_2 (@var "X1" (-> $$unsorted $$unsorted)))) (let ((_let_3 (@var "X2" $$unsorted))) (let ((_let_4 (@var "X0" $$unsorted))) (let ((_let_5 (@list _let_3))) (lambda (@list _let_4 _let_2) (_ (_ tptp.c_Sep (_ tptp.c_Power (_ (_ tptp.c_lam _let_4) (lambda _let_5 (_ tptp.c_Union (_ _let_2 _let_3)))))) (lambda _let_5 (forall (@list _let_1) (=> (_ (_ tptp.c_In _let_1) _let_4) (_ (_ tptp.c_In (_ (_ tptp.c_ap _let_3) _let_1)) (_ _let_2 _let_1))))))))))))) % 1.03/1.24 (define tptp.c_setexp () (let ((_let_1 (@var "X0" $$unsorted))) (let ((_let_2 (@var "X1" $$unsorted))) (lambda (@list _let_1 _let_2) (_ (_ tptp.c_Pi _let_2) (lambda (@list (@var "X2" $$unsorted)) _let_1)))))) % 1.03/1.24 (define tptp.c_Sep2 () (let ((_let_1 (@var "X3" $$unsorted))) (let ((_let_2 (_ tptp.c_ap _let_1))) (let ((_let_3 (@var "X2" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@list _let_1))) (let ((_let_5 (@var "X1" (-> $$unsorted $$unsorted)))) (let ((_let_6 (@var "X0" $$unsorted))) (lambda (@list _let_6 _let_5 _let_3) (_ (_ tptp.c_Sep (_ (_ tptp.c_lam _let_6) (lambda _let_4 (_ _let_5 _let_1)))) (lambda _let_4 (_ (_ _let_3 (_ _let_2 tptp.c_Empty)) (_ _let_2 (_ tptp.c_ordsucc tptp.c_Empty))))))))))))) % 1.03/1.24 (define tptp.c_set_of_pairs () (let ((_let_1 (@var "X3" $$unsorted))) (let ((_let_2 (@var "X2" $$unsorted))) (let ((_let_3 (@var "X4" $$unsorted))) (let ((_let_4 (@var "X1" $$unsorted))) (let ((_let_5 (@var "X0" $$unsorted))) (lambda (@list _let_5) (forall (@list _let_4) (=> (_ (_ tptp.c_In _let_4) _let_5) (exists (@list _let_2 _let_1) (= _let_4 (_ (_ tptp.c_lam (_ tptp.c_ordsucc (_ tptp.c_ordsucc tptp.c_Empty))) (lambda (@list _let_3) (_ (_ (_ tptp.c_If_i (= _let_3 tptp.c_Empty)) _let_2) _let_1)))))))))))))) % 1.03/1.24 (define tptp.c_lam2 () (let ((_let_1 (@var "X4" $$unsorted))) (let ((_let_2 (@var "X3" $$unsorted))) (let ((_let_3 (@var "X2" (-> $$unsorted $$unsorted $$unsorted)))) (let ((_let_4 (@var "X1" (-> $$unsorted $$unsorted)))) (let ((_let_5 (@var "X0" $$unsorted))) (lambda (@list _let_5 _let_4 _let_3) (_ (_ tptp.c_lam _let_5) (lambda (@list _let_2) (_ (_ tptp.c_lam (_ _let_4 _let_2)) (lambda (@list _let_1) (_ (_ _let_3 _let_2) _let_1)))))))))))) % 1.03/1.24 (define tptp.c_PNoEq_ () (let ((_let_1 (@var "X3" $$unsorted))) (let ((_let_2 (@var "X2" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X1" (-> $$unsorted Bool)))) (let ((_let_4 (@var "X0" $$unsorted))) (lambda (@list _let_4 _let_3 _let_2) (forall (@list _let_1) (=> (_ (_ tptp.c_In _let_1) _let_4) (_ (_ tptp.c_iff (_ _let_3 _let_1)) (_ _let_2 _let_1)))))))))) % 1.03/1.24 (define tptp.c_PNoLt_ () (let ((_let_1 (@var "X3" $$unsorted))) (let ((_let_2 (@var "X2" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X1" (-> $$unsorted Bool)))) (let ((_let_4 (@var "X0" $$unsorted))) (lambda (@list _let_4 _let_3 _let_2) (exists (@list _let_1) (_ (_ tptp.c_and (_ (_ tptp.c_In _let_1) _let_4)) (_ (_ tptp.c_and (_ (_ tptp.c_and (_ (_ (_ tptp.c_PNoEq_ _let_1) _let_3) _let_2)) (_ tptp.c_not (_ _let_3 _let_1)))) (_ _let_2 _let_1)))))))))) % 1.03/1.24 (define tptp.c_PNoLt () (let ((_let_1 (@var "X2" $$unsorted))) (let ((_let_2 (@var "X1" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X3" (-> $$unsorted Bool)))) (let ((_let_4 (@var "X0" $$unsorted))) (lambda (@list _let_4 _let_2 _let_1 _let_3) (_ (_ tptp.c_or (_ (_ tptp.c_or (_ (_ (_ tptp.c_PNoLt_ (_ (_ tptp.c_binintersect _let_4) _let_1)) _let_2) _let_3)) (_ (_ tptp.c_and (_ (_ tptp.c_and (_ (_ tptp.c_In _let_4) _let_1)) (_ (_ (_ tptp.c_PNoEq_ _let_4) _let_2) _let_3))) (_ _let_3 _let_4)))) (_ (_ tptp.c_and (_ (_ tptp.c_and (_ (_ tptp.c_In _let_1) _let_4)) (_ (_ (_ tptp.c_PNoEq_ _let_1) _let_2) _let_3))) (_ tptp.c_not (_ _let_2 _let_1)))))))))) % 1.03/1.24 (define tptp.c_PNoLe () (let ((_let_1 (@var "X3" (-> $$unsorted Bool)))) (let ((_let_2 (@var "X1" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X0" $$unsorted))) (let ((_let_4 (@var "X2" $$unsorted))) (lambda (@list _let_3 _let_2 _let_4 _let_1) (_ (_ tptp.c_or (_ (_ (_ (_ tptp.c_PNoLt _let_3) _let_2) _let_4) _let_1)) (_ (_ tptp.c_and (= _let_3 _let_4)) (_ (_ (_ tptp.c_PNoEq_ _let_3) _let_2) _let_1))))))))) % 1.03/1.24 (define tptp.c_PNo_downc () (let ((_let_1 (@var "X4" (-> $$unsorted Bool)))) (let ((_let_2 (@var "X3" $$unsorted))) (let ((_let_3 (@var "X2" (-> $$unsorted Bool)))) (let ((_let_4 (@var "X1" $$unsorted))) (let ((_let_5 (@var "X0" (-> $$unsorted (-> $$unsorted Bool) Bool)))) (lambda (@list _let_5 _let_4 _let_3) (exists (@list _let_2) (_ (_ tptp.c_and (_ tptp.c_ordinal _let_2)) (exists (@list _let_1) (_ (_ tptp.c_and (_ (_ _let_5 _let_2) _let_1)) (_ (_ (_ (_ tptp.c_PNoLe _let_4) _let_3) _let_2) _let_1)))))))))))) % 1.03/1.24 (define tptp.c_PNo_upc () (let ((_let_1 (@var "X2" (-> $$unsorted Bool)))) (let ((_let_2 (@var "X1" $$unsorted))) (let ((_let_3 (@var "X4" (-> $$unsorted Bool)))) (let ((_let_4 (@var "X3" $$unsorted))) (let ((_let_5 (@var "X0" (-> $$unsorted (-> $$unsorted Bool) Bool)))) (lambda (@list _let_5 _let_2 _let_1) (exists (@list _let_4) (_ (_ tptp.c_and (_ tptp.c_ordinal _let_4)) (exists (@list _let_3) (_ (_ tptp.c_and (_ (_ _let_5 _let_4) _let_3)) (_ (_ (_ (_ tptp.c_PNoLe _let_4) _let_3) _let_2) _let_1)))))))))))) % 1.03/1.24 (define tptp.c_SNoElts_ () (let ((_let_1 (@var "X1" $$unsorted))) (let ((_let_2 (@var "X2" $$unsorted))) (let ((_let_3 (@var "X0" $$unsorted))) (lambda (@list _let_3) (_ (_ tptp.c_binunion _let_3) (_ (_ tptp.c_Repl _let_3) (lambda (@list _let_1) (_ (lambda (@list _let_2) (_ (_ tptp.c_SetAdjoin _let_2) (_ tptp.c_Sing (_ tptp.c_ordsucc tptp.c_Empty)))) _let_1))))))))) % 1.03/1.24 (define tptp.c_SNo_ () (let ((_let_1 (@var "X1" $$unsorted))) (let ((_let_2 (@var "X2" $$unsorted))) (let ((_let_3 (_ tptp.c_In _let_2))) (let ((_let_4 (@var "X3" $$unsorted))) (let ((_let_5 (@var "X0" $$unsorted))) (lambda (@list _let_5 _let_1) (_ (_ tptp.c_and (_ (_ tptp.c_Subq _let_1) (_ tptp.c_SNoElts_ _let_5))) (forall (@list _let_2) (=> (_ _let_3 _let_5) (_ (_ tptp.c_exactly1of2 (_ (_ tptp.c_In (_ (lambda (@list _let_4) (_ (_ tptp.c_SetAdjoin _let_4) (_ tptp.c_Sing (_ tptp.c_ordsucc tptp.c_Empty)))) _let_2)) _let_1)) (_ _let_3 _let_1)))))))))))) % 1.03/1.24 (define tptp.c_PSNo () (let ((_let_1 (@var "X2" $$unsorted))) (let ((_let_2 (@var "X3" $$unsorted))) (let ((_let_3 (@list _let_1))) (let ((_let_4 (@var "X1" (-> $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_1))) (let ((_let_6 (@var "X0" $$unsorted))) (lambda (@list _let_6 _let_4) (_ (_ tptp.c_binunion (_ (_ tptp.c_Sep _let_6) (lambda _let_3 _let_5))) (_ (_ (_ tptp.c_ReplSep _let_6) (lambda _let_3 (_ tptp.c_not _let_5))) (lambda _let_3 (_ (lambda (@list _let_2) (_ (_ tptp.c_SetAdjoin _let_2) (_ tptp.c_Sing (_ tptp.c_ordsucc tptp.c_Empty)))) _let_1)))))))))))) % 1.03/1.24 (define tptp.c_SNo () (let ((_let_1 (@var "X0" $$unsorted))) (let ((_let_2 (@var "X1" $$unsorted))) (lambda (@list _let_1) (exists (@list _let_2) (_ (_ tptp.c_and (_ tptp.c_ordinal _let_2)) (_ (_ tptp.c_SNo_ _let_2) _let_1))))))) % 1.03/1.24 (define tptp.c_SNoLev () (let ((_let_1 (@var "X0" $$unsorted))) (let ((_let_2 (@var "X1" $$unsorted))) (lambda (@list _let_1) (_ tptp.c_Eps_i (lambda (@list _let_2) (_ (_ tptp.c_and (_ tptp.c_ordinal _let_2)) (_ (_ tptp.c_SNo_ _let_2) _let_1)))))))) % 1.03/1.24 (define tptp.c_SNoEq_ () (let ((_let_1 (@var "X2" $$unsorted))) (let ((_let_2 (@var "X3" $$unsorted))) (let ((_let_3 (_ tptp.c_In _let_2))) (let ((_let_4 (@list _let_2))) (let ((_let_5 (@var "X1" $$unsorted))) (let ((_let_6 (@var "X0" $$unsorted))) (lambda (@list _let_6 _let_5 _let_1) (_ (_ (_ tptp.c_PNoEq_ _let_6) (lambda _let_4 (_ _let_3 _let_5))) (lambda _let_4 (_ _let_3 _let_1))))))))))) % 1.03/1.24 (define tptp.c_SNoLt () (let ((_let_1 (@var "X1" $$unsorted))) (let ((_let_2 (@var "X2" $$unsorted))) (let ((_let_3 (_ tptp.c_In _let_2))) (let ((_let_4 (@list _let_2))) (let ((_let_5 (@var "X0" $$unsorted))) (lambda (@list _let_5 _let_1) (_ (_ (_ (_ tptp.c_PNoLt (_ tptp.c_SNoLev _let_5)) (lambda _let_4 (_ _let_3 _let_5))) (_ tptp.c_SNoLev _let_1)) (lambda _let_4 (_ _let_3 _let_1)))))))))) % 1.03/1.24 (define tptp.c_SNoLe () (let ((_let_1 (@var "X1" $$unsorted))) (let ((_let_2 (@var "X2" $$unsorted))) (let ((_let_3 (_ tptp.c_In _let_2))) (let ((_let_4 (@list _let_2))) (let ((_let_5 (@var "X0" $$unsorted))) (lambda (@list _let_5 _let_1) (_ (_ (_ (_ tptp.c_PNoLe (_ tptp.c_SNoLev _let_5)) (lambda _let_4 (_ _let_3 _let_5))) (_ tptp.c_SNoLev _let_1)) (lambda _let_4 (_ _let_3 _let_1)))))))))) % 1.03/1.24 (define tptp.c_binop_on () (let ((_let_1 (@var "X0" $$unsorted))) (let ((_let_2 (@var "X3" $$unsorted))) (let ((_let_3 (@var "X2" $$unsorted))) (let ((_let_4 (@var "X1" (-> $$unsorted $$unsorted $$unsorted)))) (lambda (@list _let_1 _let_4) (forall (@list _let_3) (=> (_ (_ tptp.c_In _let_3) _let_1) (forall (@list _let_2) (=> (_ (_ tptp.c_In _let_2) _let_1) (_ (_ tptp.c_In (_ (_ _let_4 _let_3) _let_2)) _let_1))))))))))) % 1.03/1.24 (define tptp.c_Loop () (let ((_let_1 (@var "X5" $$unsorted))) (let ((_let_2 (@var "X6" $$unsorted))) (let ((_let_3 (@var "X3" (-> $$unsorted $$unsorted $$unsorted)))) (let ((_let_4 (@var "X1" (-> $$unsorted $$unsorted $$unsorted)))) (let ((_let_5 (_ _let_4 _let_1))) (let ((_let_6 (_ _let_5 _let_2))) (let ((_let_7 (@var "X2" (-> $$unsorted $$unsorted $$unsorted)))) (let ((_let_8 (_ _let_7 _let_1))) (let ((_let_9 (@var "X0" $$unsorted))) (let ((_let_10 (_ (_ tptp.c_In _let_1) _let_9))) (let ((_let_11 (@list _let_1))) (let ((_let_12 (@var "X4" $$unsorted))) (let ((_let_13 (_ tptp.c_binop_on _let_9))) (lambda (@list _let_9 _let_4 _let_7 _let_3 _let_12) (_ (_ tptp.c_and (_ (_ tptp.c_and (_ (_ tptp.c_and (_ (_ tptp.c_and (_ _let_13 _let_4)) (_ _let_13 _let_7))) (_ _let_13 _let_3))) (forall _let_11 (=> _let_10 (_ (_ tptp.c_and (= (_ (_ _let_4 _let_12) _let_1) _let_1)) (= (_ _let_5 _let_12) _let_1)))))) (forall _let_11 (=> _let_10 (forall (@list _let_2) (=> (_ (_ tptp.c_In _let_2) _let_9) (_ (_ tptp.c_and (_ (_ tptp.c_and (_ (_ tptp.c_and (= (_ _let_8 _let_6) _let_2)) (= (_ _let_5 (_ _let_8 _let_2)) _let_2))) (= (_ (_ _let_3 _let_6) _let_2) _let_1))) (= (_ (_ _let_4 (_ (_ _let_3 _let_1) _let_2)) _let_2) _let_1)))))))))))))))))))))) % 1.03/1.24 (define tptp.c_Loop_with_defs () (let ((_let_1 (@var "X15" $$unsorted))) (let ((_let_2 (@var "X14" $$unsorted))) (let ((_let_3 (@var "X1" (-> $$unsorted $$unsorted $$unsorted)))) (let ((_let_4 (_ _let_3 _let_2))) (let ((_let_5 (_ _let_4 _let_1))) (let ((_let_6 (@var "X16" $$unsorted))) (let ((_let_7 (@var "X3" (-> $$unsorted $$unsorted $$unsorted)))) (let ((_let_8 (@var "X9" (-> $$unsorted $$unsorted $$unsorted $$unsorted)))) (let ((_let_9 (_ _let_3 _let_1))) (let ((_let_10 (_ _let_9 _let_2))) (let ((_let_11 (@var "X2" (-> $$unsorted $$unsorted $$unsorted)))) (let ((_let_12 (_ _let_11 _let_10))) (let ((_let_13 (@var "X8" (-> $$unsorted $$unsorted $$unsorted $$unsorted)))) (let ((_let_14 (@var "X0" $$unsorted))) (let ((_let_15 (_ (_ tptp.c_In _let_6) _let_14))) (let ((_let_16 (@list _let_6))) (let ((_let_17 (_ (_ tptp.c_In _let_1) _let_14))) (let ((_let_18 (@list _let_1))) (let ((_let_19 (_ (_ tptp.c_In _let_2) _let_14))) (let ((_let_20 (@list _let_2))) (let ((_let_21 (@var "X4" $$unsorted))) (let ((_let_22 (_ _let_7 _let_21))) (let ((_let_23 (_ _let_22 _let_2))) (let ((_let_24 (@var "X13" (-> $$unsorted $$unsorted $$unsorted)))) (let ((_let_25 (_ _let_11 _let_2))) (let ((_let_26 (_ _let_25 _let_21))) (let ((_let_27 (@var "X12" (-> $$unsorted $$unsorted $$unsorted)))) (let ((_let_28 (@var "X11" (-> $$unsorted $$unsorted $$unsorted)))) (let ((_let_29 (@var "X10" (-> $$unsorted $$unsorted $$unsorted)))) (let ((_let_30 (@var "X7" (-> $$unsorted $$unsorted $$unsorted)))) (let ((_let_31 (@var "X6" (-> $$unsorted $$unsorted $$unsorted $$unsorted)))) (let ((_let_32 (@var "X5" (-> $$unsorted $$unsorted $$unsorted)))) (lambda (@list _let_14 _let_3 _let_11 _let_7 _let_21 _let_32 _let_31 _let_30 _let_13 _let_8 _let_29 _let_28 _let_27 _let_24) (_ (_ tptp.c_and (_ (_ tptp.c_and (_ (_ tptp.c_and (_ (_ tptp.c_and (_ (_ (_ (_ (_ tptp.c_Loop _let_14) _let_3) _let_11) _let_7) _let_21)) (forall _let_20 (=> _let_19 (forall _let_18 (=> _let_17 (= (_ (_ _let_32 _let_2) _let_1) (_ _let_12 _let_5)))))))) (forall _let_20 (=> _let_19 (forall _let_18 (=> _let_17 (forall _let_16 (=> _let_15 (= (_ (_ (_ _let_31 _let_2) _let_1) _let_6) (_ (_ _let_11 (_ _let_4 (_ _let_9 _let_6))) (_ (_ _let_3 _let_5) _let_6))))))))))) (forall _let_20 (=> _let_19 (forall _let_18 (=> _let_17 (_ (_ tptp.c_and (_ (_ tptp.c_and (_ (_ tptp.c_and (_ (_ tptp.c_and (= (_ (_ _let_30 _let_2) _let_1) (_ _let_25 _let_10))) (= (_ (_ _let_29 _let_2) _let_1) (_ _let_4 (_ _let_9 _let_26))))) (= (_ (_ _let_28 _let_2) _let_1) (_ (_ _let_3 (_ (_ _let_3 _let_23) _let_1)) _let_2)))) (= (_ (_ _let_27 _let_2) _let_1) (_ (_ _let_3 (_ _let_25 _let_1)) (_ (_ _let_11 _let_26) _let_21))))) (= (_ (_ _let_24 _let_2) _let_1) (_ (_ _let_3 (_ _let_22 _let_23)) (_ (_ _let_7 _let_1) _let_2)))))))))) (forall _let_20 (=> _let_19 (forall _let_18 (=> _let_17 (forall _let_16 (=> _let_15 (_ (_ tptp.c_and (= (_ (_ (_ _let_13 _let_2) _let_1) _let_6) (_ _let_12 (_ _let_9 (_ _let_4 _let_6))))) (= (_ (_ (_ _let_8 _let_2) _let_1) _let_6) (_ (_ _let_7 (_ (_ _let_3 (_ (_ _let_3 _let_6) _let_2)) _let_1)) _let_5)))))))))))))))))))))))))))))))))))))))))))) % 1.03/1.24 (define tptp.c_Loop_with_defs_cex1 () (let ((_let_1 (@var "X4" $$unsorted))) (let ((_let_2 (@var "X17" $$unsorted))) (let ((_let_3 (@var "X14" $$unsorted))) (let ((_let_4 (@var "X16" $$unsorted))) (let ((_let_5 (@var "X15" $$unsorted))) (let ((_let_6 (@var "X8" (-> $$unsorted $$unsorted $$unsorted $$unsorted)))) (let ((_let_7 (@var "X2" (-> $$unsorted $$unsorted $$unsorted)))) (let ((_let_8 (@var "X1" (-> $$unsorted $$unsorted $$unsorted)))) (let ((_let_9 (@var "X5" (-> $$unsorted $$unsorted $$unsorted)))) (let ((_let_10 (@var "X0" $$unsorted))) (let ((_let_11 (@var "X13" (-> $$unsorted $$unsorted $$unsorted)))) (let ((_let_12 (@var "X12" (-> $$unsorted $$unsorted $$unsorted)))) (let ((_let_13 (@var "X11" (-> $$unsorted $$unsorted $$unsorted)))) (let ((_let_14 (@var "X10" (-> $$unsorted $$unsorted $$unsorted)))) (let ((_let_15 (@var "X9" (-> $$unsorted $$unsorted $$unsorted $$unsorted)))) (let ((_let_16 (@var "X7" (-> $$unsorted $$unsorted $$unsorted)))) (let ((_let_17 (@var "X6" (-> $$unsorted $$unsorted $$unsorted $$unsorted)))) (let ((_let_18 (@var "X3" (-> $$unsorted $$unsorted $$unsorted)))) (lambda (@list _let_10 _let_8 _let_7 _let_18 _let_1 _let_9 _let_17 _let_16 _let_6 _let_15 _let_14 _let_13 _let_12 _let_11) (_ (_ tptp.c_and (_ (_ (_ (_ (_ (_ (_ (_ (_ (_ (_ (_ (_ (_ tptp.c_Loop_with_defs _let_10) _let_8) _let_7) _let_18) _let_1) _let_9) _let_17) _let_16) _let_6) _let_15) _let_14) _let_13) _let_12) _let_11)) (exists (@list _let_3) (_ (_ tptp.c_and (_ (_ tptp.c_In _let_3) _let_10)) (exists (@list _let_5) (_ (_ tptp.c_and (_ (_ tptp.c_In _let_5) _let_10)) (exists (@list _let_4) (_ (_ tptp.c_and (_ (_ tptp.c_In _let_4) _let_10)) (exists (@list _let_2) (_ (_ tptp.c_and (_ (_ tptp.c_In _let_2) _let_10)) (_ tptp.c_not (= (_ (_ _let_9 (_ (_ _let_8 (_ (_ _let_7 (_ (_ (_ _let_6 _let_5) _let_4) _let_3)) _let_1)) _let_3)) _let_2) _let_1))))))))))))))))))))))))))))))) % 1.03/1.24 (define tptp.c_Loop_with_defs_cex2 () (let ((_let_1 (@var "X4" $$unsorted))) (let ((_let_2 (@var "X17" $$unsorted))) (let ((_let_3 (@var "X14" $$unsorted))) (let ((_let_4 (@var "X16" $$unsorted))) (let ((_let_5 (@var "X15" $$unsorted))) (let ((_let_6 (@var "X9" (-> $$unsorted $$unsorted $$unsorted $$unsorted)))) (let ((_let_7 (@var "X3" (-> $$unsorted $$unsorted $$unsorted)))) (let ((_let_8 (@var "X1" (-> $$unsorted $$unsorted $$unsorted)))) (let ((_let_9 (@var "X18" $$unsorted))) (let ((_let_10 (@var "X6" (-> $$unsorted $$unsorted $$unsorted $$unsorted)))) (let ((_let_11 (@var "X0" $$unsorted))) (let ((_let_12 (@var "X13" (-> $$unsorted $$unsorted $$unsorted)))) (let ((_let_13 (@var "X12" (-> $$unsorted $$unsorted $$unsorted)))) (let ((_let_14 (@var "X11" (-> $$unsorted $$unsorted $$unsorted)))) (let ((_let_15 (@var "X10" (-> $$unsorted $$unsorted $$unsorted)))) (let ((_let_16 (@var "X8" (-> $$unsorted $$unsorted $$unsorted $$unsorted)))) (let ((_let_17 (@var "X7" (-> $$unsorted $$unsorted $$unsorted)))) (let ((_let_18 (@var "X5" (-> $$unsorted $$unsorted $$unsorted)))) (let ((_let_19 (@var "X2" (-> $$unsorted $$unsorted $$unsorted)))) (lambda (@list _let_11 _let_8 _let_19 _let_7 _let_1 _let_18 _let_10 _let_17 _let_16 _let_6 _let_15 _let_14 _let_13 _let_12) (_ (_ tptp.c_and (_ (_ (_ (_ (_ (_ (_ (_ (_ (_ (_ (_ (_ (_ tptp.c_Loop_with_defs _let_11) _let_8) _let_19) _let_7) _let_1) _let_18) _let_10) _let_17) _let_16) _let_6) _let_15) _let_14) _let_13) _let_12)) (exists (@list _let_3) (_ (_ tptp.c_and (_ (_ tptp.c_In _let_3) _let_11)) (exists (@list _let_5) (_ (_ tptp.c_and (_ (_ tptp.c_In _let_5) _let_11)) (exists (@list _let_4) (_ (_ tptp.c_and (_ (_ tptp.c_In _let_4) _let_11)) (exists (@list _let_2) (_ (_ tptp.c_and (_ (_ tptp.c_In _let_2) _let_11)) (exists (@list _let_9) (_ (_ tptp.c_and (_ (_ tptp.c_In _let_9) _let_11)) (_ tptp.c_not (= (_ (_ (_ _let_10 _let_9) (_ (_ _let_8 (_ (_ _let_7 _let_1) _let_3)) (_ (_ (_ _let_6 _let_5) _let_4) _let_3))) _let_2) _let_1)))))))))))))))))))))))))))))))))) % 1.03/1.24 (define tptp.c_combinator () (let ((_let_1 (@var "X0" $$unsorted))) (let ((_let_2 (@var "X1" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X3" $$unsorted))) (let ((_let_4 (@var "X2" $$unsorted))) (lambda (@list _let_1) (forall (@list _let_2) (=> (_ _let_2 (_ tptp.c_Inj0 tptp.c_Empty)) (=> (_ _let_2 (_ tptp.c_Inj0 (_ tptp.c_Power tptp.c_Empty))) (=> (forall (@list _let_4 _let_3) (=> (_ _let_2 _let_4) (=> (_ _let_2 _let_3) (_ _let_2 (_ tptp.c_Inj1 (_ (_ tptp.c_setsum _let_4) _let_3)))))) (_ _let_2 _let_1))))))))))) % 1.03/1.24 (define tptp.c_combinator_equiv () (let ((_let_1 (@var "X4" $$unsorted))) (let ((_let_2 (@var "X3" $$unsorted))) (let ((_let_3 (@var "X1" $$unsorted))) (let ((_let_4 (@var "X0" $$unsorted))) (let ((_let_5 (@var "X2" (-> $$unsorted $$unsorted Bool)))) (let ((_let_6 (@var "X8" $$unsorted))) (let ((_let_7 (@var "X7" $$unsorted))) (let ((_let_8 (@var "X5" (-> $$unsorted $$unsorted $$unsorted)))) (let ((_let_9 (@var "X6" $$unsorted))) (let ((_let_10 (_ _let_8 _let_9))) (let ((_let_11 (@var "X9" $$unsorted))) (let ((_let_12 (_ _let_5 _let_9))) (let ((_let_13 (_ tptp.c_combinator _let_9))) (lambda (@list _let_4 _let_3) (forall (@list _let_5) (_ (_ (_ (lambda (@list _let_2 _let_1 _let_8) (=> (_ tptp.c_per_i _let_5) (=> (forall (@list _let_9) (=> _let_13 (_ _let_12 _let_9))) (=> (forall (@list _let_9 _let_7 _let_6 _let_11) (=> _let_13 (=> (_ tptp.c_combinator _let_7) (=> (_ tptp.c_combinator _let_6) (=> (_ tptp.c_combinator _let_11) (=> (_ _let_12 _let_6) (=> (_ (_ _let_5 _let_7) _let_11) (_ (_ _let_5 (_ _let_10 _let_7)) (_ (_ _let_8 _let_6) _let_11))))))))) (=> (forall (@list _let_9 _let_7) (_ (_ _let_5 (_ (_ _let_8 (_ (_ _let_8 _let_2) _let_9)) _let_7)) _let_9)) (=> (forall (@list _let_9 _let_7 _let_6) (_ (_ _let_5 (_ (_ _let_8 (_ (_ _let_8 (_ (_ _let_8 _let_1) _let_9)) _let_7)) _let_6)) (_ (_ _let_8 (_ _let_10 _let_6)) (_ (_ _let_8 _let_7) _let_6)))) (_ (_ _let_5 _let_4) _let_3))))))) (_ tptp.c_Inj0 tptp.c_Empty)) (_ tptp.c_Inj0 (_ tptp.c_Power tptp.c_Empty))) (lambda (@list _let_2 _let_1) (_ tptp.c_Inj1 (_ (_ tptp.c_setsum _let_2) _let_1)))))))))))))))))))) % 1.03/1.24 (define tptp.c_equip_mod () (let ((_let_1 (@var "X2" $$unsorted))) (let ((_let_2 (@var "X3" $$unsorted))) (let ((_let_3 (@var "X4" $$unsorted))) (let ((_let_4 (_ (_ tptp.c_equip (_ (_ tptp.c_setprod _let_3) _let_2)) _let_1))) (let ((_let_5 (@var "X0" $$unsorted))) (let ((_let_6 (@var "X1" $$unsorted))) (lambda (@list _let_5 _let_6 _let_1) (exists (@list _let_2 _let_3) (_ (_ tptp.c_or (_ (_ tptp.c_and (_ (_ tptp.c_equip (_ (_ tptp.c_setsum _let_5) _let_2)) _let_6)) _let_4)) (_ (_ tptp.c_and (_ (_ tptp.c_equip (_ (_ tptp.c_setsum _let_6) _let_2)) _let_5)) _let_4))))))))))) % 1.03/1.24 (define @t1 () (@var "X0" (-> $$unsorted Bool))) % 1.03/1.24 (define @t2 () (@var "X1" $$unsorted)) % 1.03/1.24 (define @t3 () (_ @t1 @t2)) % 1.03/1.24 (define @t4 () (@var "X0" Bool)) % 1.03/1.24 (define @t5 () (_ tptp.c_not @t4)) % 1.03/1.24 (define @t6 () (=> (_ tptp.c_not @t5) @t4)) % 1.03/1.24 (define @t7 () (@list @t4)) % 1.03/1.24 (define @t8 () (forall @t7 @t6)) % 1.03/1.24 (define @t9 () (@var "X1" Bool)) % 1.03/1.24 (define @t10 () (@list @t4 @t9)) % 1.03/1.24 (define @t11 () (@var "X0" $$unsorted)) % 1.03/1.24 (define @t12 () (_ tptp.c_Subq @t2)) % 1.03/1.24 (define @t13 () (_ @t12 @t11)) % 1.03/1.24 (define @t14 () (_ tptp.c_Subq @t11)) % 1.03/1.24 (define @t15 () (_ @t14 @t2)) % 1.03/1.24 (define @t16 () (@list @t11 @t2)) % 1.03/1.24 (define @t17 () (_ tptp.c_In @t11)) % 1.03/1.24 (define @t18 () (_ @t17 tptp.c_Empty)) % 1.03/1.24 (define @t19 () (@list @t11)) % 1.03/1.24 (define @t20 () (exists @t19 @t18)) % 1.03/1.24 (define @t21 () (@var "X2" $$unsorted)) % 1.03/1.24 (define @t22 () (_ tptp.c_In @t21)) % 1.03/1.24 (define @t23 () (_ @t22 @t11)) % 1.03/1.24 (define @t24 () (_ tptp.c_In @t2)) % 1.03/1.24 (define @t25 () (@list @t21)) % 1.03/1.24 (define @t26 () (_ @t24 (_ tptp.c_Power @t11))) % 1.03/1.24 (define @t27 () (forall @t16 (_ (_ tptp.c_iff @t26) @t13))) % 1.03/1.24 (define @t28 () (@var "X3" $$unsorted)) % 1.03/1.24 (define @t29 () (@var "X1" (-> $$unsorted $$unsorted))) % 1.03/1.24 (define @t30 () (_ @t29 @t28)) % 1.03/1.24 (define @t31 () (_ tptp.c_In @t28)) % 1.03/1.24 (define @t32 () (_ @t31 @t11)) % 1.03/1.24 (define @t33 () (_ tptp.c_and @t32)) % 1.03/1.24 (define @t34 () (@list @t28)) % 1.03/1.24 (define @t35 () (lambda @t34 @t30)) % 1.03/1.24 (define @t36 () (_ tptp.c_Repl @t11)) % 1.03/1.24 (define @t37 () (@list @t2)) % 1.03/1.24 (define @t38 () (forall @t37 @t3)) % 1.03/1.24 (define @t39 () (@var "X2" (-> $$unsorted $$unsorted))) % 1.03/1.24 (define @t40 () (_ @t39 @t28)) % 1.03/1.24 (define @t41 () (lambda @t34 @t40)) % 1.03/1.24 (define @t42 () (_ tptp.c_Repl @t2)) % 1.03/1.24 (define @t43 () (_ @t31 @t2)) % 1.03/1.24 (define @t44 () (@list @t39)) % 1.03/1.24 (define @t45 () (_ tptp.c_Power @t2)) % 1.03/1.24 (define @t46 () (_ @t1 @t21)) % 1.03/1.24 (define @t47 () (_ @t22 @t2)) % 1.03/1.24 (define @t48 () (forall @t25 (=> @t47 @t46))) % 1.03/1.24 (define @t49 () (@list @t1)) % 1.03/1.24 (define @t50 () (_ @t29 @t21)) % 1.03/1.24 (define @t51 () (_ tptp.c_famunion @t11)) % 1.03/1.24 (define @t52 () (@list @t11 @t29)) % 1.03/1.24 (define @t53 () (lambda @t25 @t50)) % 1.03/1.24 (define @t54 () (_ @t36 @t53)) % 1.03/1.24 (define @t55 () (_ tptp.c_Sing tptp.c_Empty)) % 1.03/1.24 (define @t56 () (@var "X9" $$unsorted)) % 1.03/1.24 (define @t57 () (@var "X6" $$unsorted)) % 1.03/1.24 (define @t58 () (= @t57 @t56)) % 1.03/1.24 (define @t59 () (@var "X5" $$unsorted)) % 1.03/1.24 (define @t60 () (@var "X7" $$unsorted)) % 1.03/1.24 (define @t61 () (@var "X1" (-> $$unsorted $$unsorted $$unsorted))) % 1.03/1.24 (define @t62 () (@var "X4" (-> $$unsorted $$unsorted))) % 1.03/1.24 (define @t63 () (@var "X3" (-> $$unsorted Bool))) % 1.03/1.24 (define @t64 () (_ @t63 (_ @t62 (_ @t62 (_ (_ @t61 @t60) @t59))))) % 1.03/1.24 (define @t65 () (@list (@var "X11" $$unsorted))) % 1.03/1.24 (define @t66 () (exists @t65 (= @t60 @t60))) % 1.03/1.24 (define @t67 () (@var "X10" $$unsorted)) % 1.03/1.24 (define @t68 () (_ @t63 @t67)) % 1.03/1.24 (define @t69 () (exists @t65 @t68)) % 1.03/1.24 (define @t70 () (@var "X8" $$unsorted)) % 1.03/1.24 (define @t71 () (forall @t65 (= @t56 @t70))) % 1.03/1.24 (define @t72 () (= @t60 @t59)) % 1.03/1.24 (define @t73 () (=> @t72 (_ (_ tptp.c_and @t71) @t69))) % 1.03/1.24 (define @t74 () (@var "X2" (-> $$unsorted Bool))) % 1.03/1.24 (define @t75 () (_ @t74 @t67)) % 1.03/1.24 (define @t76 () (=> (_ (_ tptp.c_and @t75) @t73) @t66)) % 1.03/1.24 (define @t77 () (_ @t62 @t56)) % 1.03/1.24 (define @t78 () (= @t77 @t67)) % 1.03/1.24 (define @t79 () (=> @t78 @t76)) % 1.03/1.24 (define @t80 () (@list @t67)) % 1.03/1.24 (define @t81 () (forall @t80 @t79)) % 1.03/1.24 (define @t82 () (=> (_ (_ tptp.c_and @t81) (_ tptp.c_not @t64)) @t58)) % 1.03/1.24 (define @t83 () (@var "X0" (-> $$unsorted $$unsorted Bool))) % 1.03/1.24 (define @t84 () (@list @t83 @t61 @t74 @t63 @t62 @t59 @t57 @t60 @t70 @t56)) % 1.03/1.24 (define @t85 () (forall @t84 @t82)) % 1.03/1.24 (define @t86 () (not (_ tptp.c_not @t85))) % 1.03/1.24 (define @t87 () (=> @t4 tptp.c_False)) % 1.03/1.24 (define @t88 () (lambda @t7 @t87)) % 1.03/1.24 (define @t89 () (@var "X2" Bool)) % 1.03/1.24 (define @t90 () (=> @t9 @t89)) % 1.03/1.24 (define @t91 () (=> @t4 @t90)) % 1.03/1.24 (define @t92 () (@list @t89)) % 1.03/1.24 (define @t93 () (forall @t92 (=> @t91 @t89))) % 1.03/1.24 (define @t94 () (lambda @t10 @t93)) % 1.03/1.24 (define @t95 () (lambda @t10 (forall @t92 (=> (=> @t4 @t89) (=> @t90 @t89))))) % 1.03/1.24 (define @t96 () (=> @t9 @t4)) % 1.03/1.24 (define @t97 () (=> @t4 @t9)) % 1.03/1.24 (define @t98 () (lambda @t10 (_ (_ tptp.c_and @t97) @t96))) % 1.03/1.24 (define @t99 () (forall @t25 (=> @t23 @t47))) % 1.03/1.24 (define @t100 () (lambda @t16 @t99)) % 1.03/1.24 (define @t101 () (_ @t24 @t11)) % 1.03/1.24 (define @t102 () (lambda @t19 (forall @t37 (=> @t101 @t13)))) % 1.03/1.24 (define @t103 () (lambda @t19 (exists @t37 (_ (_ tptp.c_and @t101) (_ tptp.c_not (_ @t14 @t45)))))) % 1.03/1.24 (define @t104 () (_ tptp.c_not @t15)) % 1.03/1.24 (define @t105 () (_ tptp.c_and @t104)) % 1.03/1.24 (define @t106 () (_ tptp.c_and @t13)) % 1.03/1.24 (define @t107 () (lambda @t19 (exists @t37 (_ @t106 (_ @t105 (_ tptp.c_atleast2 @t2)))))) % 1.03/1.24 (define @t108 () (lambda @t19 (exists @t37 (_ @t106 (_ @t105 (_ tptp.c_atleast3 @t2)))))) % 1.03/1.24 (define @t109 () (lambda @t19 (exists @t37 (_ @t106 (_ @t105 (_ tptp.c_atleast4 @t2)))))) % 1.03/1.24 (define @t110 () (lambda @t19 (exists @t37 (_ @t106 (_ @t105 (_ tptp.c_atleast5 @t2)))))) % 1.03/1.24 (define @t111 () (_ tptp.c_atleast3 @t11)) % 1.03/1.24 (define @t112 () (lambda @t19 (_ (_ tptp.c_and (_ tptp.c_atleast2 @t11)) (_ tptp.c_not @t111)))) % 1.03/1.24 (define @t113 () (_ tptp.c_atleast4 @t11)) % 1.03/1.24 (define @t114 () (lambda @t19 (_ (_ tptp.c_and @t111) (_ tptp.c_not @t113)))) % 1.03/1.24 (define @t115 () (_ tptp.c_atleast5 @t11)) % 1.03/1.24 (define @t116 () (lambda @t19 (_ (_ tptp.c_and @t113) (_ tptp.c_not @t115)))) % 1.03/1.24 (define @t117 () (lambda @t19 (_ (_ tptp.c_and @t115) (_ tptp.c_not (_ tptp.c_atleast6 @t11))))) % 1.03/1.24 (define @t118 () (= @t2 @t21)) % 1.03/1.24 (define @t119 () (@list @t2 @t21)) % 1.03/1.24 (define @t120 () (lambda @t49 (_ (_ tptp.c_and (exists @t37 @t3)) (forall @t119 (=> @t3 (=> @t46 @t118)))))) % 1.03/1.24 (define @t121 () (_ @t83 @t2)) % 1.03/1.24 (define @t122 () (_ @t121 @t2)) % 1.03/1.24 (define @t123 () (@list @t83)) % 1.03/1.24 (define @t124 () (lambda @t123 (forall @t37 @t122))) % 1.03/1.24 (define @t125 () (lambda @t123 (forall @t37 (_ tptp.c_not @t122)))) % 1.03/1.24 (define @t126 () (_ @t83 @t21)) % 1.03/1.24 (define @t127 () (_ @t126 @t2)) % 1.03/1.24 (define @t128 () (_ @t121 @t21)) % 1.03/1.24 (define @t129 () (lambda @t123 (forall @t119 (=> @t128 @t127)))) % 1.03/1.24 (define @t130 () (lambda @t123 (forall @t119 (=> @t128 (=> @t127 @t118))))) % 1.03/1.24 (define @t131 () (lambda @t123 (forall (@list @t2 @t21 @t28) (=> @t128 (=> (_ @t126 @t28) (_ @t121 @t28)))))) % 1.03/1.24 (define @t132 () (_ tptp.c_transitive_i @t83)) % 1.03/1.24 (define @t133 () (_ tptp.c_symmetric_i @t83)) % 1.03/1.24 (define @t134 () (_ tptp.c_and (_ tptp.c_reflexive_i @t83))) % 1.03/1.24 (define @t135 () (lambda @t123 (_ (_ tptp.c_and (_ @t134 @t133)) @t132))) % 1.03/1.24 (define @t136 () (lambda @t123 (_ (_ tptp.c_and @t133) @t132))) % 1.03/1.24 (define @t137 () (_ tptp.c_or @t128)) % 1.03/1.24 (define @t138 () (lambda @t123 (forall @t119 (_ @t137 @t127)))) % 1.03/1.24 (define @t139 () (lambda @t123 (forall @t119 (_ (_ tptp.c_or (_ @t137 @t118)) @t127)))) % 1.03/1.24 (define @t140 () (lambda @t123 (_ (_ tptp.c_and (_ @t134 (_ tptp.c_antisymmetric_i @t83))) @t132))) % 1.03/1.24 (define @t141 () (lambda @t123 (_ (_ tptp.c_and (_ tptp.c_partialorder_i @t83)) (_ tptp.c_linear_i @t83)))) % 1.03/1.24 (define @t142 () (lambda @t123 (_ (_ tptp.c_and (_ tptp.c_irreflexive_i @t83)) @t132))) % 1.03/1.24 (define @t143 () (lambda @t123 (_ (_ tptp.c_and (_ tptp.c_strictpartialorder_i @t83)) (_ tptp.c_trichotomous_or_i @t83)))) % 1.03/1.24 (define @t144 () (_ tptp.c_and @t5)) % 1.03/1.24 (define @t145 () (_ tptp.c_and @t4)) % 1.03/1.24 (define @t146 () (lambda (@list @t4 @t2 @t21) (_ tptp.c_Eps_i (lambda @t34 (_ (_ tptp.c_or (_ @t145 (= @t28 @t2))) (_ @t144 (= @t28 @t21))))))) % 1.03/1.24 (define @t147 () (_ tptp.c_not @t9)) % 1.03/1.24 (define @t148 () (lambda @t10 (_ (_ tptp.c_or (_ @t145 @t147)) (_ @t144 @t9)))) % 1.03/1.24 (define @t149 () (lambda (@list @t4 @t9 @t89) (_ (_ tptp.c_or (_ (_ tptp.c_and (_ (_ tptp.c_exactly1of2 @t4) @t9)) (_ tptp.c_not @t89))) (_ (_ tptp.c_and (_ @t144 @t147)) @t89)))) % 1.03/1.24 (define @t150 () (lambda @t16 (_ tptp.c_not (_ @t17 @t2)))) % 1.03/1.24 (define @t151 () (lambda @t16 @t104)) % 1.03/1.24 (define @t152 () (_ tptp.c_Power tptp.c_Empty)) % 1.03/1.24 (define @t153 () (lambda @t16 (_ (_ tptp.c_Repl (_ tptp.c_Power @t152)) (lambda @t25 (_ (_ (_ tptp.c_If_i (_ (_ tptp.c_In tptp.c_Empty) @t21)) @t11) @t2))))) % 1.03/1.24 (define @t154 () (_ tptp.c_UPair @t11)) % 1.03/1.24 (define @t155 () (lambda @t19 (_ @t154 @t11))) % 1.03/1.24 (define @t156 () (lambda @t16 (_ tptp.c_Union (_ @t154 @t2)))) % 1.03/1.24 (define @t157 () (_ tptp.c_binunion @t11)) % 1.03/1.24 (define @t158 () (lambda @t16 (_ @t157 (_ tptp.c_Sing @t2)))) % 1.03/1.24 (define @t159 () (lambda @t52 (_ tptp.c_Union @t54))) % 1.03/1.24 (define @t160 () (@var "X4" $$unsorted)) % 1.03/1.24 (define @t161 () (@var "X1" (-> $$unsorted Bool))) % 1.03/1.24 (define @t162 () (_ (_ tptp.c_In @t160) @t11)) % 1.03/1.24 (define @t163 () (_ tptp.c_and @t162)) % 1.03/1.24 (define @t164 () (@list @t160)) % 1.03/1.24 (define @t165 () (_ @t161 @t28)) % 1.03/1.24 (define @t166 () (_ @t161 @t21)) % 1.03/1.24 (define @t167 () (_ tptp.c_and @t23)) % 1.03/1.24 (define @t168 () (@list @t11 @t161)) % 1.03/1.24 (define @t169 () (lambda @t168 (_ (_ (_ tptp.c_If_i (exists @t25 (_ @t167 @t166))) (_ @t36 (lambda @t25 (_ (lambda @t34 (_ (_ (_ tptp.c_If_i @t165) @t28) (_ tptp.c_Eps_i (lambda @t164 (_ @t163 (_ @t161 @t160)))))) @t21)))) tptp.c_Empty))) % 1.03/1.24 (define @t170 () (_ tptp.c_Sep @t11)) % 1.03/1.24 (define @t171 () (lambda (@list @t11 @t161 @t39) (_ (_ tptp.c_Repl (_ @t170 (lambda @t34 @t165))) @t41))) % 1.03/1.24 (define @t172 () (lambda @t25 @t47)) % 1.03/1.24 (define @t173 () (lambda @t16 (_ @t170 @t172))) % 1.03/1.24 (define @t174 () (lambda @t16 (_ @t170 (lambda @t25 (_ (_ tptp.c_nIn @t21) @t2))))) % 1.03/1.24 (define @t175 () (_ @t39 @t160)) % 1.03/1.24 (define @t176 () (@list @t11 @t2 @t39)) % 1.03/1.24 (define @t177 () (lambda @t176 (_ (_ tptp.c_and (forall @t34 (=> @t32 (_ (_ tptp.c_In @t40) @t2)))) (forall @t34 (=> @t32 (forall @t164 (=> @t162 (=> (= @t40 @t175) (= @t28 @t160))))))))) % 1.03/1.24 (define @t178 () (_ (_ (_ tptp.c_inj @t11) @t2) @t39)) % 1.03/1.24 (define @t179 () (lambda @t176 (_ (_ tptp.c_and @t178) (forall @t34 (=> @t43 (exists @t164 (_ @t163 (= @t175 @t28)))))))) % 1.03/1.24 (define @t180 () (lambda @t16 (exists @t44 @t178))) % 1.03/1.24 (define @t181 () (lambda @t16 (exists @t44 (_ (_ (_ tptp.c_bij @t11) @t2) @t39)))) % 1.03/1.24 (define @t182 () (@var "X3" (-> $$unsorted $$unsorted Bool))) % 1.03/1.24 (define @t183 () (@var "X5" (-> $$unsorted $$unsorted))) % 1.03/1.24 (define @t184 () (@var "X0" (-> $$unsorted (-> $$unsorted $$unsorted) $$unsorted))) % 1.03/1.24 (define @t185 () (_ tptp.c_In @t57)) % 1.03/1.24 (define @t186 () (@list @t57)) % 1.03/1.24 (define @t187 () (lambda (@list @t184 @t2 @t21) (forall (@list @t182) (=> (forall (@list @t160 @t183) (=> (forall @t186 (=> (_ @t185 @t160) (_ (_ @t182 @t57) (_ @t183 @t57)))) (_ (_ @t182 @t160) (_ (_ @t184 @t160) @t183)))) (_ (_ @t182 @t2) @t21))))) % 1.03/1.24 (define @t188 () (lambda (@list @t184 @t2) (_ tptp.c_Eps_i (lambda @t25 (_ (_ (_ tptp.c_In_rec_poly_G_i @t184) @t2) @t21))))) % 1.03/1.24 (define @t189 () (lambda @t19 (_ @t157 (_ tptp.c_Sing @t11)))) % 1.03/1.24 (define @t190 () (_ @t161 @t11)) % 1.03/1.24 (define @t191 () (@list @t161)) % 1.03/1.24 (define @t192 () (lambda @t19 (forall @t191 (=> (_ @t161 tptp.c_Empty) (=> (forall @t25 (=> @t166 (_ @t161 (_ tptp.c_ordsucc @t21)))) @t190))))) % 1.03/1.24 (define @t193 () (@var "__flatten_var_0" $$unsorted)) % 1.03/1.24 (define @t194 () (_ tptp.c_Union @t21)) % 1.03/1.24 (define @t195 () (@var "X3" (-> $$unsorted $$unsorted))) % 1.03/1.24 (define @t196 () (lambda (@list @t11 @t61 @t193) (_ (_ tptp.c_In_rec_poly_i (lambda (@list @t21 @t195) (_ (_ (_ tptp.c_If_i (_ (_ tptp.c_In @t194) @t21)) (_ (_ @t61 @t194) (_ @t195 @t194))) @t11))) @t193))) % 1.03/1.24 (define @t197 () (@list @t21 @t28)) % 1.03/1.24 (define @t198 () (lambda @t16 (_ (_ (_ tptp.c_nat_primrec @t11) (lambda @t197 (_ tptp.c_ordsucc @t28))) @t2))) % 1.03/1.24 (define @t199 () (lambda @t16 (_ (_ (_ tptp.c_nat_primrec tptp.c_Empty) (lambda @t197 (_ (_ tptp.c_add_nat @t11) @t28))) @t2))) % 1.03/1.24 (define @t200 () (lambda @t19 (_ (_ tptp.c_and (_ tptp.c_TransSet @t11)) (forall @t37 (=> @t101 (_ tptp.c_TransSet @t2)))))) % 1.03/1.24 (define @t201 () (lambda @t19 (_ @t36 (lambda @t37 (_ tptp.c_Inj1 @t2))))) % 1.03/1.24 (define @t202 () (_ tptp.c_Unj @t160)) % 1.03/1.24 (define @t203 () (lambda (@list @t11 @t2 @t39 @t195 @t160) (_ (_ (_ tptp.c_If_i (= @t160 (_ tptp.c_Inj0 @t202))) (_ @t39 @t202)) (_ @t195 @t202)))) % 1.03/1.24 (define @t204 () (_ tptp.c_Inj1 @t21)) % 1.03/1.24 (define @t205 () (_ tptp.c_Inj0 @t21)) % 1.03/1.24 (define @t206 () (lambda @t16 (_ (_ tptp.c_binunion (_ @t36 (lambda @t25 @t205))) (_ @t42 (lambda @t25 @t204))))) % 1.03/1.24 (define @t207 () (lambda @t37 (_ tptp.c_Unj @t2))) % 1.03/1.24 (define @t208 () (_ tptp.c_ReplSep @t11)) % 1.03/1.24 (define @t209 () (lambda @t19 (_ (_ @t208 (lambda @t37 (exists @t25 (= @t205 @t2)))) @t207))) % 1.03/1.24 (define @t210 () (lambda @t19 (_ (_ @t208 (lambda @t37 (exists @t25 (= @t204 @t2)))) @t207))) % 1.03/1.24 (define @t211 () (_ tptp.c_setsum @t11)) % 1.03/1.24 (define @t212 () (lambda @t16 (_ @t211 @t45))) % 1.03/1.24 (define @t213 () (_ (_ tptp.c_setsum @t21) @t28)) % 1.03/1.24 (define @t214 () (lambda @t52 (_ @t51 (lambda @t25 (_ (_ tptp.c_Repl @t50) (lambda @t34 @t213)))))) % 1.03/1.24 (define @t215 () (_ tptp.c_lam @t11)) % 1.03/1.24 (define @t216 () (lambda @t16 (_ @t215 (lambda @t25 @t2)))) % 1.03/1.24 (define @t217 () (_ (_ tptp.c_setsum @t2) @t28)) % 1.03/1.24 (define @t218 () (lambda @t16 (_ (_ @t208 (lambda @t25 (exists @t34 (= @t21 @t217)))) (lambda @t25 (_ tptp.c_proj1 @t21))))) % 1.03/1.24 (define @t219 () (_ tptp.c_ordsucc tptp.c_Empty)) % 1.03/1.24 (define @t220 () (_ tptp.c_ap @t11)) % 1.03/1.24 (define @t221 () (lambda @t19 (= (_ (_ tptp.c_setsum (_ @t220 tptp.c_Empty)) (_ @t220 @t219)) @t11))) % 1.03/1.24 (define @t222 () (_ (_ tptp.c_setsum @t28) @t160)) % 1.03/1.24 (define @t223 () (lambda @t16 (forall @t25 (=> @t47 (exists @t34 (_ @t33 (exists @t164 (= @t21 @t222)))))))) % 1.03/1.24 (define @t224 () (lambda @t52 (_ (_ tptp.c_Sep (_ tptp.c_Power (_ @t215 (lambda @t25 (_ tptp.c_Union @t50))))) (lambda @t25 (forall @t34 (=> @t32 (_ (_ tptp.c_In (_ (_ tptp.c_ap @t21) @t28)) @t30))))))) % 1.03/1.24 (define @t225 () (lambda @t16 (_ (_ tptp.c_Pi @t2) (lambda @t25 @t11)))) % 1.03/1.24 (define @t226 () (_ tptp.c_ap @t28)) % 1.03/1.24 (define @t227 () (@var "X2" (-> $$unsorted $$unsorted Bool))) % 1.03/1.24 (define @t228 () (lambda (@list @t11 @t29 @t227) (_ (_ tptp.c_Sep (_ @t215 @t35)) (lambda @t34 (_ (_ @t227 (_ @t226 tptp.c_Empty)) (_ @t226 @t219)))))) % 1.03/1.24 (define @t229 () (lambda @t19 (forall @t37 (=> @t101 (exists @t197 (= @t2 (_ (_ tptp.c_lam (_ tptp.c_ordsucc @t219)) (lambda @t164 (_ (_ (_ tptp.c_If_i (= @t160 tptp.c_Empty)) @t21) @t28))))))))) % 1.03/1.24 (define @t230 () (@var "X2" (-> $$unsorted $$unsorted $$unsorted))) % 1.03/1.24 (define @t231 () (lambda (@list @t11 @t29 @t230) (_ @t215 (lambda @t34 (_ (_ tptp.c_lam @t30) (lambda @t164 (_ (_ @t230 @t28) @t160))))))) % 1.03/1.24 (define @t232 () (_ @t74 @t28)) % 1.03/1.24 (define @t233 () (@list @t11 @t161 @t74)) % 1.03/1.24 (define @t234 () (lambda @t233 (forall @t34 (=> @t32 (_ (_ tptp.c_iff @t165) @t232))))) % 1.03/1.24 (define @t235 () (lambda @t233 (exists @t34 (_ @t33 (_ (_ tptp.c_and (_ (_ tptp.c_and (_ (_ (_ tptp.c_PNoEq_ @t28) @t161) @t74)) (_ tptp.c_not @t165))) @t232))))) % 1.03/1.24 (define @t236 () (_ tptp.c_not @t166)) % 1.03/1.24 (define @t237 () (_ tptp.c_PNoEq_ @t11)) % 1.03/1.24 (define @t238 () (_ (_ @t237 @t161) @t63)) % 1.03/1.24 (define @t239 () (@list @t11 @t161 @t21 @t63)) % 1.03/1.24 (define @t240 () (lambda @t239 (_ (_ tptp.c_or (_ (_ tptp.c_or (_ (_ (_ tptp.c_PNoLt_ (_ (_ tptp.c_binintersect @t11) @t21)) @t161) @t63)) (_ (_ tptp.c_and (_ (_ tptp.c_and (_ @t17 @t21)) @t238)) (_ @t63 @t11)))) (_ (_ tptp.c_and (_ @t167 (_ (_ (_ tptp.c_PNoEq_ @t21) @t161) @t63))) @t236)))) % 1.03/1.24 (define @t241 () (lambda @t239 (_ (_ tptp.c_or (_ (_ (_ (_ tptp.c_PNoLt @t11) @t161) @t21) @t63)) (_ (_ tptp.c_and (= @t11 @t21)) @t238)))) % 1.03/1.24 (define @t242 () (@var "X4" (-> $$unsorted Bool))) % 1.03/1.24 (define @t243 () (@var "X0" (-> $$unsorted (-> $$unsorted Bool) Bool))) % 1.03/1.24 (define @t244 () (_ tptp.c_and (_ (_ @t243 @t28) @t242))) % 1.03/1.24 (define @t245 () (@list @t242)) % 1.03/1.24 (define @t246 () (_ tptp.c_and (_ tptp.c_ordinal @t28))) % 1.03/1.24 (define @t247 () (@list @t243 @t2 @t74)) % 1.03/1.24 (define @t248 () (lambda @t247 (exists @t34 (_ @t246 (exists @t245 (_ @t244 (_ (_ (_ (_ tptp.c_PNoLe @t2) @t74) @t28) @t242))))))) % 1.03/1.24 (define @t249 () (lambda @t247 (exists @t34 (_ @t246 (exists @t245 (_ @t244 (_ (_ (_ (_ tptp.c_PNoLe @t28) @t242) @t2) @t74))))))) % 1.03/1.24 (define @t250 () (_ tptp.c_Sing @t219)) % 1.03/1.24 (define @t251 () (lambda @t19 (_ @t157 (_ @t36 (lambda @t37 (_ (lambda @t25 (_ (_ tptp.c_SetAdjoin @t21) @t250)) @t2)))))) % 1.03/1.24 (define @t252 () (_ (lambda @t34 (_ (_ tptp.c_SetAdjoin @t28) @t250)) @t21)) % 1.03/1.24 (define @t253 () (lambda @t16 (_ (_ tptp.c_and (_ @t12 (_ tptp.c_SNoElts_ @t11))) (forall @t25 (=> @t23 (_ (_ tptp.c_exactly1of2 (_ (_ tptp.c_In @t252) @t2)) @t47)))))) % 1.03/1.24 (define @t254 () (lambda @t168 (_ (_ tptp.c_binunion (_ @t170 (lambda @t25 @t166))) (_ (_ @t208 (lambda @t25 @t236)) (lambda @t25 @t252))))) % 1.03/1.24 (define @t255 () (_ (_ tptp.c_and (_ tptp.c_ordinal @t2)) (_ (_ tptp.c_SNo_ @t2) @t11))) % 1.03/1.24 (define @t256 () (lambda @t19 (exists @t37 @t255))) % 1.03/1.24 (define @t257 () (lambda @t19 (_ tptp.c_Eps_i (lambda @t37 @t255)))) % 1.03/1.24 (define @t258 () (@list @t11 @t2 @t21)) % 1.03/1.24 (define @t259 () (lambda @t258 (_ (_ @t237 (lambda @t34 @t43)) (lambda @t34 (_ @t31 @t21))))) % 1.03/1.24 (define @t260 () (_ tptp.c_SNoLev @t2)) % 1.03/1.24 (define @t261 () (lambda @t25 @t23)) % 1.03/1.24 (define @t262 () (_ tptp.c_SNoLev @t11)) % 1.03/1.24 (define @t263 () (lambda @t16 (_ (_ (_ (_ tptp.c_PNoLt @t262) @t261) @t260) @t172))) % 1.03/1.24 (define @t264 () (lambda @t16 (_ (_ (_ (_ tptp.c_PNoLe @t262) @t261) @t260) @t172))) % 1.03/1.24 (define @t265 () (lambda (@list @t11 @t61) (forall @t25 (=> @t23 (forall @t34 (=> @t32 (_ (_ tptp.c_In (_ (_ @t61 @t21) @t28)) @t11))))))) % 1.03/1.24 (define @t266 () (@var "X3" (-> $$unsorted $$unsorted $$unsorted))) % 1.03/1.24 (define @t267 () (_ @t61 @t59)) % 1.03/1.24 (define @t268 () (_ @t267 @t57)) % 1.03/1.24 (define @t269 () (_ @t230 @t59)) % 1.03/1.24 (define @t270 () (_ (_ tptp.c_In @t59) @t11)) % 1.03/1.24 (define @t271 () (@list @t59)) % 1.03/1.24 (define @t272 () (_ tptp.c_binop_on @t11)) % 1.03/1.24 (define @t273 () (lambda (@list @t11 @t61 @t230 @t266 @t160) (_ (_ tptp.c_and (_ (_ tptp.c_and (_ (_ tptp.c_and (_ (_ tptp.c_and (_ @t272 @t61)) (_ @t272 @t230))) (_ @t272 @t266))) (forall @t271 (=> @t270 (_ (_ tptp.c_and (= (_ (_ @t61 @t160) @t59) @t59)) (= (_ @t267 @t160) @t59)))))) (forall @t271 (=> @t270 (forall @t186 (=> (_ @t185 @t11) (_ (_ tptp.c_and (_ (_ tptp.c_and (_ (_ tptp.c_and (= (_ @t269 @t268) @t57)) (= (_ @t267 (_ @t269 @t57)) @t57))) (= (_ (_ @t266 @t268) @t57) @t59))) (= (_ (_ @t61 (_ (_ @t266 @t59) @t57)) @t57) @t59))))))))) % 1.03/1.24 (define @t274 () (@var "X15" $$unsorted)) % 1.03/1.24 (define @t275 () (@var "X14" $$unsorted)) % 1.03/1.24 (define @t276 () (_ @t61 @t275)) % 1.03/1.24 (define @t277 () (_ @t276 @t274)) % 1.03/1.24 (define @t278 () (@var "X16" $$unsorted)) % 1.03/1.24 (define @t279 () (@var "X9" (-> $$unsorted $$unsorted $$unsorted $$unsorted))) % 1.03/1.24 (define @t280 () (_ @t61 @t274)) % 1.03/1.24 (define @t281 () (_ @t280 @t275)) % 1.03/1.24 (define @t282 () (_ @t230 @t281)) % 1.03/1.24 (define @t283 () (@var "X8" (-> $$unsorted $$unsorted $$unsorted $$unsorted))) % 1.03/1.24 (define @t284 () (_ (_ tptp.c_In @t278) @t11)) % 1.03/1.24 (define @t285 () (@list @t278)) % 1.03/1.24 (define @t286 () (_ (_ tptp.c_In @t274) @t11)) % 1.03/1.24 (define @t287 () (@list @t274)) % 1.03/1.24 (define @t288 () (_ (_ tptp.c_In @t275) @t11)) % 1.03/1.24 (define @t289 () (@list @t275)) % 1.03/1.24 (define @t290 () (_ @t266 @t160)) % 1.03/1.24 (define @t291 () (_ @t290 @t275)) % 1.03/1.24 (define @t292 () (@var "X13" (-> $$unsorted $$unsorted $$unsorted))) % 1.03/1.24 (define @t293 () (_ @t230 @t275)) % 1.03/1.24 (define @t294 () (_ @t293 @t160)) % 1.03/1.24 (define @t295 () (@var "X12" (-> $$unsorted $$unsorted $$unsorted))) % 1.03/1.24 (define @t296 () (_ @t61 @t291)) % 1.03/1.24 (define @t297 () (@var "X11" (-> $$unsorted $$unsorted $$unsorted))) % 1.03/1.24 (define @t298 () (@var "X10" (-> $$unsorted $$unsorted $$unsorted))) % 1.03/1.24 (define @t299 () (@var "X7" (-> $$unsorted $$unsorted $$unsorted))) % 1.03/1.24 (define @t300 () (@var "X6" (-> $$unsorted $$unsorted $$unsorted $$unsorted))) % 1.03/1.24 (define @t301 () (@var "X5" (-> $$unsorted $$unsorted $$unsorted))) % 1.03/1.24 (define @t302 () (@list @t11 @t61 @t230 @t266 @t160 @t301 @t300 @t299 @t283 @t279 @t298 @t297 @t295 @t292)) % 1.03/1.24 (define @t303 () (lambda @t302 (_ (_ tptp.c_and (_ (_ tptp.c_and (_ (_ tptp.c_and (_ (_ tptp.c_and (_ (_ (_ (_ (_ tptp.c_Loop @t11) @t61) @t230) @t266) @t160)) (forall @t289 (=> @t288 (forall @t287 (=> @t286 (= (_ (_ @t301 @t275) @t274) (_ @t282 @t277)))))))) (forall @t289 (=> @t288 (forall @t287 (=> @t286 (forall @t285 (=> @t284 (= (_ (_ (_ @t300 @t275) @t274) @t278) (_ (_ @t230 (_ @t276 (_ @t280 @t278))) (_ (_ @t61 @t277) @t278))))))))))) (forall @t289 (=> @t288 (forall @t287 (=> @t286 (_ (_ tptp.c_and (_ (_ tptp.c_and (_ (_ tptp.c_and (_ (_ tptp.c_and (= (_ (_ @t299 @t275) @t274) (_ @t293 @t281))) (= (_ (_ @t298 @t275) @t274) (_ @t276 (_ @t280 @t294))))) (= (_ (_ @t297 @t275) @t274) (_ (_ @t61 (_ @t296 @t274)) @t275)))) (= (_ (_ @t295 @t275) @t274) (_ (_ @t61 (_ @t293 @t274)) (_ (_ @t230 @t294) @t160))))) (= (_ (_ @t292 @t275) @t274) (_ (_ @t61 (_ @t290 @t291)) (_ (_ @t266 @t274) @t275)))))))))) (forall @t289 (=> @t288 (forall @t287 (=> @t286 (forall @t285 (=> @t284 (_ (_ tptp.c_and (= (_ (_ (_ @t283 @t275) @t274) @t278) (_ @t282 (_ @t280 (_ @t276 @t278))))) (= (_ (_ (_ @t279 @t275) @t274) @t278) (_ (_ @t266 (_ (_ @t61 (_ (_ @t61 @t278) @t275)) @t274)) @t277)))))))))))) % 1.03/1.24 (define @t304 () (@var "X17" $$unsorted)) % 1.03/1.24 (define @t305 () (_ tptp.c_and (_ (_ tptp.c_In @t304) @t11))) % 1.03/1.24 (define @t306 () (@list @t304)) % 1.03/1.24 (define @t307 () (_ tptp.c_and @t284)) % 1.03/1.24 (define @t308 () (_ tptp.c_and @t286)) % 1.03/1.24 (define @t309 () (_ tptp.c_and @t288)) % 1.03/1.24 (define @t310 () (_ tptp.c_and (_ (_ (_ (_ (_ (_ (_ (_ (_ (_ (_ (_ (_ (_ tptp.c_Loop_with_defs @t11) @t61) @t230) @t266) @t160) @t301) @t300) @t299) @t283) @t279) @t298) @t297) @t295) @t292))) % 1.03/1.24 (define @t311 () (lambda @t302 (_ @t310 (exists @t289 (_ @t309 (exists @t287 (_ @t308 (exists @t285 (_ @t307 (exists @t306 (_ @t305 (_ tptp.c_not (= (_ (_ @t301 (_ (_ @t61 (_ (_ @t230 (_ (_ (_ @t283 @t274) @t278) @t275)) @t160)) @t275)) @t304) @t160))))))))))))) % 1.03/1.24 (define @t312 () (@var "X18" $$unsorted)) % 1.03/1.24 (define @t313 () (lambda @t302 (_ @t310 (exists @t289 (_ @t309 (exists @t287 (_ @t308 (exists @t285 (_ @t307 (exists @t306 (_ @t305 (exists (@list @t312) (_ (_ tptp.c_and (_ (_ tptp.c_In @t312) @t11)) (_ tptp.c_not (= (_ (_ (_ @t300 @t312) (_ @t296 (_ (_ (_ @t279 @t274) @t278) @t275))) @t304) @t160))))))))))))))) % 1.03/1.24 (define @t314 () (_ tptp.c_Inj0 @t152)) % 1.03/1.24 (define @t315 () (_ tptp.c_Inj0 tptp.c_Empty)) % 1.03/1.24 (define @t316 () (lambda @t19 (forall @t191 (=> (_ @t161 @t315) (=> (_ @t161 @t314) (=> (forall @t197 (=> @t166 (=> @t165 (_ @t161 (_ tptp.c_Inj1 @t213))))) @t190)))))) % 1.03/1.24 (define @t317 () (@list @t28 @t160)) % 1.03/1.24 (define @t318 () (_ @t301 @t57)) % 1.03/1.24 (define @t319 () (_ @t227 @t57)) % 1.03/1.24 (define @t320 () (_ tptp.c_combinator @t57)) % 1.03/1.24 (define @t321 () (lambda @t16 (forall (@list @t227) (_ (_ (_ (lambda (@list @t28 @t160 @t301) (=> (_ tptp.c_per_i @t227) (=> (forall @t186 (=> @t320 (_ @t319 @t57))) (=> (forall (@list @t57 @t60 @t70 @t56) (=> @t320 (=> (_ tptp.c_combinator @t60) (=> (_ tptp.c_combinator @t70) (=> (_ tptp.c_combinator @t56) (=> (_ @t319 @t70) (=> (_ (_ @t227 @t60) @t56) (_ (_ @t227 (_ @t318 @t60)) (_ (_ @t301 @t70) @t56))))))))) (=> (forall (@list @t57 @t60) (_ (_ @t227 (_ (_ @t301 (_ (_ @t301 @t28) @t57)) @t60)) @t57)) (=> (forall (@list @t57 @t60 @t70) (_ (_ @t227 (_ (_ @t301 (_ (_ @t301 (_ (_ @t301 @t160) @t57)) @t60)) @t70)) (_ (_ @t301 (_ @t318 @t70)) (_ (_ @t301 @t60) @t70)))) (_ (_ @t227 @t11) @t2))))))) @t315) @t314) (lambda @t317 (_ tptp.c_Inj1 @t222)))))) % 1.03/1.24 (define @t322 () (_ (_ tptp.c_equip (_ (_ tptp.c_setprod @t160) @t28)) @t21)) % 1.03/1.24 (define @t323 () (lambda @t258 (exists @t317 (_ (_ tptp.c_or (_ (_ tptp.c_and (_ (_ tptp.c_equip (_ @t211 @t28)) @t2)) @t322)) (_ (_ tptp.c_and (_ (_ tptp.c_equip @t217) @t11)) @t322))))) % 1.03/1.24 (define @t324 () (@var "BOUND_VARIABLE_24174" $$unsorted)) % 1.03/1.24 (define @t325 () (_ tptp.c_Power @t324)) % 1.03/1.24 (define @t326 () (@var "BOUND_VARIABLE_24176" $$unsorted)) % 1.03/1.24 (define @t327 () (tptp.c_Power @t324)) % 1.03/1.24 (define @t328 () (tptp.c_In @t326 @t327)) % 1.03/1.24 (define @t329 () (_ tptp.c_In @t326)) % 1.03/1.24 (define @t330 () (_ @t329 @t325)) % 1.03/1.24 (define @t331 () (not (forall @t25 (or (not (tptp.c_In @t21 @t326)) (tptp.c_In @t21 @t324))))) % 1.03/1.24 (define @t332 () (or @t331 @t330)) % 1.03/1.24 (define @t333 () (@list @t324 @t326)) % 1.03/1.24 (define @t334 () (forall @t333 @t332)) % 1.03/1.24 (define @t335 () (@var "BOUND_VARIABLE_24158" $$unsorted)) % 1.03/1.24 (define @t336 () (@var "BOUND_VARIABLE_24197" $$unsorted)) % 1.03/1.24 (define @t337 () (tptp.c_In @t336 @t335)) % 1.03/1.24 (define @t338 () (@var "BOUND_VARIABLE_24160" $$unsorted)) % 1.03/1.24 (define @t339 () (not (tptp.c_In @t336 @t338))) % 1.03/1.24 (define @t340 () (tptp.c_Power @t335)) % 1.03/1.24 (define @t341 () (tptp.c_In @t338 @t340)) % 1.03/1.24 (define @t342 () (not @t341)) % 1.03/1.24 (define @t343 () (or @t339 @t337)) % 1.03/1.24 (define @t344 () (or @t342 @t343)) % 1.03/1.24 (define @t345 () (forall (@list @t335 @t338 @t336) @t344)) % 1.03/1.24 (define @t346 () (@list @t336)) % 1.03/1.24 (define @t347 () (forall @t346 @t344)) % 1.03/1.24 (define @t348 () (@list @t335 @t338)) % 1.03/1.24 (define @t349 () (forall @t346 @t343)) % 1.03/1.24 (define @t350 () (or @t342 @t349)) % 1.03/1.24 (define @t351 () (forall @t25 (or (not (tptp.c_In @t21 @t338)) (tptp.c_In @t21 @t335)))) % 1.03/1.24 (define @t352 () (_ tptp.c_Power @t335)) % 1.03/1.24 (define @t353 () (_ tptp.c_In @t338)) % 1.03/1.24 (define @t354 () (_ @t353 @t352)) % 1.03/1.24 (define @t355 () (not @t354)) % 1.03/1.24 (define @t356 () (or @t355 @t351)) % 1.03/1.24 (define @t357 () (forall @t348 @t356)) % 1.03/1.24 (define @t358 () (tptp.c_In @t21 @t11)) % 1.03/1.24 (define @t359 () (tptp.c_In @t21 @t2)) % 1.03/1.24 (define @t360 () (not @t359)) % 1.03/1.24 (define @t361 () (forall @t25 (or @t360 @t358))) % 1.03/1.24 (define @t362 () (or (not @t361) @t26)) % 1.03/1.24 (define @t363 () (forall @t16 @t362)) % 1.03/1.24 (define @t364 () (@list @t11 @t2)) % 1.03/1.24 (define @t365 () (or (not @t26) @t361)) % 1.03/1.24 (define @t366 () (forall @t16 @t365)) % 1.03/1.24 (define @t367 () (and @t366 @t363)) % 1.03/1.24 (define @t368 () (and (=> @t26 @t361) (=> @t361 @t26))) % 1.03/1.24 (define @t369 () (lambda (@list @t9) (and (=> @t26 @t9) (=> @t9 @t26)))) % 1.03/1.24 (define @t370 () (@var "BOUND_VARIABLE_7802" $$unsorted)) % 1.03/1.24 (define @t371 () (tptp.c_In @t21 @t370)) % 1.03/1.24 (define @t372 () (lambda (@list @t370) (forall @t25 (or @t360 @t371)))) % 1.03/1.24 (define @t373 () (not @t358)) % 1.03/1.24 (define @t374 () (lambda @t16 (forall @t25 (or @t373 @t359)))) % 1.03/1.24 (define @t375 () (and @t97 @t96)) % 1.03/1.24 (define @t376 () (_ (lambda @t10 @t375) @t26)) % 1.03/1.24 (define @t377 () (not @t23)) % 1.03/1.24 (define @t378 () (or @t377 @t47)) % 1.03/1.24 (define @t379 () (@var "BOUND_VARIABLE_7743" Bool)) % 1.03/1.24 (define @t380 () (@list @t379)) % 1.03/1.24 (define @t381 () (= @t379 false)) % 1.03/1.24 (define @t382 () (not @t381)) % 1.03/1.24 (define @t383 () (ite @t381 false true)) % 1.03/1.24 (define @t384 () (= @t97 true)) % 1.03/1.24 (define @t385 () (lambda @t380 (ite @t384 @t383 false))) % 1.03/1.24 (define @t386 () (@var "BOUND_VARIABLE_7741" Bool)) % 1.03/1.24 (define @t387 () (lambda (@list @t386 @t379) (ite (= @t386 true) @t383 false))) % 1.03/1.24 (define @t388 () (and @t4 @t9)) % 1.03/1.24 (define @t389 () (lambda @t10 @t388)) % 1.03/1.24 (define @t390 () (not false)) % 1.03/1.24 (define @t391 () (and @t4 @t9 @t390)) % 1.03/1.24 (define @t392 () (or @t391 false)) % 1.03/1.24 (define @t393 () (not @t89)) % 1.03/1.24 (define @t394 () (and @t4 @t9 @t393)) % 1.03/1.24 (define @t395 () (or @t89 @t394 @t89)) % 1.03/1.24 (define @t396 () (or @t394 @t89)) % 1.03/1.24 (define @t397 () (@const 0 $$unsorted)) % 1.03/1.24 (define @t398 () (tptp.c_Power @t397)) % 1.03/1.24 (define @t399 () (tptp.c_In @t397 @t398)) % 1.03/1.24 (define @t400 () (not true)) % 1.03/1.24 (define @t401 () (tptp.c_In @t21 @t397)) % 1.03/1.24 (define @t402 () (forall @t25 (or (not @t401) @t401))) % 1.03/1.24 (define @t403 () (not @t402)) % 1.03/1.24 (define @t404 () (or @t403 @t399)) % 1.03/1.24 (define @t405 () (forall @t333 (or @t331 @t328))) % 1.03/1.24 (define @t406 () (@list false)) % 1.03/1.24 (define @t407 () (@var "BOUND_VARIABLE_25504" $$unsorted)) % 1.03/1.24 (define @t408 () (@var "BOUND_VARIABLE_25506" $$unsorted)) % 1.03/1.24 (define @t409 () (@var "BOUND_VARIABLE_25498" (-> $$unsorted $$unsorted $$unsorted))) % 1.03/1.24 (define @t410 () (_ @t409 @t408 @t407)) % 1.03/1.24 (define @t411 () (@var "BOUND_VARIABLE_25502" (-> $$unsorted $$unsorted))) % 1.03/1.24 (define @t412 () (_ @t411 @t410)) % 1.03/1.24 (define @t413 () (_ @t411 @t412)) % 1.03/1.24 (define @t414 () (@var "BOUND_VARIABLE_25500" (-> $$unsorted Bool))) % 1.03/1.24 (define @t415 () (_ @t414 @t413)) % 1.03/1.24 (define @t416 () (@list @t409 @t414 @t411 @t407 @t408)) % 1.03/1.24 (define @t417 () (forall @t416 @t415)) % 1.03/1.24 (define @t418 () (lambda (@list (@var "BOUND_VARIABLE_71058" $$unsorted)) false)) % 1.03/1.24 (define @t419 () (@var "BOUND_VARIABLE_71772" $$unsorted)) % 1.03/1.24 (define @t420 () (lambda (@list @t419) @t419)) % 1.03/1.24 (define @t421 () (@var "BOUND_VARIABLE_68501" $$unsorted)) % 1.03/1.24 (define @t422 () (lambda (@list @t421 (@var "BOUND_VARIABLE_68502" $$unsorted)) @t421)) % 1.03/1.24 (define @t423 () (_ @t422 @t397 @t397)) % 1.03/1.24 (define @t424 () (_ @t420 @t423)) % 1.03/1.24 (define @t425 () (_ @t420 @t424)) % 1.03/1.24 (define @t426 () (_ @t418 @t425)) % 1.03/1.24 (define @t427 () (forall (@list @t57 @t56) @t58)) % 1.03/1.24 (define @t428 () (and @t417 @t390)) % 1.03/1.24 (define @t429 () (or @t428 @t427)) % 1.03/1.24 (define @t430 () (not tptp.c_False)) % 1.03/1.24 (define @t431 () (or @t390 tptp.c_False)) % 1.03/1.24 (define @t432 () (and @t431 @t430)) % 1.03/1.24 (define @t433 () (or @t432 false)) % 1.03/1.24 (define @t434 () (not @t4)) % 1.03/1.24 (define @t435 () (and (or @t434 tptp.c_False) @t430)) % 1.03/1.24 (define @t436 () (or @t4 @t435 @t4)) % 1.03/1.24 (define @t437 () (or @t435 @t4)) % 1.03/1.24 (define @t438 () (=> @t87 tptp.c_False)) % 1.03/1.24 (define @t439 () (_ @t88 @t4)) % 1.03/1.24 (define @t440 () (=> (_ @t88 @t439) @t4)) % 1.03/1.24 (define @t441 () (and @t417 @t430)) % 1.03/1.24 (define @t442 () (or @t441 @t427)) % 1.03/1.24 (define @t443 () (=> @t442 tptp.c_False)) % 1.03/1.24 (define @t444 () (_ (_ @t409 @t408) @t407)) % 1.03/1.24 (define @t445 () (_ @t411 @t444)) % 1.03/1.24 (define @t446 () (_ @t411 @t445)) % 1.03/1.24 (define @t447 () (_ @t414 @t446)) % 1.03/1.24 (define @t448 () (forall @t416 @t447)) % 1.03/1.24 (define @t449 () (@list @t61 @t63 @t62 @t59 @t60)) % 1.03/1.24 (define @t450 () (forall @t449 @t430)) % 1.03/1.24 (define @t451 () (forall @t449 @t64)) % 1.03/1.24 (define @t452 () (and @t451 @t450)) % 1.03/1.24 (define @t453 () (and @t64 @t430)) % 1.03/1.24 (define @t454 () (forall @t449 @t453)) % 1.03/1.24 (define @t455 () (or @t454 @t427)) % 1.03/1.24 (define @t456 () (or @t453 @t58)) % 1.03/1.24 (define @t457 () (forall (@list @t61 @t63 @t62 @t59 @t60 @t57 @t56) @t456)) % 1.03/1.24 (define @t458 () (forall (@list @t61 @t63 @t62 @t59 @t57 @t60 @t56) @t456)) % 1.03/1.24 (define @t459 () (=> @t64 tptp.c_False)) % 1.03/1.24 (define @t460 () (= @t459 false)) % 1.03/1.24 (define @t461 () (not @t460)) % 1.03/1.24 (define @t462 () (@var "BOUND_VARIABLE_25477" Bool)) % 1.03/1.24 (define @t463 () (= @t462 false)) % 1.03/1.24 (define @t464 () (ite @t463 false true)) % 1.03/1.24 (define @t465 () (@list @t462)) % 1.03/1.24 (define @t466 () (lambda @t465 @t464)) % 1.03/1.24 (define @t467 () (_ @t88 @t64)) % 1.03/1.24 (define @t468 () (= false @t462)) % 1.03/1.24 (define @t469 () (= true true)) % 1.03/1.24 (define @t470 () (lambda @t380 (ite @t469 @t383 false))) % 1.03/1.24 (define @t471 () (= @t70 @t56)) % 1.03/1.24 (define @t472 () (and @t471 @t68)) % 1.03/1.24 (define @t473 () (=> (= @t59 @t60) @t472)) % 1.03/1.24 (define @t474 () (and @t75 @t473)) % 1.03/1.24 (define @t475 () (forall @t65 @t400)) % 1.03/1.24 (define @t476 () (not @t475)) % 1.03/1.24 (define @t477 () (not @t68)) % 1.03/1.24 (define @t478 () (forall @t65 @t477)) % 1.03/1.24 (define @t479 () (not @t478)) % 1.03/1.24 (define @t480 () (= @t471 true)) % 1.03/1.24 (define @t481 () (lambda @t380 (ite @t480 @t383 false))) % 1.03/1.24 (define @t482 () (=> @t72 (_ (_ @t389 @t71) @t69))) % 1.03/1.24 (define @t483 () (= @t75 true)) % 1.03/1.24 (define @t484 () (lambda @t380 (ite @t483 @t383 false))) % 1.03/1.24 (define @t485 () (=> (_ (_ @t389 @t75) @t482) @t66)) % 1.03/1.24 (define @t486 () (=> @t78 @t485)) % 1.03/1.24 (define @t487 () (forall @t80 @t486)) % 1.03/1.24 (define @t488 () (=> (_ (_ @t389 @t487) @t467) @t58)) % 1.03/1.24 (define @t489 () (forall @t84 @t488)) % 1.03/1.24 (define @t490 () (= @t397 @t398)) % 1.03/1.24 (define @t491 () (@list @t427)) % 1.03/1.24 (define @t492 () (= @t397 tptp.c_Empty)) % 1.03/1.24 (define @t493 () (= tptp.c_Empty @t397)) % 1.03/1.24 (define @t494 () (tptp.c_In @t11 tptp.c_Empty)) % 1.03/1.24 (define @t495 () (forall @t19 (not @t494))) % 1.03/1.24 (define @t496 () (not @t495)) % 1.03/1.24 (define @t497 () (=> @t496 tptp.c_False)) % 1.03/1.24 (define @t498 () (not @t18)) % 1.03/1.24 (define @t499 () (forall @t19 @t498)) % 1.03/1.24 (define @t500 () (not @t499)) % 1.03/1.24 (define @t501 () (tptp.c_In @t397 tptp.c_Empty)) % 1.03/1.24 (define @t502 () (not @t493)) % 1.03/1.24 (define @t503 () (not @t490)) % 1.03/1.24 (define @t504 () (not @t399)) % 1.03/1.24 (define @t505 () (not @t501)) % 1.03/1.24 (define @t506 () (and @t505 @t493 @t490 @t399)) % 1.03/1.24 (assume @p1 (forall (@list @t1 @t2) (=> @t3 (_ @t1 (_ tptp.c_Eps_i @t1))))) % 1.03/1.24 (assume @p2 @t8) % 1.03/1.24 (assume @p3 (forall @t10 (=> (_ (_ tptp.c_iff @t4) @t9) (= @t4 @t9)))) % 1.03/1.24 (assume @p4 (forall @t16 (=> @t15 (=> @t13 (= @t11 @t2))))) % 1.03/1.24 (assume @p5 (_ tptp.c_not @t20)) % 1.03/1.24 (assume @p6 (forall @t16 (_ (_ tptp.c_iff (_ @t24 (_ tptp.c_Union @t11))) (exists @t25 (_ (_ tptp.c_and (_ @t24 @t21)) @t23))))) % 1.03/1.24 (assume @p7 @t27) % 1.03/1.24 (assume @p8 (forall (@list @t11 @t29 @t21) (_ (_ tptp.c_iff (_ @t22 (_ @t36 @t35))) (exists @t34 (_ @t33 (= @t21 @t30)))))) % 1.03/1.24 (assume @p9 (forall @t49 (=> (forall @t37 (=> @t3 @t48)) (=> (_ @t1 tptp.c_Empty) (=> (forall @t37 (=> @t3 (_ @t1 (_ tptp.c_Union @t2)))) (=> (forall @t37 (=> @t3 (_ @t1 @t45))) (=> (forall @t37 (=> @t3 (forall @t44 (=> (forall @t34 (=> @t43 (_ @t1 @t40))) (_ @t1 (_ @t42 @t41)))))) @t38))))))) % 1.03/1.24 (assume @p10 (forall @t49 (=> (forall @t37 (=> @t48 @t3)) @t38))) % 1.03/1.24 (assume @p11 (= tptp.c_False (forall @t7 @t4))) % 1.03/1.24 (assume @p12 (= tptp.c_True (forall @t7 (=> @t4 @t4)))) % 1.03/1.24 (assume @p13 (= tptp.c_V_ (_ tptp.c_In_rec_poly_i (lambda @t52 (_ @t51 (lambda @t25 (_ tptp.c_Power @t50))))))) % 1.03/1.24 (assume @p14 (= tptp.c_Inj1 (_ tptp.c_In_rec_poly_i (lambda @t52 (_ (_ tptp.c_binunion @t55) @t54))))) % 1.03/1.24 (assume @p15 (= tptp.c_Unj (_ tptp.c_In_rec_poly_i (lambda @t52 (_ (_ tptp.c_Repl (_ (_ tptp.c_setminus @t11) @t55)) @t53))))) % 1.03/1.24 (assume @p16 @t86) % 1.03/1.24 (assume @p17 true) % 1.03/1.24 (step @p18 (= tptp.c_not @t88) :rule refl :args (@t88)) % 1.03/1.24 (step @p19 (= tptp.c_and @t94) :rule refl :args (@t94)) % 1.03/1.24 (step @p20 (= tptp.c_or @t95) :rule refl :args (@t95)) % 1.03/1.24 (step @p21 (= tptp.c_iff @t98) :rule refl :args (@t98)) % 1.03/1.24 (step @p22 (= tptp.c_Subq @t100) :rule refl :args (@t100)) % 1.03/1.24 (step @p23 (= tptp.c_TransSet @t102) :rule refl :args (@t102)) % 1.03/1.24 (step @p24 (= tptp.c_atleast2 @t103) :rule refl :args (@t103)) % 1.03/1.24 (step @p25 (= tptp.c_atleast3 @t107) :rule refl :args (@t107)) % 1.03/1.24 (step @p26 (= tptp.c_atleast4 @t108) :rule refl :args (@t108)) % 1.03/1.24 (step @p27 (= tptp.c_atleast5 @t109) :rule refl :args (@t109)) % 1.03/1.24 (step @p28 (= tptp.c_atleast6 @t110) :rule refl :args (@t110)) % 1.03/1.24 (step @p29 (= tptp.c_exactly2 @t112) :rule refl :args (@t112)) % 1.03/1.24 (step @p30 (= tptp.c_exactly3 @t114) :rule refl :args (@t114)) % 1.03/1.24 (step @p31 (= tptp.c_exactly4 @t116) :rule refl :args (@t116)) % 1.03/1.24 (step @p32 (= tptp.c_exactly5 @t117) :rule refl :args (@t117)) % 1.03/1.24 (step @p33 (= tptp.c_exu_i @t120) :rule refl :args (@t120)) % 1.03/1.24 (step @p34 (= tptp.c_reflexive_i @t124) :rule refl :args (@t124)) % 1.03/1.24 (step @p35 (= tptp.c_irreflexive_i @t125) :rule refl :args (@t125)) % 1.03/1.24 (step @p36 (= tptp.c_symmetric_i @t129) :rule refl :args (@t129)) % 1.03/1.24 (step @p37 (= tptp.c_antisymmetric_i @t130) :rule refl :args (@t130)) % 1.03/1.24 (step @p38 (= tptp.c_transitive_i @t131) :rule refl :args (@t131)) % 1.03/1.24 (step @p39 (= tptp.c_eqreln_i @t135) :rule refl :args (@t135)) % 1.03/1.24 (step @p40 (= tptp.c_per_i @t136) :rule refl :args (@t136)) % 1.03/1.24 (step @p41 (= tptp.c_linear_i @t138) :rule refl :args (@t138)) % 1.03/1.24 (step @p42 (= tptp.c_trichotomous_or_i @t139) :rule refl :args (@t139)) % 1.03/1.24 (step @p43 (= tptp.c_partialorder_i @t140) :rule refl :args (@t140)) % 1.03/1.24 (step @p44 (= tptp.c_totalorder_i @t141) :rule refl :args (@t141)) % 1.03/1.24 (step @p45 (= tptp.c_strictpartialorder_i @t142) :rule refl :args (@t142)) % 1.03/1.24 (step @p46 (= tptp.c_stricttotalorder_i @t143) :rule refl :args (@t143)) % 1.03/1.24 (step @p47 (= tptp.c_If_i @t146) :rule refl :args (@t146)) % 1.03/1.24 (step @p48 (= tptp.c_exactly1of2 @t148) :rule refl :args (@t148)) % 1.03/1.24 (step @p49 (= tptp.c_exactly1of3 @t149) :rule refl :args (@t149)) % 1.03/1.24 (step @p50 (= tptp.c_nIn @t150) :rule refl :args (@t150)) % 1.03/1.24 (step @p51 (= tptp.c_nSubq @t151) :rule refl :args (@t151)) % 1.03/1.24 (step @p52 (= tptp.c_UPair @t153) :rule refl :args (@t153)) % 1.03/1.24 (step @p53 (= tptp.c_Sing @t155) :rule refl :args (@t155)) % 1.03/1.24 (step @p54 (= tptp.c_binunion @t156) :rule refl :args (@t156)) % 1.03/1.24 (step @p55 (= tptp.c_SetAdjoin @t158) :rule refl :args (@t158)) % 1.03/1.24 (step @p56 (= tptp.c_famunion @t159) :rule refl :args (@t159)) % 1.03/1.24 (step @p57 (= tptp.c_Sep @t169) :rule refl :args (@t169)) % 1.03/1.24 (step @p58 (= tptp.c_ReplSep @t171) :rule refl :args (@t171)) % 1.03/1.24 (step @p59 (= tptp.c_binintersect @t173) :rule refl :args (@t173)) % 1.03/1.24 (step @p60 (= tptp.c_setminus @t174) :rule refl :args (@t174)) % 1.03/1.24 (step @p61 (= tptp.c_inj @t177) :rule refl :args (@t177)) % 1.03/1.24 (step @p62 (= tptp.c_bij @t179) :rule refl :args (@t179)) % 1.03/1.24 (step @p63 (= tptp.c_atleastp @t180) :rule refl :args (@t180)) % 1.03/1.24 (step @p64 (= tptp.c_equip @t181) :rule refl :args (@t181)) % 1.03/1.24 (step @p65 (= tptp.c_In_rec_poly_G_i @t187) :rule refl :args (@t187)) % 1.03/1.24 (step @p66 (= tptp.c_In_rec_poly_i @t188) :rule refl :args (@t188)) % 1.03/1.24 (step @p67 (= tptp.c_ordsucc @t189) :rule refl :args (@t189)) % 1.03/1.24 (step @p68 (= tptp.c_nat_p @t192) :rule refl :args (@t192)) % 1.03/1.24 (step @p69 (= tptp.c_nat_primrec @t196) :rule refl :args (@t196)) % 1.03/1.24 (step @p70 (= tptp.c_add_nat @t198) :rule refl :args (@t198)) % 1.03/1.24 (step @p71 (= tptp.c_mul_nat @t199) :rule refl :args (@t199)) % 1.03/1.24 (step @p72 (= tptp.c_ordinal @t200) :rule refl :args (@t200)) % 1.03/1.24 (step @p73 (= tptp.c_Inj0 @t201) :rule refl :args (@t201)) % 1.03/1.24 (step @p74 (= tptp.c_combine_funcs @t203) :rule refl :args (@t203)) % 1.03/1.24 (step @p75 (= tptp.c_setsum @t206) :rule refl :args (@t206)) % 1.03/1.24 (step @p76 (= tptp.c_proj0 @t209) :rule refl :args (@t209)) % 1.03/1.24 (step @p77 (= tptp.c_proj1 @t210) :rule refl :args (@t210)) % 1.03/1.24 (step @p78 (= tptp.c_binrep @t212) :rule refl :args (@t212)) % 1.03/1.24 (step @p79 (= tptp.c_lam @t214) :rule refl :args (@t214)) % 1.03/1.24 (step @p80 (= tptp.c_setprod @t216) :rule refl :args (@t216)) % 1.03/1.24 (step @p81 (= tptp.c_ap @t218) :rule refl :args (@t218)) % 1.03/1.24 (step @p82 (= tptp.c_setsum_p @t221) :rule refl :args (@t221)) % 1.03/1.24 (step @p83 (= tptp.c_tuple_p @t223) :rule refl :args (@t223)) % 1.03/1.24 (step @p84 (= tptp.c_Pi @t224) :rule refl :args (@t224)) % 1.03/1.24 (step @p85 (= tptp.c_setexp @t225) :rule refl :args (@t225)) % 1.03/1.24 (step @p86 (= tptp.c_Sep2 @t228) :rule refl :args (@t228)) % 1.03/1.24 (step @p87 (= tptp.c_set_of_pairs @t229) :rule refl :args (@t229)) % 1.03/1.24 (step @p88 (= tptp.c_lam2 @t231) :rule refl :args (@t231)) % 1.03/1.24 (step @p89 (= tptp.c_PNoEq_ @t234) :rule refl :args (@t234)) % 1.03/1.24 (step @p90 (= tptp.c_PNoLt_ @t235) :rule refl :args (@t235)) % 1.03/1.24 (step @p91 (= tptp.c_PNoLt @t240) :rule refl :args (@t240)) % 1.03/1.24 (step @p92 (= tptp.c_PNoLe @t241) :rule refl :args (@t241)) % 1.03/1.24 (step @p93 (= tptp.c_PNo_downc @t248) :rule refl :args (@t248)) % 1.03/1.24 (step @p94 (= tptp.c_PNo_upc @t249) :rule refl :args (@t249)) % 1.03/1.24 (step @p95 (= tptp.c_SNoElts_ @t251) :rule refl :args (@t251)) % 1.03/1.24 (step @p96 (= tptp.c_SNo_ @t253) :rule refl :args (@t253)) % 1.03/1.24 (step @p97 (= tptp.c_PSNo @t254) :rule refl :args (@t254)) % 1.03/1.24 (step @p98 (= tptp.c_SNo @t256) :rule refl :args (@t256)) % 1.03/1.24 (step @p99 (= tptp.c_SNoLev @t257) :rule refl :args (@t257)) % 1.03/1.24 (step @p100 (= tptp.c_SNoEq_ @t259) :rule refl :args (@t259)) % 1.03/1.24 (step @p101 (= tptp.c_SNoLt @t263) :rule refl :args (@t263)) % 1.03/1.24 (step @p102 (= tptp.c_SNoLe @t264) :rule refl :args (@t264)) % 1.03/1.24 (step @p103 (= tptp.c_binop_on @t265) :rule refl :args (@t265)) % 1.03/1.24 (step @p104 (= tptp.c_Loop @t273) :rule refl :args (@t273)) % 1.03/1.24 (step @p105 (= tptp.c_Loop_with_defs @t303) :rule refl :args (@t303)) % 1.03/1.24 (step @p106 (= tptp.c_Loop_with_defs_cex1 @t311) :rule refl :args (@t311)) % 1.03/1.24 (step @p107 (= tptp.c_Loop_with_defs_cex2 @t313) :rule refl :args (@t313)) % 1.03/1.24 (step @p108 (= tptp.c_combinator @t316) :rule refl :args (@t316)) % 1.03/1.24 (step @p109 (= tptp.c_combinator_equiv @t321) :rule refl :args (@t321)) % 1.03/1.24 (step @p110 (= tptp.c_equip_mod @t323) :rule refl :args (@t323)) % 1.03/1.24 (step @p111 :rule refl :args ((tptp.c_In @t326 @t325))) % 1.03/1.24 (step @p112 :rule refl :args (@t327)) % 1.03/1.24 (step @p113 :rule refl :args (@t326)) % 1.03/1.24 (step @p114 :rule cong :premises (@p113 @p112) :args (@t328)) % 1.03/1.24 (step @p115 :rule trans :premises (@p114 @p111)) % 1.03/1.24 (step @p116 :rule refl :args (@t329)) % 1.03/1.24 (step @p117 :rule ho_cong :premises (@p116 @p112)) % 1.03/1.24 (step @p118 :rule cong :premises (@p117 @p115) :args ((= (_ @t329 @t327) @t328))) % 1.03/1.24 (step @p119 :rule symm :premises (@p118)) % 1.03/1.24 (step @p120 :rule refl :args (@t330)) % 1.03/1.24 (step @p121 :rule eq_resolve :premises (@p120 @p119)) % 1.03/1.24 (step @p122 :rule refl :args (@t325)) % 1.03/1.24 (step @p123 :rule cong :premises (@p122 @p112) :args ((= @t325 @t327))) % 1.03/1.24 (step @p124 :rule symm :premises (@p123)) % 1.03/1.24 (step @p125 :rule eq_resolve :premises (@p122 @p124)) % 1.03/1.24 (step @p126 :rule ho_cong :premises (@p116 @p125)) % 1.03/1.24 (step @p127 :rule trans :premises (@p126 @p121)) % 1.03/1.24 (step @p128 :rule refl :args (@t331)) % 1.03/1.24 (step @p129 :rule nary_cong :premises (@p128 @p127) :args (@t332)) % 1.03/1.24 (step @p130 :rule cong :premises (@p129) :args (@t334)) % 1.03/1.24 (step @p131 :rule aci_norm :args ((= @t344 (or @t342 @t339 @t337)))) % 1.03/1.24 (step @p132 :rule cong :premises (@p131) :args (@t345)) % 1.03/1.24 (step @p133 :rule quant-merge-prenex :args ((= (forall @t348 @t347) @t345))) % 1.03/1.24 (step @p134 :rule alpha_equiv :args (@t349 (@list @t336) (@list @t21))) % 1.03/1.24 (step @p135 :rule refl :args (@t342)) % 1.03/1.24 (step @p136 :rule nary_cong :premises (@p135 @p134) :args (@t350)) % 1.03/1.24 (step @p137 :rule quant-miniscope-or :args ((= @t347 @t350))) % 1.03/1.24 (step @p138 :rule trans :premises (@p137 @p136)) % 1.03/1.24 (step @p139 :rule symm :premises (@p138)) % 1.03/1.24 (step @p140 :rule cong :premises (@p139) :args ((forall @t348 (or @t342 @t351)))) % 1.03/1.24 (step @p141 :rule trans :premises (@p140 @p133)) % 1.03/1.24 (step @p142 :rule trans :premises (@p141 @p132)) % 1.03/1.24 (step @p143 :rule refl :args (@t351)) % 1.03/1.24 (step @p144 :rule refl :args ((tptp.c_In @t338 @t352))) % 1.03/1.24 (step @p145 :rule refl :args (@t340)) % 1.03/1.24 (step @p146 :rule refl :args (@t338)) % 1.03/1.24 (step @p147 :rule cong :premises (@p146 @p145) :args (@t341)) % 1.03/1.24 (step @p148 :rule trans :premises (@p147 @p144)) % 1.03/1.24 (step @p149 :rule refl :args (@t353)) % 1.03/1.24 (step @p150 :rule ho_cong :premises (@p149 @p145)) % 1.03/1.24 (step @p151 :rule cong :premises (@p150 @p148) :args ((= (_ @t353 @t340) @t341))) % 1.03/1.24 (step @p152 :rule symm :premises (@p151)) % 1.03/1.24 (step @p153 :rule refl :args (@t354)) % 1.03/1.24 (step @p154 :rule eq_resolve :premises (@p153 @p152)) % 1.03/1.24 (step @p155 :rule refl :args (@t352)) % 1.03/1.24 (step @p156 :rule cong :premises (@p155 @p145) :args ((= @t352 @t340))) % 1.03/1.24 (step @p157 :rule symm :premises (@p156)) % 1.03/1.24 (step @p158 :rule eq_resolve :premises (@p155 @p157)) % 1.03/1.24 (step @p159 :rule ho_cong :premises (@p149 @p158)) % 1.03/1.24 (step @p160 :rule trans :premises (@p159 @p154)) % 1.03/1.24 (step @p161 :rule cong :premises (@p160) :args (@t355)) % 1.03/1.24 (step @p162 :rule nary_cong :premises (@p161 @p143) :args (@t356)) % 1.03/1.24 (step @p163 :rule cong :premises (@p162) :args (@t357)) % 1.03/1.24 (step @p164 :rule trans :premises (@p163 @p142)) % 1.03/1.24 (step @p165 :rule nary_cong :premises (@p164 @p130) :args ((and @t357 @t334))) % 1.03/1.24 (step @p166 :rule alpha_equiv :args (@t363 @t364 (@list @t324 @t326))) % 1.03/1.24 (step @p167 :rule alpha_equiv :args (@t366 @t364 (@list @t335 @t338))) % 1.03/1.24 (step @p168 :rule nary_cong :premises (@p167 @p166) :args (@t367)) % 1.03/1.24 (step @p169 :rule quant-miniscope-and :args ((= (forall @t16 (and @t365 @t362)) @t367))) % 1.03/1.24 (step @p170 :rule trans :premises (@p169 @p168)) % 1.03/1.24 (step @p171 :rule trans :premises (@p170 @p165)) % 1.03/1.24 (step @p172 :rule bool-impl-elim :args (@t361 @t26)) % 1.03/1.24 (step @p173 :rule bool-impl-elim :args (@t26 @t361)) % 1.03/1.24 (step @p174 :rule nary_cong :premises (@p173 @p172) :args (@t368)) % 1.03/1.24 (step @p175 :rule cong :premises (@p174) :args ((forall @t16 @t368))) % 1.03/1.24 (step @p176 :rule trans :premises (@p175 @p171)) % 1.03/1.24 (step @p177 :rule beta-reduce :args ((= (_ @t369 @t361) @t368))) % 1.03/1.24 (step @p178 :rule beta-reduce :args ((= (_ @t372 @t11) @t361))) % 1.03/1.24 (step @p179 :rule refl :args (@t11)) % 1.03/1.24 (step @p180 :rule beta-reduce :args ((= (_ (lambda (@list @t11 @t370) (forall @t25 (or @t373 @t371))) @t2) @t372))) % 1.03/1.24 (step @p181 :rule refl :args (@t2)) % 1.03/1.24 (step @p182 :rule alpha_equiv :args (@t374 (@list @t2) (@list @t370))) % 1.03/1.24 (step @p183 :rule ho_cong :premises (@p182 @p181)) % 1.03/1.24 (step @p184 :rule trans :premises (@p183 @p180)) % 1.03/1.24 (step @p185 :rule ho_cong :premises (@p184 @p179)) % 1.03/1.24 (step @p186 :rule trans :premises (@p185 @p178)) % 1.03/1.24 (step @p187 :rule beta-reduce :args ((= @t376 @t369))) % 1.03/1.24 (step @p188 :rule ho_cong :premises (@p187 @p186)) % 1.03/1.24 (step @p189 :rule trans :premises (@p188 @p177)) % 1.03/1.24 (step @p190 :rule cong :premises (@p189) :args ((forall @t16 (_ @t376 (_ (_ @t374 @t2) @t11))))) % 1.03/1.24 (step @p191 :rule trans :premises (@p190 @p176)) % 1.03/1.24 (step @p192 :rule refl :args (@t2)) % 1.03/1.24 (step @p193 :rule refl :args (@t359)) % 1.03/1.24 (step @p194 :rule refl :args (@t47)) % 1.03/1.24 (step @p195 :rule cong :premises (@p194 @p193) :args ((= @t47 @t359))) % 1.03/1.24 (step @p196 :rule symm :premises (@p195)) % 1.03/1.24 (step @p197 :rule eq_resolve :premises (@p194 @p196)) % 1.03/1.24 (step @p198 :rule refl :args (@t358)) % 1.03/1.24 (step @p199 :rule refl :args (@t23)) % 1.03/1.24 (step @p200 :rule cong :premises (@p199 @p198) :args ((= @t23 @t358))) % 1.03/1.24 (step @p201 :rule symm :premises (@p200)) % 1.03/1.24 (step @p202 :rule eq_resolve :premises (@p199 @p201)) % 1.03/1.24 (step @p203 :rule cong :premises (@p202) :args (@t377)) % 1.03/1.24 (step @p204 :rule nary_cong :premises (@p203 @p197) :args (@t378)) % 1.03/1.24 (step @p205 :rule cong :premises (@p204) :args ((forall @t25 @t378))) % 1.03/1.24 (step @p206 :rule bool-impl-elim :args (@t23 @t47)) % 1.03/1.24 (step @p207 :rule cong :premises (@p206) :args (@t99)) % 1.03/1.24 (step @p208 :rule trans :premises (@p207 @p205)) % 1.03/1.24 (step @p209 :rule cong :premises (@p208) :args (@t100)) % 1.03/1.24 (step @p210 :rule trans :premises (@p22 @p209)) % 1.03/1.24 (step @p211 :rule ho_cong :premises (@p210 @p192)) % 1.03/1.24 (step @p212 :rule ho_cong :premises (@p211 @p179)) % 1.03/1.24 (step @p213 :rule refl :args (@t26)) % 1.03/1.24 (step @p214 :rule beta-reduce :args ((= (_ (lambda @t380 (and @t97 @t379)) @t96) @t375))) % 1.03/1.24 (step @p215 :rule refl :args (@t96)) % 1.03/1.24 (step @p216 :rule bool-double-not-elim :args (@t379)) % 1.03/1.24 (step @p217 :rule bool-eq-false :args (@t379)) % 1.03/1.24 (step @p218 :rule cong :premises (@p217) :args (@t382)) % 1.03/1.24 (step @p219 :rule trans :premises (@p218 @p216)) % 1.03/1.24 (step @p220 :rule aci_norm :args ((= (and @t382 true) @t382))) % 1.03/1.24 (step @p221 :rule ite-then-false :args (@t381 true)) % 1.03/1.24 (step @p222 :rule trans :premises (@p221 @p220)) % 1.03/1.24 (step @p223 :rule trans :premises (@p222 @p219)) % 1.03/1.24 (step @p224 :rule bool-eq-true :args (@t97)) % 1.03/1.24 (step @p225 :rule nary_cong :premises (@p224 @p223) :args ((and @t384 @t383))) % 1.03/1.24 (step @p226 :rule ite-else-false :args (@t384 @t383)) % 1.03/1.24 (step @p227 :rule trans :premises (@p226 @p225)) % 1.03/1.24 (step @p228 :rule cong :premises (@p227) :args (@t385)) % 1.03/1.24 (step @p229 :rule beta-reduce :args ((= (_ @t387 @t97) @t385))) % 1.03/1.24 (step @p230 :rule trans :premises (@p229 @p228)) % 1.03/1.24 (step @p231 :rule refl :args (@t97)) % 1.03/1.24 ; WARNING: add trust step for TRUST_THEORY_REWRITE % 1.03/1.24 ; trust TRUST_THEORY_REWRITE % 1.03/1.24 (step @p232 :rule trust :premises () :args ((= @t389 @t387))) % 1.03/1.24 (step @p233 :rule ho_cong :premises (@p232 @p231)) % 1.03/1.24 (step @p234 :rule trans :premises (@p233 @p230)) % 1.03/1.24 (step @p235 :rule ho_cong :premises (@p234 @p215)) % 1.03/1.24 (step @p236 :rule trans :premises (@p235 @p214)) % 1.03/1.24 (step @p237 :rule aci_norm :args ((= (and @t4 @t9 true) @t388))) % 1.03/1.24 (step @p238 :rule evaluate :args (@t390)) % 1.03/1.24 (step @p239 :rule refl :args (@t9)) % 1.03/1.24 (step @p240 :rule refl :args (@t4)) % 1.03/1.24 (step @p241 :rule nary_cong :premises (@p240 @p239 @p238) :args (@t391)) % 1.03/1.24 (step @p242 :rule trans :premises (@p241 @p237)) % 1.03/1.24 (step @p243 :rule aci_norm :args ((= @t392 @t391))) % 1.03/1.24 (step @p244 :rule trans :premises (@p243 @p242)) % 1.03/1.24 (step @p245 :rule quant-var-elim-eq :args ((= (forall @t92 (or (not (= @t89 false)) @t394 @t89)) @t392))) % 1.03/1.24 (step @p246 :rule refl :args (@t89)) % 1.03/1.24 (step @p247 :rule refl :args (@t394)) % 1.03/1.24 (step @p248 :rule bool-eq-false :args (@t89)) % 1.03/1.24 (step @p249 :rule symm :premises (@p248)) % 1.03/1.24 (step @p250 :rule cong :premises (@p249) :args ((not @t393))) % 1.03/1.24 (step @p251 :rule bool-double-not-elim :args (@t89)) % 1.03/1.24 (step @p252 :rule symm :premises (@p251)) % 1.03/1.24 (step @p253 :rule trans :premises (@p252 @p250)) % 1.03/1.24 (step @p254 :rule nary_cong :premises (@p253 @p247 @p246) :args (@t395)) % 1.03/1.24 (step @p255 :rule aci_norm :args ((= @t396 @t395))) % 1.03/1.24 (step @p256 :rule trans :premises (@p255 @p254)) % 1.03/1.24 (step @p257 :rule cong :premises (@p256) :args ((forall @t92 @t396))) % 1.03/1.24 (step @p258 :rule trans :premises (@p257 @p245)) % 1.03/1.24 (step @p259 :rule trans :premises (@p258 @p244)) % 1.03/1.24 (step @p260 :rule aci_norm :args ((= (and @t4 (and @t9 @t393)) @t394))) % 1.03/1.24 (step @p261 :rule bool-implies-de-morgan :args (@t9 @t89)) % 1.03/1.24 (step @p262 :rule refl :args (@t4)) % 1.03/1.24 (step @p263 :rule nary_cong :premises (@p262 @p261) :args ((and @t4 (not @t90)))) % 1.03/1.24 (step @p264 :rule trans :premises (@p263 @p260)) % 1.03/1.24 (step @p265 :rule bool-implies-de-morgan :args (@t4 @t90)) % 1.03/1.24 (step @p266 :rule trans :premises (@p265 @p264)) % 1.03/1.24 (step @p267 :rule nary_cong :premises (@p266 @p246) :args ((or (not @t91) @t89))) % 1.03/1.24 (step @p268 :rule bool-impl-elim :args (@t91 @t89)) % 1.03/1.24 (step @p269 :rule trans :premises (@p268 @p267)) % 1.03/1.24 (step @p270 :rule cong :premises (@p269) :args (@t93)) % 1.03/1.24 (step @p271 :rule trans :premises (@p270 @p259)) % 1.03/1.24 (step @p272 :rule cong :premises (@p271) :args (@t94)) % 1.03/1.24 (step @p273 :rule trans :premises (@p19 @p272)) % 1.03/1.24 (step @p274 :rule ho_cong :premises (@p273 @p231)) % 1.03/1.24 (step @p275 :rule ho_cong :premises (@p274 @p215)) % 1.03/1.24 (step @p276 :rule trans :premises (@p275 @p236)) % 1.03/1.24 (step @p277 :rule cong :premises (@p276) :args (@t98)) % 1.03/1.24 (step @p278 :rule trans :premises (@p21 @p277)) % 1.03/1.24 (step @p279 :rule ho_cong :premises (@p278 @p213)) % 1.03/1.24 (step @p280 :rule ho_cong :premises (@p279 @p212)) % 1.03/1.24 (step @p281 :rule cong :premises (@p280) :args (@t27)) % 1.03/1.24 (step @p282 :rule trans :premises (@p281 @p191)) % 1.03/1.24 (step @p283 :rule eq_resolve :premises (@p7 @p282)) % 1.03/1.24 (step @p284 :rule and_elim :premises (@p283) :args (1)) % 1.03/1.24 (step @p285 :rule aci_norm :args ((= (or false @t399) @t399))) % 1.03/1.24 (step @p286 :rule refl :args (@t399)) % 1.03/1.24 (step @p287 :rule evaluate :args (@t400)) % 1.03/1.24 (step @p288 :rule quant-unused-vars :args ((= (forall @t25 true) true))) % 1.03/1.24 (step @p289 :rule bool-or-taut2 :args (false @t401 false false)) % 1.03/1.24 (step @p290 :rule cong :premises (@p289) :args (@t402)) % 1.03/1.24 (step @p291 :rule trans :premises (@p290 @p288)) % 1.03/1.24 (step @p292 :rule cong :premises (@p291) :args (@t403)) % 1.03/1.24 (step @p293 :rule trans :premises (@p292 @p287)) % 1.03/1.24 (step @p294 :rule nary_cong :premises (@p293 @p286) :args (@t404)) % 1.03/1.24 (step @p295 :rule trans :premises (@p294 @p285)) % 1.03/1.24 (step @p296 :rule refl :args (@t405)) % 1.03/1.24 (step @p297 :rule cong :premises (@p296 @p295) :args ((=> @t405 @t404))) % 1.03/1.24 (assume-push @p669 @t405) % 1.03/1.24 (step @p299 :rule instantiate :premises (@p284) :args ((@list @t397 @t397))) % 1.03/1.24 (step-pop @p670 :rule scope :premises (@p299)) % 1.03/1.24 (step @p300 :rule process_scope :premises (@p670) :args (@t404)) % 1.03/1.24 (step @p302 :rule eq_resolve :premises (@p300 @p297)) % 1.03/1.24 (step @p303 :rule implies_elim :premises (@p302)) % 1.03/1.24 (step @p304 :rule chain_m_resolution :premises (@p303 @p284) :args (@t399 @t406 (@list @t405))) % 1.03/1.24 (step @p305 :rule bool-impl-false1 :args (@t417)) % 1.03/1.24 (step @p306 :rule beta-reduce :args ((= (_ @t418 @t397) false))) % 1.03/1.24 (step @p307 :rule beta-reduce :args ((= (_ @t420 @t397) @t397))) % 1.03/1.24 (step @p308 :rule beta-reduce :args ((= @t423 @t397))) % 1.03/1.24 (step @p309 :rule cong :premises (@p308) :args (@t424)) % 1.03/1.24 (step @p310 :rule trans :premises (@p309 @p307)) % 1.03/1.24 (step @p311 :rule cong :premises (@p310) :args (@t425)) % 1.03/1.24 (step @p312 :rule trans :premises (@p311 @p307)) % 1.03/1.24 (step @p313 :rule cong :premises (@p312) :args (@t426)) % 1.03/1.24 (step @p314 :rule trans :premises (@p313 @p306)) % 1.03/1.24 (step @p315 :rule refl :args (@t417)) % 1.03/1.24 (step @p316 :rule cong :premises (@p315 @p314) :args ((=> @t417 @t426))) % 1.03/1.24 (step @p317 :rule trans :premises (@p316 @p305)) % 1.03/1.24 (assume-push @p671 @t417) % 1.03/1.24 (step @p319 :rule instantiate :premises (@p671) :args ((@list @t422 @t418 @t420 @t397 @t397))) % 1.03/1.24 (step-pop @p672 :rule scope :premises (@p319)) % 1.03/1.24 (step @p320 :rule process_scope :premises (@p672) :args (@t426)) % 1.03/1.24 (step @p322 :rule eq_resolve :premises (@p320 @p317)) % 1.03/1.24 (step @p323 :rule bool-double-not-elim :args ((or @t417 @t427))) % 1.03/1.24 (step @p324 :rule refl :args (@t427)) % 1.03/1.24 (step @p325 :rule aci_norm :args ((= (and @t417 true) @t417))) % 1.03/1.24 (step @p326 :rule nary_cong :premises (@p315 @p238) :args (@t428)) % 1.03/1.24 (step @p327 :rule trans :premises (@p326 @p325)) % 1.03/1.24 (step @p328 :rule nary_cong :premises (@p327 @p324) :args (@t429)) % 1.03/1.24 (step @p329 :rule cong :premises (@p328) :args ((not @t429))) % 1.03/1.24 (step @p330 :rule bool-impl-false1 :args (@t429)) % 1.03/1.24 (step @p331 :rule trans :premises (@p330 @p329)) % 1.03/1.24 (step @p332 :rule cong :premises (@p331) :args ((not (=> @t429 false)))) % 1.03/1.24 (step @p333 :rule trans :premises (@p332 @p323)) % 1.03/1.24 (step @p334 :rule bool-eq-false :args (tptp.c_False)) % 1.03/1.24 (step @p335 :rule symm :premises (@p334)) % 1.03/1.24 (step @p336 :rule aci_norm :args ((= (and true @t430) @t430))) % 1.03/1.24 (step @p337 :rule refl :args (@t430)) % 1.03/1.24 (step @p338 :rule absorb :args ((= (or true tptp.c_False) true))) % 1.03/1.24 (step @p339 :rule refl :args (tptp.c_False)) % 1.03/1.24 (step @p340 :rule nary_cong :premises (@p238 @p339) :args (@t431)) % 1.03/1.24 (step @p341 :rule trans :premises (@p340 @p338)) % 1.03/1.24 (step @p342 :rule nary_cong :premises (@p341 @p337) :args (@t432)) % 1.03/1.24 (step @p343 :rule trans :premises (@p342 @p336)) % 1.03/1.24 (step @p344 :rule aci_norm :args ((= @t433 @t432))) % 1.03/1.24 (step @p345 :rule trans :premises (@p344 @p343)) % 1.03/1.24 (step @p346 :rule quant-var-elim-eq :args ((= (forall @t7 (or (not (= @t4 false)) @t435 @t4)) @t433))) % 1.03/1.24 (step @p347 :rule refl :args (@t435)) % 1.03/1.24 (step @p348 :rule bool-eq-false :args (@t4)) % 1.03/1.24 (step @p349 :rule symm :premises (@p348)) % 1.03/1.24 (step @p350 :rule cong :premises (@p349) :args ((not @t434))) % 1.03/1.24 (step @p351 :rule bool-double-not-elim :args (@t4)) % 1.03/1.24 (step @p352 :rule symm :premises (@p351)) % 1.03/1.24 (step @p353 :rule trans :premises (@p352 @p350)) % 1.03/1.24 (step @p354 :rule nary_cong :premises (@p353 @p347 @p262) :args (@t436)) % 1.03/1.24 (step @p355 :rule aci_norm :args ((= @t437 @t436))) % 1.03/1.24 (step @p356 :rule trans :premises (@p355 @p354)) % 1.03/1.24 (step @p357 :rule cong :premises (@p356) :args ((forall @t7 @t437))) % 1.03/1.24 (step @p358 :rule trans :premises (@p357 @p346)) % 1.03/1.24 (step @p359 :rule trans :premises (@p358 @p345)) % 1.03/1.24 (step @p360 :rule refl :args (@t430)) % 1.03/1.24 (step @p361 :rule bool-impl-elim :args (@t4 tptp.c_False)) % 1.03/1.24 (step @p362 :rule nary_cong :premises (@p361 @p360) :args ((and @t87 @t430))) % 1.03/1.24 (step @p363 :rule bool-implies-de-morgan :args (@t87 tptp.c_False)) % 1.03/1.24 (step @p364 :rule trans :premises (@p363 @p362)) % 1.03/1.24 (step @p365 :rule nary_cong :premises (@p364 @p262) :args ((or (not @t438) @t4))) % 1.03/1.24 (step @p366 :rule bool-impl-elim :args (@t438 @t4)) % 1.03/1.24 (step @p367 :rule trans :premises (@p366 @p365)) % 1.03/1.24 (step @p368 :rule cong :premises (@p367) :args ((forall @t7 (=> @t438 @t4)))) % 1.03/1.24 (step @p369 :rule trans :premises (@p368 @p359)) % 1.03/1.24 (step @p370 :rule beta-reduce :args ((= (_ @t88 @t87) @t438))) % 1.03/1.24 (step @p371 :rule beta-reduce :args ((= @t439 @t87))) % 1.03/1.24 (step @p372 :rule refl :args (@t88)) % 1.03/1.24 (step @p373 :rule ho_cong :premises (@p372 @p371)) % 1.03/1.24 (step @p374 :rule trans :premises (@p373 @p370)) % 1.03/1.24 (step @p375 :rule cong :premises (@p374 @p240) :args (@t440)) % 1.03/1.24 (step @p376 :rule cong :premises (@p375) :args ((forall @t7 @t440))) % 1.03/1.24 (step @p377 :rule trans :premises (@p376 @p369)) % 1.03/1.24 (step @p378 :rule ho_cong :premises (@p18 @p240)) % 1.03/1.24 (step @p379 :rule ho_cong :premises (@p18 @p378)) % 1.03/1.24 (step @p380 :rule cong :premises (@p379 @p240) :args (@t6)) % 1.03/1.24 (step @p381 :rule cong :premises (@p380) :args (@t8)) % 1.03/1.24 (step @p382 :rule trans :premises (@p381 @p377)) % 1.03/1.24 (step @p383 :rule eq_resolve :premises (@p2 @p382)) % 1.03/1.24 (step @p384 :rule eq_resolve :premises (@p383 @p335)) % 1.03/1.24 (step @p385 :rule cong :premises (@p384) :args (@t430)) % 1.03/1.24 (step @p386 :rule nary_cong :premises (@p315 @p385) :args (@t441)) % 1.03/1.24 (step @p387 :rule nary_cong :premises (@p386 @p324) :args (@t442)) % 1.03/1.24 (step @p388 :rule cong :premises (@p387 @p384) :args (@t443)) % 1.03/1.24 (step @p389 :rule cong :premises (@p388) :args ((not @t443))) % 1.03/1.24 (step @p390 :rule trans :premises (@p389 @p333)) % 1.03/1.24 (step @p391 :rule beta-reduce :args ((= (_ @t88 @t442) @t443))) % 1.03/1.24 (step @p392 :rule refl :args ((_ @t414 @t446))) % 1.03/1.24 (step @p393 :rule refl :args ((_ @t411 @t445))) % 1.03/1.24 (step @p394 :rule refl :args ((_ @t411 @t444))) % 1.03/1.24 (step @p395 :rule refl :args (@t410)) % 1.03/1.24 (step @p396 :rule cong :premises (@p395) :args (@t412)) % 1.03/1.24 (step @p397 :rule trans :premises (@p396 @p394)) % 1.03/1.24 (step @p398 :rule cong :premises (@p397) :args (@t413)) % 1.03/1.24 (step @p399 :rule trans :premises (@p398 @p393)) % 1.03/1.24 (step @p400 :rule cong :premises (@p399) :args (@t415)) % 1.03/1.24 (step @p401 :rule trans :premises (@p400 @p392)) % 1.03/1.24 (step @p402 :rule refl :args (@t414)) % 1.03/1.24 (step @p403 :rule ho_cong :premises (@p402 @p399)) % 1.03/1.24 (step @p404 :rule cong :premises (@p403 @p401) :args ((= (_ @t414 @t413) @t415))) % 1.03/1.24 (step @p405 :rule symm :premises (@p404)) % 1.03/1.24 (step @p406 :rule refl :args (@t447)) % 1.03/1.24 (step @p407 :rule eq_resolve :premises (@p406 @p405)) % 1.03/1.24 (step @p408 :rule refl :args (@t411)) % 1.03/1.24 (step @p409 :rule ho_cong :premises (@p408 @p397)) % 1.03/1.24 (step @p410 :rule cong :premises (@p409 @p399) :args ((= (_ @t411 @t412) @t413))) % 1.03/1.24 (step @p411 :rule symm :premises (@p410)) % 1.03/1.24 (step @p412 :rule refl :args (@t446)) % 1.03/1.24 (step @p413 :rule eq_resolve :premises (@p412 @p411)) % 1.03/1.24 (step @p414 :rule ho_cong :premises (@p408 @p395)) % 1.03/1.24 (step @p415 :rule cong :premises (@p414 @p397) :args ((= (_ @t411 @t410) @t412))) % 1.03/1.24 (step @p416 :rule symm :premises (@p415)) % 1.03/1.24 (step @p417 :rule refl :args (@t445)) % 1.03/1.24 (step @p418 :rule eq_resolve :premises (@p417 @p416)) % 1.03/1.24 (step @p419 :rule refl :args (@t444)) % 1.03/1.24 (step @p420 :rule cong :premises (@p419 @p395) :args ((= @t444 @t410))) % 1.03/1.24 (step @p421 :rule symm :premises (@p420)) % 1.03/1.24 (step @p422 :rule eq_resolve :premises (@p419 @p421)) % 1.03/1.24 (step @p423 :rule ho_cong :premises (@p408 @p422)) % 1.03/1.24 (step @p424 :rule trans :premises (@p423 @p418)) % 1.03/1.24 (step @p425 :rule ho_cong :premises (@p408 @p424)) % 1.03/1.24 (step @p426 :rule trans :premises (@p425 @p413)) % 1.03/1.24 (step @p427 :rule ho_cong :premises (@p402 @p426)) % 1.03/1.24 (step @p428 :rule trans :premises (@p427 @p407)) % 1.03/1.24 (step @p429 :rule cong :premises (@p428) :args (@t448)) % 1.03/1.24 (step @p430 :rule nary_cong :premises (@p429 @p337) :args ((and @t448 @t430))) % 1.03/1.24 (step @p431 :rule quant-unused-vars :args ((= @t450 @t430))) % 1.03/1.24 (step @p432 :rule alpha_equiv :args (@t451 (@list @t61 @t63 @t62 @t59 @t60) (@list @t409 @t414 @t411 @t407 @t408))) % 1.03/1.24 (step @p433 :rule nary_cong :premises (@p432 @p431) :args (@t452)) % 1.03/1.24 (step @p434 :rule quant-miniscope-and :args ((= @t454 @t452))) % 1.03/1.24 (step @p435 :rule trans :premises (@p434 @p433)) % 1.03/1.24 (step @p436 :rule trans :premises (@p435 @p430)) % 1.03/1.24 (step @p437 :rule nary_cong :premises (@p436 @p324) :args (@t455)) % 1.03/1.24 (step @p438 :rule quant-miniscope-or :args ((= @t457 @t455))) % 1.03/1.24 (step @p439 :rule aci_norm :args ((= @t456 @t456))) % 1.03/1.24 (step @p440 :rule cong :premises (@p439) :args (@t457)) % 1.03/1.24 (step @p441 :rule quant_var_reordering :args ((= @t458 @t457))) % 1.03/1.24 (step @p442 :rule quant-unused-vars :args ((= (forall @t84 @t456) @t458))) % 1.03/1.24 (step @p443 :rule trans :premises (@p442 @p441 @p440 @p438)) % 1.03/1.24 (step @p444 :rule trans :premises (@p443 @p437)) % 1.03/1.24 (step @p445 :rule refl :args (@t58)) % 1.03/1.24 (step @p446 :rule bool-implies-de-morgan :args (@t64 tptp.c_False)) % 1.03/1.24 (step @p447 :rule nary_cong :premises (@p446 @p445) :args ((or (not @t459) @t58))) % 1.03/1.24 (step @p448 :rule bool-impl-elim :args (@t459 @t58)) % 1.03/1.24 (step @p449 :rule trans :premises (@p448 @p447)) % 1.03/1.24 (step @p450 :rule cong :premises (@p449) :args ((forall @t84 (=> @t459 @t58)))) % 1.03/1.24 (step @p451 :rule trans :premises (@p450 @p444)) % 1.03/1.24 (step @p452 :rule refl :args (@t58)) % 1.03/1.24 (step @p453 :rule bool-double-not-elim :args (@t459)) % 1.03/1.24 (step @p454 :rule bool-eq-false :args (@t459)) % 1.03/1.24 (step @p455 :rule cong :premises (@p454) :args (@t461)) % 1.03/1.24 (step @p456 :rule trans :premises (@p455 @p453)) % 1.03/1.24 (step @p457 :rule aci_norm :args ((= (and @t461 true) @t461))) % 1.03/1.24 (step @p458 :rule ite-then-false :args (@t460 true)) % 1.03/1.24 (step @p459 :rule trans :premises (@p458 @p457)) % 1.03/1.24 (step @p460 :rule trans :premises (@p459 @p456)) % 1.03/1.24 (step @p461 :rule beta-reduce :args ((= (_ @t466 @t459) (ite @t460 false true)))) % 1.03/1.24 (step @p462 :rule trans :premises (@p461 @p460)) % 1.03/1.24 (step @p463 :rule beta-reduce :args ((= @t467 @t459))) % 1.03/1.24 (step @p464 :rule refl :args (@t466)) % 1.03/1.24 (step @p465 :rule symm :premises (@p464)) % 1.03/1.24 (step @p466 :rule eq-symm :args (false @t462)) % 1.03/1.24 (step @p467 :rule true_intro :premises (@p466)) % 1.03/1.24 (step @p468 :rule eq-symm :args (@t463 @t468)) % 1.03/1.24 (step @p469 :rule trans :premises (@p468 @p467)) % 1.03/1.24 (step @p470 :rule refl :args (@t462)) % 1.03/1.24 (step @p471 :rule evaluate :args (@t400)) % 1.03/1.24 (step @p472 :rule cong :premises (@p471 @p470) :args ((= @t400 @t462))) % 1.03/1.24 (step @p473 :rule bool-not-eq-elim1 :args (true @t462)) % 1.03/1.24 (step @p474 :rule trans :premises (@p473 @p472)) % 1.03/1.24 (step @p475 :rule ite-neg-branch :premises (@p474) :args (@t463 @t468 (= true @t462))) % 1.03/1.24 (step @p476 :rule trans :premises (@p475 @p469)) % 1.03/1.24 (step @p477 :rule eq-ite-lift :args (@t463 false true @t462)) % 1.03/1.24 (step @p478 :rule trans :premises (@p477 @p476)) % 1.03/1.24 (step @p479 :rule eq-symm :args (@t462 @t464)) % 1.03/1.24 (step @p480 :rule trans :premises (@p479 @p478)) % 1.03/1.24 (step @p481 :rule true_elim :premises (@p480)) % 1.03/1.24 (step @p482 :rule cong :premises (@p481) :args ((lambda @t465 @t462))) % 1.03/1.24 (step @p483 :rule alpha_equiv :args ((lambda @t380 @t379) (@list @t379) (@list @t462))) % 1.03/1.24 (step @p484 :rule trans :premises (@p483 @p482)) % 1.03/1.24 (step @p485 :rule trans :premises (@p484 @p465)) % 1.03/1.24 (step @p486 :rule aci_norm :args ((= (and true @t379) @t379))) % 1.03/1.24 (step @p487 :rule evaluate :args (@t469)) % 1.03/1.24 (step @p488 :rule nary_cong :premises (@p487 @p223) :args ((and @t469 @t383))) % 1.03/1.24 (step @p489 :rule trans :premises (@p488 @p486)) % 1.03/1.24 (step @p490 :rule ite-else-false :args (@t469 @t383)) % 1.03/1.24 (step @p491 :rule trans :premises (@p490 @p489)) % 1.03/1.24 (step @p492 :rule cong :premises (@p491) :args (@t470)) % 1.03/1.24 (step @p493 :rule trans :premises (@p492 @p485)) % 1.03/1.24 (step @p494 :rule beta-reduce :args ((= (_ @t387 true) @t470))) % 1.03/1.24 (step @p495 :rule trans :premises (@p494 @p493)) % 1.03/1.24 (step @p496 :rule quant-unused-vars :args ((= (forall @t80 true) true))) % 1.03/1.24 (step @p497 :rule bool-impl-true1 :args ((= @t67 @t77))) % 1.03/1.24 (step @p498 :rule bool-impl-true1 :args (@t474)) % 1.03/1.24 (step @p499 :rule quant-unused-vars :args ((= (forall @t65 false) false))) % 1.03/1.24 (step @p500 :rule cong :premises (@p287) :args (@t475)) % 1.03/1.24 (step @p501 :rule trans :premises (@p500 @p499)) % 1.03/1.24 (step @p502 :rule cong :premises (@p501) :args (@t476)) % 1.03/1.24 (step @p503 :rule trans :premises (@p502 @p238)) % 1.03/1.24 (step @p504 :rule exists-elim :args ((= (exists @t65 true) @t476))) % 1.03/1.24 (step @p505 :rule trans :premises (@p504 @p503)) % 1.03/1.24 (step @p506 :rule eq-refl :args (@t60)) % 1.03/1.24 (step @p507 :rule cong :premises (@p506) :args (@t66)) % 1.03/1.24 (step @p508 :rule trans :premises (@p507 @p505)) % 1.03/1.24 (step @p509 :rule beta-reduce :args ((= (_ (lambda @t380 (and @t75 @t379)) @t473) @t474))) % 1.03/1.24 (step @p510 :rule beta-reduce :args ((= (_ (lambda @t380 (and @t471 @t379)) @t68) @t472))) % 1.03/1.24 (step @p511 :rule bool-double-not-elim :args (@t68)) % 1.03/1.24 (step @p512 :rule quant-unused-vars :args ((= @t478 @t477))) % 1.03/1.24 (step @p513 :rule cong :premises (@p512) :args (@t479)) % 1.03/1.24 (step @p514 :rule trans :premises (@p513 @p511)) % 1.03/1.24 (step @p515 :rule exists-elim :args ((= @t69 @t479))) % 1.03/1.24 (step @p516 :rule trans :premises (@p515 @p514)) % 1.03/1.24 (step @p517 :rule bool-eq-true :args (@t471)) % 1.03/1.24 (step @p518 :rule nary_cong :premises (@p517 @p223) :args ((and @t480 @t383))) % 1.03/1.24 (step @p519 :rule ite-else-false :args (@t480 @t383)) % 1.03/1.24 (step @p520 :rule trans :premises (@p519 @p518)) % 1.03/1.24 (step @p521 :rule cong :premises (@p520) :args (@t481)) % 1.03/1.24 (step @p522 :rule beta-reduce :args ((= (_ @t387 @t471) @t481))) % 1.03/1.24 (step @p523 :rule trans :premises (@p522 @p521)) % 1.03/1.24 (step @p524 :rule quant-unused-vars :args ((= (forall @t65 @t471) @t471))) % 1.03/1.24 (step @p525 :rule eq-symm :args (@t56 @t70)) % 1.03/1.24 (step @p526 :rule cong :premises (@p525) :args (@t71)) % 1.03/1.24 (step @p527 :rule trans :premises (@p526 @p524)) % 1.03/1.24 (step @p528 :rule ho_cong :premises (@p232 @p527)) % 1.03/1.24 (step @p529 :rule trans :premises (@p528 @p523)) % 1.03/1.24 (step @p530 :rule ho_cong :premises (@p529 @p516)) % 1.03/1.24 (step @p531 :rule trans :premises (@p530 @p510)) % 1.03/1.24 (step @p532 :rule eq-symm :args (@t60 @t59)) % 1.03/1.24 (step @p533 :rule cong :premises (@p532 @p531) :args (@t482)) % 1.03/1.24 (step @p534 :rule bool-eq-true :args (@t75)) % 1.03/1.24 (step @p535 :rule nary_cong :premises (@p534 @p223) :args ((and @t483 @t383))) % 1.03/1.24 (step @p536 :rule ite-else-false :args (@t483 @t383)) % 1.03/1.24 (step @p537 :rule trans :premises (@p536 @p535)) % 1.03/1.24 (step @p538 :rule cong :premises (@p537) :args (@t484)) % 1.03/1.24 (step @p539 :rule beta-reduce :args ((= (_ @t387 @t75) @t484))) % 1.03/1.24 (step @p540 :rule trans :premises (@p539 @p538)) % 1.03/1.24 (step @p541 :rule refl :args (@t75)) % 1.03/1.24 (step @p542 :rule ho_cong :premises (@p232 @p541)) % 1.03/1.24 (step @p543 :rule trans :premises (@p542 @p540)) % 1.03/1.24 (step @p544 :rule ho_cong :premises (@p543 @p533)) % 1.03/1.24 (step @p545 :rule trans :premises (@p544 @p509)) % 1.03/1.24 (step @p546 :rule cong :premises (@p545 @p508) :args (@t485)) % 1.03/1.24 (step @p547 :rule trans :premises (@p546 @p498)) % 1.03/1.24 (step @p548 :rule eq-symm :args (@t77 @t67)) % 1.03/1.24 (step @p549 :rule cong :premises (@p548 @p547) :args (@t486)) % 1.03/1.24 (step @p550 :rule trans :premises (@p549 @p497)) % 1.03/1.24 (step @p551 :rule cong :premises (@p550) :args (@t487)) % 1.03/1.24 (step @p552 :rule trans :premises (@p551 @p496)) % 1.03/1.24 (step @p553 :rule ho_cong :premises (@p232 @p552)) % 1.03/1.24 (step @p554 :rule trans :premises (@p553 @p495)) % 1.03/1.24 (step @p555 :rule ho_cong :premises (@p554 @p463)) % 1.03/1.24 (step @p556 :rule trans :premises (@p555 @p462)) % 1.03/1.24 (step @p557 :rule cong :premises (@p556 @p452) :args (@t488)) % 1.03/1.24 (step @p558 :rule cong :premises (@p557) :args (@t489)) % 1.03/1.24 (step @p559 :rule trans :premises (@p558 @p451)) % 1.03/1.24 (step @p560 :rule ho_cong :premises (@p372 @p559)) % 1.03/1.24 (step @p561 :rule trans :premises (@p560 @p391)) % 1.03/1.24 (step @p562 :rule cong :premises (@p561) :args ((not (_ @t88 @t489)))) % 1.03/1.24 (step @p563 :rule refl :args (@t64)) % 1.03/1.24 (step @p564 :rule ho_cong :premises (@p18 @p563)) % 1.03/1.24 (step @p565 :rule refl :args (@t66)) % 1.03/1.24 (step @p566 :rule refl :args (@t69)) % 1.03/1.24 (step @p567 :rule refl :args (@t71)) % 1.03/1.24 (step @p568 :rule ho_cong :premises (@p273 @p567)) % 1.03/1.24 (step @p569 :rule ho_cong :premises (@p568 @p566)) % 1.03/1.24 (step @p570 :rule refl :args (@t72)) % 1.03/1.24 (step @p571 :rule cong :premises (@p570 @p569) :args (@t73)) % 1.03/1.24 (step @p572 :rule ho_cong :premises (@p273 @p541)) % 1.03/1.24 (step @p573 :rule ho_cong :premises (@p572 @p571)) % 1.03/1.24 (step @p574 :rule cong :premises (@p573 @p565) :args (@t76)) % 1.03/1.24 (step @p575 :rule refl :args (@t78)) % 1.03/1.24 (step @p576 :rule cong :premises (@p575 @p574) :args (@t79)) % 1.03/1.24 (step @p577 :rule cong :premises (@p576) :args (@t81)) % 1.03/1.24 (step @p578 :rule ho_cong :premises (@p273 @p577)) % 1.03/1.24 (step @p579 :rule ho_cong :premises (@p578 @p564)) % 1.03/1.24 (step @p580 :rule cong :premises (@p579 @p452) :args (@t82)) % 1.03/1.24 (step @p581 :rule cong :premises (@p580) :args (@t85)) % 1.03/1.24 (step @p582 :rule ho_cong :premises (@p18 @p581)) % 1.03/1.24 (step @p583 :rule cong :premises (@p582) :args (@t86)) % 1.03/1.24 (step @p584 :rule trans :premises (@p583 @p562)) % 1.03/1.24 (step @p585 :rule trans :premises (@p584 @p390)) % 1.03/1.24 (step @p586 :rule eq_resolve :premises (@p16 @p585)) % 1.03/1.24 (step @p587 :rule reordering :premises (@p586) :args ((or @t427 @t417))) % 1.03/1.24 (step @p588 :rule chain_m_resolution :premises (@p587 @p322) :args (@t427 (@list true) (@list @t417))) % 1.03/1.24 (assume-push @p673 @t427) % 1.03/1.24 (step @p590 :rule instantiate :premises (@p673) :args ((@list @t397 @t398))) % 1.03/1.24 (step-pop @p674 :rule scope :premises (@p590)) % 1.03/1.24 (step @p591 :rule process_scope :premises (@p674) :args (@t490)) % 1.03/1.24 (step @p593 :rule implies_elim :premises (@p591)) % 1.03/1.24 (step @p594 :rule chain_m_resolution :premises (@p593 @p588) :args (@t490 @t406 @t491)) % 1.03/1.24 (step @p595 :rule eq-symm :args (@t397 tptp.c_Empty)) % 1.03/1.24 (step @p596 :rule cong :premises (@p324 @p595) :args ((=> @t427 @t492))) % 1.03/1.24 (assume-push @p675 @t427) % 1.03/1.24 (step @p598 :rule instantiate :premises (@p675) :args ((@list @t397 tptp.c_Empty))) % 1.03/1.24 (step-pop @p676 :rule scope :premises (@p598)) % 1.03/1.24 (step @p599 :rule process_scope :premises (@p676) :args (@t492)) % 1.03/1.24 (step @p601 :rule eq_resolve :premises (@p599 @p596)) % 1.03/1.24 (step @p602 :rule implies_elim :premises (@p601)) % 1.03/1.24 (step @p603 :rule chain_m_resolution :premises (@p602 @p588) :args (@t493 @t406 @t491)) % 1.03/1.24 (step @p604 :rule bool-double-not-elim :args (@t495)) % 1.03/1.24 (step @p605 :rule bool-impl-false1 :args (@t496)) % 1.03/1.24 (step @p606 :rule trans :premises (@p605 @p604)) % 1.03/1.24 (step @p607 :rule refl :args (@t496)) % 1.03/1.24 (step @p608 :rule cong :premises (@p607 @p384) :args (@t497)) % 1.03/1.24 (step @p609 :rule trans :premises (@p608 @p606)) % 1.03/1.24 (step @p610 :rule beta-reduce :args ((= (_ @t88 @t496) @t497))) % 1.03/1.24 (step @p611 :rule refl :args (@t494)) % 1.03/1.24 (step @p612 :rule refl :args (@t18)) % 1.03/1.24 (step @p613 :rule cong :premises (@p612 @p611) :args ((= @t18 @t494))) % 1.03/1.24 (step @p614 :rule symm :premises (@p613)) % 1.03/1.24 (step @p615 :rule eq_resolve :premises (@p612 @p614)) % 1.03/1.24 (step @p616 :rule cong :premises (@p615) :args (@t498)) % 1.03/1.24 (step @p617 :rule cong :premises (@p616) :args (@t499)) % 1.03/1.24 (step @p618 :rule cong :premises (@p617) :args (@t500)) % 1.03/1.24 (step @p619 :rule exists-elim :args ((= @t20 @t500))) % 1.03/1.24 (step @p620 :rule trans :premises (@p619 @p618)) % 1.03/1.24 (step @p621 :rule ho_cong :premises (@p372 @p620)) % 1.03/1.24 (step @p622 :rule trans :premises (@p621 @p610)) % 1.03/1.24 (step @p623 :rule refl :args (@t20)) % 1.03/1.24 (step @p624 :rule ho_cong :premises (@p18 @p623)) % 1.03/1.24 (step @p625 :rule trans :premises (@p624 @p622)) % 1.03/1.24 (step @p626 :rule trans :premises (@p625 @p609)) % 1.03/1.24 (step @p627 :rule eq_resolve :premises (@p5 @p626)) % 1.03/1.24 (step @p628 :rule instantiate :premises (@p627) :args ((@list @t397))) % 1.03/1.24 (step @p629 :rule bool-double-not-elim :args (@t501)) % 1.03/1.24 (step @p630 :rule refl :args (@t502)) % 1.03/1.24 (step @p631 :rule refl :args (@t503)) % 1.03/1.24 (step @p632 :rule refl :args (@t504)) % 1.03/1.24 (step @p633 :rule nary_cong :premises (@p632 @p631 @p630 @p629) :args ((or @t504 @t503 @t502 (not @t505)))) % 1.03/1.24 (assume-push @p677 @t505) % 1.03/1.24 (assume-push @p678 @t493) % 1.03/1.24 (assume-push @p679 @t490) % 1.03/1.24 (assume-push @p680 @t399) % 1.03/1.24 (step @p638 :rule evaluate :args ((= true false))) % 1.03/1.24 (step @p639 :rule false_intro :premises (@p628)) % 1.03/1.24 (step @p640 :rule symm :premises (@p678)) % 1.03/1.24 (step @p641 :rule symm :premises (@p679)) % 1.03/1.24 (step @p642 :rule trans :premises (@p641 @p640)) % 1.03/1.24 (step @p643 :rule refl :args (@t397)) % 1.03/1.24 (step @p644 :rule cong :premises (@p643 @p642) :args (@t399)) % 1.03/1.24 (step @p645 :rule true_intro :premises (@p304)) % 1.03/1.24 (step @p646 :rule symm :premises (@p645)) % 1.03/1.24 (step @p647 :rule trans :premises (@p646 @p644 @p639)) % 1.03/1.24 (step @p648 false :rule eq_resolve :premises (@p647 @p638)) % 1.03/1.24 (step-pop @p681 :rule scope :premises (@p648)) % 1.03/1.24 (step-pop @p682 :rule scope :premises (@p681)) % 1.03/1.24 (step-pop @p683 :rule scope :premises (@p682)) % 1.03/1.24 (step-pop @p684 :rule scope :premises (@p683)) % 1.03/1.24 (step @p649 :rule process_scope :premises (@p684) :args (false)) % 1.03/1.24 (assume-push @p685 @t399) % 1.03/1.24 (assume-push @p686 @t490) % 1.03/1.24 (assume-push @p687 @t493) % 1.03/1.24 (assume-push @p688 @t505) % 1.03/1.24 (step @p658 :rule and_intro :premises (@p628 @p687 @p686 @p304)) % 1.03/1.24 (step-pop @p689 :rule scope :premises (@p658)) % 1.03/1.24 (step-pop @p690 :rule scope :premises (@p689)) % 1.03/1.24 (step-pop @p691 :rule scope :premises (@p690)) % 1.03/1.24 (step-pop @p692 :rule scope :premises (@p691)) % 1.03/1.24 (step @p659 :rule process_scope :premises (@p692) :args (@t506)) % 1.03/1.24 (step @p664 :rule implies_elim :premises (@p659)) % 1.03/1.24 (step @p665 :rule resolution :premises (@p664 @p649) :args (true @t506)) % 1.03/1.24 (step @p666 :rule not_and :premises (@p665)) % 1.03/1.24 (step @p667 :rule eq_resolve :premises (@p666 @p633)) % 1.03/1.24 (step @p668 false :rule chain_m_resolution :premises (@p667 @p628 @p603 @p594 @p304) :args (false (@list true false false false) (@list @t501 @t493 @t490 @t399))) % 1.03/1.24 ) % 1.03/1.24 % SZS output end Proof % 1.03/1.24 % cvc5 exiting %------------------------------------------------------------------------------