%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : GEG014^1 : TPTP v9.2.1. Released v4.1.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n014.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 08:15:59 AM UTC 2026 % Result : Theorem 182.18s 182.45s % Output : Proof 182.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : GEG014^1 : TPTP v9.2.1. Released v4.1.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.33 % Computer : n014.cluster.edu % 0.16/0.33 % Model : x86_64 x86_64 % 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.33 % Memory : 8042.1875MB % 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.33 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Mon Jun 1 23:03:43 EDT 2026 % 0.16/0.34 % CPUTime : % 0.31/0.49 %----Proving TH0 % 182.18/182.45 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 182.18/182.45 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --mbqi-enum-choice-grammar-all --no-cegqi --no-sygus-inst at 30s... % 182.18/182.45 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-mbqi-nested-check --no-cegqi --no-sygus-inst at 30s... % 182.18/182.45 --- Run --ho-elim --full-saturate-quant at 18s... % 182.18/182.45 --- Run --ho-elim --no-e-matching --full-saturate-quant at 12s... % 182.18/182.45 --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 12s... % 182.18/182.45 % SZS status Theorem % 182.18/182.45 % SZS output start Proof % 182.18/182.45 ( % 182.18/182.45 (declare-sort tptp.reg 0) % 182.18/182.45 (declare-sort $$unsorted 0) % 182.18/182.45 (declare-sort tptp.mu 0) % 182.18/182.45 (declare-const tptp.c (-> tptp.reg tptp.reg Bool)) % 182.18/182.45 (declare-const tptp.france tptp.reg) % 182.18/182.45 (declare-const tptp.catalunya tptp.reg) % 182.18/182.45 (declare-const tptp.a (-> $$unsorted $$unsorted Bool)) % 182.18/182.45 (declare-const tptp.spain tptp.reg) % 182.18/182.45 (declare-const tptp.fool (-> $$unsorted $$unsorted Bool)) % 182.18/182.45 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 182.18/182.45 (declare-const tptp.paris tptp.reg) % 182.18/182.45 (define tptp.meq_ind () (let ((_let_1 (@var "Y" tptp.mu))) (let ((_let_2 (@var "X" tptp.mu))) (lambda (@list _let_2 _let_1 (@var "W" $$unsorted)) (= _let_2 _let_1))))) % 182.18/182.45 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (= (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 182.18/182.45 (define tptp.mnot () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 182.18/182.45 (define tptp.mor () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 182.18/182.45 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mor (_ tptp.mnot _let_3)) (_ tptp.mnot _let_2))) _let_1)))))) % 182.18/182.45 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 182.18/182.45 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 182.18/182.45 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimplies _let_2) _let_3)) (_ (_ tptp.mimplies _let_3) _let_2)) _let_1)))))) % 182.18/182.45 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mequiv _let_3) _let_2)) _let_1)))))) % 182.18/182.45 (define tptp.mforall_ind () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 182.18/182.45 (define tptp.mforall_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 182.18/182.45 (define tptp.mexists_ind () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 182.18/182.45 (define tptp.mexists_prop () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 182.18/182.45 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 182.18/182.45 (define tptp.mbox () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "W" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ _let_4 _let_3) _let_1)) (_ _let_2 _let_1))))))))) % 182.18/182.45 (define tptp.mdia () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mbox _let_3) (_ tptp.mnot _let_2))) _let_1)))))) % 182.18/182.45 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 182.18/182.45 (define tptp.msymmetric () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 182.18/182.45 (define tptp.mserial () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 182.18/182.45 (define tptp.mtransitive () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (_ _let_3 _let_2))) (let ((_let_5 (@var "T" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_2 _let_5 _let_1) (=> (and (_ _let_4 _let_5) (_ (_ _let_3 _let_5) _let_1)) (_ _let_4 _let_1)))))))))) % 182.18/182.45 (define tptp.meuclidean () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "S" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (_ (_ _let_3 _let_2) _let_1)))))))))) % 182.18/182.45 (define tptp.mpartially_functional () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "S" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (= _let_2 _let_1)))))))))) % 182.18/182.45 (define tptp.mfunctional () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "S" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3) (exists (@list _let_2) (and (_ _let_5 _let_2) (forall (@list _let_1) (=> (_ _let_5 _let_1) (= _let_2 _let_1))))))))))))) % 182.18/182.45 (define tptp.mweakly_dense () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "S" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (_ _let_5 _let_1) (exists (@list _let_2) (and (_ _let_5 _let_2) (_ (_ _let_3 _let_2) _let_1)))))))))))) % 182.18/182.45 (define tptp.mweakly_connected () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "S" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_1) (_ _let_5 _let_2)) (or (_ (_ _let_3 _let_1) _let_2) (= _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1))))))))))) % 182.18/182.45 (define tptp.mweakly_directed () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "T" $$unsorted))) (let ((_let_5 (@var "S" $$unsorted))) (let ((_let_6 (_ _let_3 _let_5))) (lambda (@list _let_3) (forall (@list _let_5 _let_4 _let_2) (=> (and (_ _let_6 _let_4) (_ _let_6 _let_2)) (exists (@list _let_1) (and (_ (_ _let_3 _let_4) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))))))) % 182.18/182.45 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 182.18/182.45 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 182.18/182.45 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 182.18/182.45 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 182.18/182.45 (define tptp.dc () (let ((_let_1 (@var "Y" tptp.reg))) (let ((_let_2 (@var "X" tptp.reg))) (lambda (@list _let_2 _let_1) (not (_ (_ tptp.c _let_2) _let_1)))))) % 182.18/182.45 (define tptp.p () (let ((_let_1 (@var "Y" tptp.reg))) (let ((_let_2 (@var "Z" tptp.reg))) (let ((_let_3 (_ tptp.c _let_2))) (let ((_let_4 (@var "X" tptp.reg))) (lambda (@list _let_4 _let_1) (forall (@list _let_2) (=> (_ _let_3 _let_4) (_ _let_3 _let_1))))))))) % 182.18/182.45 (define tptp.eq () (let ((_let_1 (@var "X" tptp.reg))) (let ((_let_2 (@var "Y" tptp.reg))) (lambda (@list _let_1 _let_2) (and (_ (_ tptp.p _let_1) _let_2) (_ (_ tptp.p _let_2) _let_1)))))) % 182.18/182.45 (define tptp.o () (let ((_let_1 (@var "Y" tptp.reg))) (let ((_let_2 (@var "Z" tptp.reg))) (let ((_let_3 (_ tptp.p _let_2))) (let ((_let_4 (@var "X" tptp.reg))) (lambda (@list _let_4 _let_1) (exists (@list _let_2) (and (_ _let_3 _let_4) (_ _let_3 _let_1))))))))) % 182.18/182.45 (define tptp.po () (let ((_let_1 (@var "X" tptp.reg))) (let ((_let_2 (@var "Y" tptp.reg))) (lambda (@list _let_1 _let_2) (and (_ (_ tptp.o _let_1) _let_2) (not (_ (_ tptp.p _let_1) _let_2)) (not (_ (_ tptp.p _let_2) _let_1))))))) % 182.18/182.45 (define tptp.ec () (let ((_let_1 (@var "Y" tptp.reg))) (let ((_let_2 (@var "X" tptp.reg))) (lambda (@list _let_2 _let_1) (and (_ (_ tptp.c _let_2) _let_1) (not (_ (_ tptp.o _let_2) _let_1))))))) % 182.18/182.45 (define tptp.pp () (let ((_let_1 (@var "X" tptp.reg))) (let ((_let_2 (@var "Y" tptp.reg))) (lambda (@list _let_1 _let_2) (and (_ (_ tptp.p _let_1) _let_2) (not (_ (_ tptp.p _let_2) _let_1))))))) % 182.18/182.45 (define tptp.tpp () (let ((_let_1 (@var "Y" tptp.reg))) (let ((_let_2 (@var "Z" tptp.reg))) (let ((_let_3 (_ tptp.ec _let_2))) (let ((_let_4 (@var "X" tptp.reg))) (lambda (@list _let_4 _let_1) (and (_ (_ tptp.pp _let_4) _let_1) (exists (@list _let_2) (and (_ _let_3 _let_4) (_ _let_3 _let_1)))))))))) % 182.18/182.45 (define tptp.ntpp () (let ((_let_1 (@var "Y" tptp.reg))) (let ((_let_2 (@var "Z" tptp.reg))) (let ((_let_3 (_ tptp.ec _let_2))) (let ((_let_4 (@var "X" tptp.reg))) (lambda (@list _let_4 _let_1) (and (_ (_ tptp.pp _let_4) _let_1) (not (exists (@list _let_2) (and (_ _let_3 _let_4) (_ _let_3 _let_1))))))))))) % 182.18/182.45 (define @t1 () (@var "X" tptp.reg)) % 182.18/182.45 (define @t2 () (_ tptp.c @t1)) % 182.18/182.45 (define @t3 () (_ @t2 @t1)) % 182.18/182.45 (define @t4 () (@list @t1)) % 182.18/182.45 (define @t5 () (forall @t4 @t3)) % 182.18/182.45 (define @t6 () (@var "Y" tptp.reg)) % 182.18/182.45 (define @t7 () (_ (_ tptp.c @t6) @t1)) % 182.18/182.45 (define @t8 () (_ @t2 @t6)) % 182.18/182.45 (define @t9 () (@list @t1 @t6)) % 182.18/182.45 (define @t10 () (forall @t9 (=> @t8 @t7))) % 182.18/182.45 (define @t11 () (@var "__flatten_var_0" $$unsorted)) % 182.18/182.45 (define @t12 () (@var "A" (-> $$unsorted Bool))) % 182.18/182.45 (define @t13 () (_ tptp.mbox tptp.fool)) % 182.18/182.45 (define @t14 () (_ @t13 @t12)) % 182.18/182.45 (define @t15 () (_ tptp.mimplies @t14)) % 182.18/182.45 (define @t16 () (@list @t12 @t11)) % 182.18/182.45 (define @t17 () (@var "Phi" (-> $$unsorted Bool))) % 182.18/182.45 (define @t18 () (_ tptp.mbox tptp.a)) % 182.18/182.45 (define @t19 () (@list (@var "X" $$unsorted))) % 182.18/182.45 (define @t20 () (lambda @t19 (_ (_ tptp.tpp tptp.catalunya) tptp.spain))) % 182.18/182.45 (define @t21 () (@var "Z" tptp.reg)) % 182.18/182.45 (define @t22 () (_ (_ tptp.o @t21) tptp.france)) % 182.18/182.45 (define @t23 () (not (_ (_ tptp.eq @t21) @t6))) % 182.18/182.45 (define @t24 () (and @t23 @t22 @t22)) % 182.18/182.45 (define @t25 () (@list @t21 @t6)) % 182.18/182.45 (define @t26 () (exists @t25 @t24)) % 182.18/182.45 (define @t27 () (lambda @t19 @t26)) % 182.18/182.45 (define @t28 () (not (_ tptp.mvalid (_ @t18 @t27)))) % 182.18/182.45 (define @t29 () (@var "Y" tptp.mu)) % 182.18/182.45 (define @t30 () (@var "X" tptp.mu)) % 182.18/182.45 (define @t31 () (@var "W" $$unsorted)) % 182.18/182.45 (define @t32 () (lambda (@list @t30 @t29 @t31) (= @t30 @t29))) % 182.18/182.45 (define @t33 () (@var "Y" (-> $$unsorted Bool))) % 182.18/182.45 (define @t34 () (@var "X" (-> $$unsorted Bool))) % 182.18/182.45 (define @t35 () (lambda (@list @t34 @t33 @t31) (= (_ @t34 @t31) (_ @t33 @t31)))) % 182.18/182.45 (define @t36 () (_ @t17 @t31)) % 182.18/182.45 (define @t37 () (not @t36)) % 182.18/182.45 (define @t38 () (@list @t17 @t31)) % 182.18/182.45 (define @t39 () (lambda @t38 @t37)) % 182.18/182.45 (define @t40 () (@var "Psi" (-> $$unsorted Bool))) % 182.18/182.45 (define @t41 () (lambda (@list @t17 @t40 @t31) (or @t36 (_ @t40 @t31)))) % 182.18/182.45 (define @t42 () (_ tptp.mnot @t40)) % 182.18/182.45 (define @t43 () (_ tptp.mnot @t17)) % 182.18/182.45 (define @t44 () (_ tptp.mor @t43)) % 182.18/182.45 (define @t45 () (@list @t17 @t40 @t11)) % 182.18/182.45 (define @t46 () (lambda @t45 (_ (_ tptp.mnot (_ @t44 @t42)) @t11))) % 182.18/182.45 (define @t47 () (lambda @t45 (_ (_ @t44 @t40) @t11))) % 182.18/182.45 (define @t48 () (lambda @t45 (_ (_ (_ tptp.mor @t42) @t17) @t11))) % 182.18/182.45 (define @t49 () (lambda @t45 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t17) @t40)) (_ (_ tptp.mimplies @t40) @t17)) @t11))) % 182.18/182.45 (define @t50 () (lambda @t45 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t17) @t40)) @t11))) % 182.18/182.45 (define @t51 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 182.18/182.45 (define @t52 () (_ @t51 @t30)) % 182.18/182.45 (define @t53 () (lambda (@list @t51 @t31) (forall (@list @t30) (_ @t52 @t31)))) % 182.18/182.45 (define @t54 () (@var "P" (-> $$unsorted Bool))) % 182.18/182.45 (define @t55 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 182.18/182.45 (define @t56 () (_ @t55 @t54)) % 182.18/182.45 (define @t57 () (lambda (@list @t55 @t31) (forall (@list @t54) (_ @t56 @t31)))) % 182.18/182.45 (define @t58 () (lambda (@list @t51 @t11) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list @t30 @t11) (_ (_ tptp.mnot @t52) @t11)))) @t11))) % 182.18/182.45 (define @t59 () (lambda (@list @t55 @t11) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t54 @t11) (_ (_ tptp.mnot @t56) @t11)))) @t11))) % 182.18/182.45 (define @t60 () (@list @t31)) % 182.18/182.45 (define @t61 () (lambda @t60 true)) % 182.18/182.45 (define @t62 () (@var "V" $$unsorted)) % 182.18/182.45 (define @t63 () (_ @t17 @t62)) % 182.18/182.45 (define @t64 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 182.18/182.45 (define @t65 () (_ (_ @t64 @t31) @t62)) % 182.18/182.45 (define @t66 () (not @t65)) % 182.18/182.45 (define @t67 () (or @t66 @t63)) % 182.18/182.45 (define @t68 () (@list @t62)) % 182.18/182.45 (define @t69 () (forall @t68 @t67)) % 182.18/182.45 (define @t70 () (@list @t64 @t17 @t31)) % 182.18/182.45 (define @t71 () (lambda @t70 @t69)) % 182.18/182.45 (define @t72 () (lambda (@list @t64 @t17 @t11) (_ (_ tptp.mnot (_ (_ tptp.mbox @t64) @t43)) @t11))) % 182.18/182.45 (define @t73 () (@var "S" $$unsorted)) % 182.18/182.45 (define @t74 () (_ @t64 @t73)) % 182.18/182.45 (define @t75 () (@list @t73)) % 182.18/182.45 (define @t76 () (@list @t64)) % 182.18/182.45 (define @t77 () (lambda @t76 (forall @t75 (_ @t74 @t73)))) % 182.18/182.45 (define @t78 () (@var "T" $$unsorted)) % 182.18/182.45 (define @t79 () (_ @t64 @t78)) % 182.18/182.45 (define @t80 () (_ @t74 @t78)) % 182.18/182.45 (define @t81 () (lambda @t76 (forall (@list @t73 @t78) (=> @t80 (_ @t79 @t73))))) % 182.18/182.45 (define @t82 () (@list @t78)) % 182.18/182.45 (define @t83 () (lambda @t76 (forall @t75 (exists @t82 @t80)))) % 182.18/182.45 (define @t84 () (@var "U" $$unsorted)) % 182.18/182.45 (define @t85 () (_ @t74 @t84)) % 182.18/182.45 (define @t86 () (_ @t79 @t84)) % 182.18/182.45 (define @t87 () (@list @t73 @t78 @t84)) % 182.18/182.45 (define @t88 () (lambda @t76 (forall @t87 (=> (and @t80 @t86) @t85)))) % 182.18/182.45 (define @t89 () (and @t80 @t85)) % 182.18/182.45 (define @t90 () (lambda @t76 (forall @t87 (=> @t89 @t86)))) % 182.18/182.45 (define @t91 () (= @t78 @t84)) % 182.18/182.45 (define @t92 () (lambda @t76 (forall @t87 (=> @t89 @t91)))) % 182.18/182.45 (define @t93 () (@list @t84)) % 182.18/182.45 (define @t94 () (lambda @t76 (forall @t75 (exists @t82 (and @t80 (forall @t93 (=> @t85 @t91))))))) % 182.18/182.45 (define @t95 () (_ @t64 @t84)) % 182.18/182.45 (define @t96 () (_ @t95 @t78)) % 182.18/182.45 (define @t97 () (lambda @t76 (forall @t87 (=> @t80 (exists @t93 (and @t85 @t96)))))) % 182.18/182.45 (define @t98 () (lambda @t76 (forall @t87 (=> @t89 (or @t86 @t91 @t96))))) % 182.18/182.45 (define @t99 () (lambda @t76 (forall @t87 (=> @t89 (exists @t68 (and (_ @t79 @t62) (_ @t95 @t62))))))) % 182.18/182.45 (define @t100 () (forall @t60 @t36)) % 182.18/182.45 (define @t101 () (@list @t17)) % 182.18/182.45 (define @t102 () (lambda @t101 @t100)) % 182.18/182.45 (define @t103 () (lambda @t101 (forall @t60 @t37))) % 182.18/182.45 (define @t104 () (lambda @t101 (exists @t60 @t36))) % 182.18/182.45 (define @t105 () (lambda @t101 (exists @t60 @t37))) % 182.18/182.45 (define @t106 () (not @t8)) % 182.18/182.45 (define @t107 () (lambda @t9 @t106)) % 182.18/182.45 (define @t108 () (_ tptp.c @t21)) % 182.18/182.45 (define @t109 () (_ @t108 @t6)) % 182.18/182.45 (define @t110 () (_ @t108 @t1)) % 182.18/182.45 (define @t111 () (@list @t21)) % 182.18/182.45 (define @t112 () (forall @t111 (=> @t110 @t109))) % 182.18/182.45 (define @t113 () (lambda @t9 @t112)) % 182.18/182.45 (define @t114 () (_ (_ tptp.p @t6) @t1)) % 182.18/182.45 (define @t115 () (_ (_ tptp.p @t1) @t6)) % 182.18/182.45 (define @t116 () (and @t115 @t114)) % 182.18/182.45 (define @t117 () (lambda @t9 @t116)) % 182.18/182.45 (define @t118 () (_ tptp.p @t21)) % 182.18/182.45 (define @t119 () (and (_ @t118 @t1) (_ @t118 @t6))) % 182.18/182.45 (define @t120 () (exists @t111 @t119)) % 182.18/182.45 (define @t121 () (lambda @t9 @t120)) % 182.18/182.45 (define @t122 () (not @t114)) % 182.18/182.45 (define @t123 () (_ (_ tptp.o @t1) @t6)) % 182.18/182.45 (define @t124 () (lambda @t9 (and @t123 (not @t115) @t122))) % 182.18/182.45 (define @t125 () (not @t123)) % 182.18/182.45 (define @t126 () (and @t8 @t125)) % 182.18/182.45 (define @t127 () (lambda @t9 @t126)) % 182.18/182.45 (define @t128 () (and @t115 @t122)) % 182.18/182.45 (define @t129 () (lambda @t9 @t128)) % 182.18/182.45 (define @t130 () (_ tptp.ec @t21)) % 182.18/182.45 (define @t131 () (and (_ @t130 @t1) (_ @t130 @t6))) % 182.18/182.45 (define @t132 () (exists @t111 @t131)) % 182.18/182.45 (define @t133 () (_ (_ tptp.pp @t1) @t6)) % 182.18/182.45 (define @t134 () (and @t133 @t132)) % 182.18/182.45 (define @t135 () (lambda @t9 @t134)) % 182.18/182.45 (define @t136 () (lambda @t9 (and @t133 (not @t132)))) % 182.18/182.45 (define @t137 () (@const 0 (@ho-elim-sort (-> tptp.reg tptp.reg Bool)))) % 182.18/182.45 (define @t138 () (@const 1 (-> (@ho-elim-sort (-> tptp.reg tptp.reg Bool)) tptp.reg (@ho-elim-sort (-> tptp.reg Bool))))) % 182.18/182.45 (define @t139 () (@const 2 (-> (@ho-elim-sort (-> tptp.reg Bool)) tptp.reg Bool))) % 182.18/182.45 (define @t140 () (_ @t138 @t137 @t1)) % 182.18/182.45 (define @t141 () (tptp.c @t6 @t1)) % 182.18/182.45 (define @t142 () (tptp.c @t1 @t6)) % 182.18/182.45 (define @t143 () (or @t106 @t7)) % 182.18/182.45 (define @t144 () (_ @t138 @t137 @t21)) % 182.18/182.45 (define @t145 () (_ @t139 @t144 tptp.catalunya)) % 182.18/182.45 (define @t146 () (_ @t139 @t144 tptp.spain)) % 182.18/182.45 (define @t147 () (not @t146)) % 182.18/182.45 (define @t148 () (forall @t111 (or @t147 @t145))) % 182.18/182.45 (define @t149 () (@quantifiers_skolemize @t148 0)) % 182.18/182.45 (define @t150 () (@list @t31 @t62)) % 182.18/182.45 (define @t151 () (forall @t150 (not (_ (@const 5 (-> (@ho-elim-sort (-> $$unsorted Bool)) $$unsorted Bool)) (_ (@const 4 (-> (@ho-elim-sort (-> $$unsorted $$unsorted Bool)) $$unsorted (@ho-elim-sort (-> $$unsorted Bool)))) (@const 3 (@ho-elim-sort (-> $$unsorted $$unsorted Bool))) @t31) @t62)))) % 182.18/182.45 (define @t152 () (@var "BOUND_VARIABLE_8328" tptp.reg)) % 182.18/182.45 (define @t153 () (_ @t138 @t137 @t152)) % 182.18/182.45 (define @t154 () (_ @t139 @t153 tptp.france)) % 182.18/182.45 (define @t155 () (@var "BOUND_VARIABLE_9183" tptp.reg)) % 182.18/182.45 (define @t156 () (not (_ @t139 @t153 @t155))) % 182.18/182.45 (define @t157 () (@list @t152)) % 182.18/182.45 (define @t158 () (_ @t139 @t153 @t21)) % 182.18/182.45 (define @t159 () (@var "BOUND_VARIABLE_9176" tptp.reg)) % 182.18/182.45 (define @t160 () (_ @t138 @t137 @t159)) % 182.18/182.45 (define @t161 () (@var "BOUND_VARIABLE_9170" tptp.reg)) % 182.18/182.45 (define @t162 () (_ @t138 @t137 @t161)) % 182.18/182.45 (define @t163 () (@list @t21 @t6 @t161 @t159 @t155)) % 182.18/182.45 (define @t164 () (forall @t163 (or (and (or (not (_ @t139 @t162 @t21)) (_ @t139 @t162 @t6)) (or (not (_ @t139 @t160 @t6)) (_ @t139 @t160 @t21))) (not (forall @t157 (or @t156 @t158))) (not (forall @t157 (or @t156 @t154)))))) % 182.18/182.45 (define @t165 () (not (tptp.a @t31 @t62))) % 182.18/182.45 (define @t166 () (forall @t150 @t165)) % 182.18/182.45 (define @t167 () (tptp.c @t152 tptp.france)) % 182.18/182.45 (define @t168 () (not (tptp.c @t152 @t155))) % 182.18/182.45 (define @t169 () (not (forall @t157 (or @t168 @t167)))) % 182.18/182.45 (define @t170 () (tptp.c @t152 @t21)) % 182.18/182.45 (define @t171 () (not (forall @t157 (or @t168 @t170)))) % 182.18/182.45 (define @t172 () (or (not (tptp.c @t159 @t6)) (tptp.c @t159 @t21))) % 182.18/182.45 (define @t173 () (or (not (tptp.c @t161 @t21)) (tptp.c @t161 @t6))) % 182.18/182.45 (define @t174 () (and @t173 @t172)) % 182.18/182.45 (define @t175 () (or @t174 @t171 @t169)) % 182.18/182.45 (define @t176 () (not (forall @t163 @t175))) % 182.18/182.45 (define @t177 () (forall @t68 @t165)) % 182.18/182.45 (define @t178 () (forall @t60 @t177)) % 182.18/182.45 (define @t179 () (or @t176 @t178)) % 182.18/182.45 (define @t180 () (or @t176 @t177)) % 182.18/182.45 (define @t181 () (lambda @t60 @t180)) % 182.18/182.45 (define @t182 () (_ @t181 @t31)) % 182.18/182.45 (define @t183 () (forall @t60 @t182)) % 182.18/182.45 (define @t184 () (_ @t17 @t31)) % 182.18/182.45 (define @t185 () (lambda @t101 (forall @t60 @t184))) % 182.18/182.45 (define @t186 () (or @t176 @t165)) % 182.18/182.45 (define @t187 () (or @t165 @t176)) % 182.18/182.45 (define @t188 () (lambda @t19 @t176)) % 182.18/182.45 (define @t189 () (_ @t188 @t62)) % 182.18/182.45 (define @t190 () (or @t165 @t189)) % 182.18/182.45 (define @t191 () (forall @t68 @t190)) % 182.18/182.45 (define @t192 () (lambda @t60 @t191)) % 182.18/182.45 (define @t193 () (_ @t17 @t62)) % 182.18/182.45 (define @t194 () (lambda @t38 (forall @t68 (or @t165 @t193)))) % 182.18/182.45 (define @t195 () (or @t171 @t169)) % 182.18/182.45 (define @t196 () (or @t174 @t195)) % 182.18/182.45 (define @t197 () (forall @t163 @t196)) % 182.18/182.45 (define @t198 () (forall (@list @t161 @t159 @t155) @t196)) % 182.18/182.45 (define @t199 () (forall (@list @t155) @t195)) % 182.18/182.45 (define @t200 () (@var "BOUND_VARIABLE_9132" tptp.reg)) % 182.18/182.45 (define @t201 () (@list @t200)) % 182.18/182.45 (define @t202 () (forall (@list @t159) @t172)) % 182.18/182.45 (define @t203 () (@var "BOUND_VARIABLE_9101" tptp.reg)) % 182.18/182.45 (define @t204 () (@list @t203)) % 182.18/182.45 (define @t205 () (@list @t161 @t159)) % 182.18/182.45 (define @t206 () (forall @t205 @t172)) % 182.18/182.45 (define @t207 () (forall (@list @t161) @t173)) % 182.18/182.45 (define @t208 () (@var "BOUND_VARIABLE_9109" tptp.reg)) % 182.18/182.45 (define @t209 () (@list @t208)) % 182.18/182.45 (define @t210 () (forall @t205 @t173)) % 182.18/182.45 (define @t211 () (and @t210 @t206)) % 182.18/182.45 (define @t212 () (forall @t205 @t174)) % 182.18/182.45 (define @t213 () (or @t212 @t199)) % 182.18/182.45 (define @t214 () (not (tptp.c @t152 @t200))) % 182.18/182.45 (define @t215 () (not (forall @t157 (or @t214 @t170)))) % 182.18/182.45 (define @t216 () (@list @t200)) % 182.18/182.45 (define @t217 () (forall @t216 (or @t215 (not (forall @t157 (or @t214 @t167)))))) % 182.18/182.45 (define @t218 () (not (tptp.c @t203 @t6))) % 182.18/182.45 (define @t219 () (@list @t203)) % 182.18/182.45 (define @t220 () (tptp.c @t208 @t6)) % 182.18/182.45 (define @t221 () (@list @t208)) % 182.18/182.45 (define @t222 () (and (forall @t221 (or (not (tptp.c @t208 @t21)) @t220)) (forall @t219 (or @t218 (tptp.c @t203 @t21))))) % 182.18/182.45 (define @t223 () (or @t222 @t217)) % 182.18/182.45 (define @t224 () (not @t217)) % 182.18/182.45 (define @t225 () (not @t224)) % 182.18/182.45 (define @t226 () (not @t222)) % 182.18/182.45 (define @t227 () (not @t226)) % 182.18/182.45 (define @t228 () (or @t227 @t225 @t225)) % 182.18/182.45 (define @t229 () (and @t226 @t224 @t224)) % 182.18/182.45 (define @t230 () (forall @t25 (not @t229))) % 182.18/182.45 (define @t231 () (not @t230)) % 182.18/182.45 (define @t232 () (tptp.c @t152 @t6)) % 182.18/182.45 (define @t233 () (not (forall @t157 (or @t214 @t232)))) % 182.18/182.45 (define @t234 () (@list @t6)) % 182.18/182.45 (define @t235 () (lambda @t234 (not (forall @t216 (or @t215 @t233))))) % 182.18/182.45 (define @t236 () (tptp.c @t152 @t1)) % 182.18/182.45 (define @t237 () (not @t170)) % 182.18/182.45 (define @t238 () (forall @t157 (or @t237 @t232))) % 182.18/182.45 (define @t239 () (forall @t157 (or @t237 @t236))) % 182.18/182.45 (define @t240 () (forall @t111 (or (not @t239) (not @t238)))) % 182.18/182.45 (define @t241 () (@list @t21)) % 182.18/182.45 (define @t242 () (not @t240)) % 182.18/182.45 (define @t243 () (lambda @t9 @t242)) % 182.18/182.45 (define @t244 () (lambda @t234 @t222)) % 182.18/182.45 (define @t245 () (tptp.c @t21 @t1)) % 182.18/182.45 (define @t246 () (tptp.c @t21 @t6)) % 182.18/182.45 (define @t247 () (not @t246)) % 182.18/182.45 (define @t248 () (forall @t111 (or @t247 @t245))) % 182.18/182.45 (define @t249 () (not @t245)) % 182.18/182.45 (define @t250 () (forall @t111 (or @t249 @t246))) % 182.18/182.45 (define @t251 () (and @t250 @t248)) % 182.18/182.45 (define @t252 () (lambda @t9 @t251)) % 182.18/182.45 (define @t253 () (not (_ (_ @t252 @t21) @t6))) % 182.18/182.45 (define @t254 () (_ (_ @t243 @t21) tptp.france)) % 182.18/182.45 (define @t255 () (and @t253 @t254 @t254)) % 182.18/182.45 (define @t256 () (exists @t25 @t255)) % 182.18/182.45 (define @t257 () (lambda @t19 @t256)) % 182.18/182.45 (define @t258 () (_ @t64 @t31 @t62)) % 182.18/182.45 (define @t259 () (_ (lambda @t70 (forall @t68 (or (not @t258) @t193))) tptp.a)) % 182.18/182.45 (define @t260 () (and @t239 @t238)) % 182.18/182.45 (define @t261 () (forall @t111 (not @t260))) % 182.18/182.45 (define @t262 () (not @t261)) % 182.18/182.45 (define @t263 () (lambda @t234 @t238)) % 182.18/182.45 (define @t264 () (lambda @t9 @t250)) % 182.18/182.45 (define @t265 () (_ @t264 @t21)) % 182.18/182.45 (define @t266 () (and (_ @t265 @t1) (_ @t265 @t6))) % 182.18/182.45 (define @t267 () (not @t110)) % 182.18/182.45 (define @t268 () (or @t267 @t109)) % 182.18/182.45 (define @t269 () (@var "BOUND_VARIABLE_8290" tptp.reg)) % 182.18/182.45 (define @t270 () (tptp.c @t21 @t269)) % 182.18/182.45 (define @t271 () (lambda (@list @t269) (forall @t111 (or @t247 @t270)))) % 182.18/182.45 (define @t272 () (lambda @t234 @t250)) % 182.18/182.45 (define @t273 () (_ @t264 @t1)) % 182.18/182.45 (define @t274 () (_ (_ @t264 @t6) @t1)) % 182.18/182.45 (define @t275 () (_ @t273 @t6)) % 182.18/182.45 (define @t276 () (not @t148)) % 182.18/182.45 (define @t277 () (not @t145)) % 182.18/182.45 (define @t278 () (@var "BOUND_VARIABLE_8441" tptp.reg)) % 182.18/182.45 (define @t279 () (not (_ @t139 @t153 @t278))) % 182.18/182.45 (define @t280 () (not (forall @t157 (or @t279 @t158)))) % 182.18/182.45 (define @t281 () (@list @t278)) % 182.18/182.45 (define @t282 () (and (not (forall @t111 (or @t277 (not (forall @t281 (or @t280 (not (forall @t157 (or @t279 (_ @t139 @t153 tptp.catalunya))))))) @t147 (not (forall @t281 (or @t280 (not (forall @t157 (or @t279 (_ @t139 @t153 tptp.spain)))))))))) (forall @t111 (or @t277 @t146)) @t276)) % 182.18/182.45 (define @t283 () (tptp.c @t21 tptp.catalunya)) % 182.18/182.45 (define @t284 () (tptp.c @t21 tptp.spain)) % 182.18/182.45 (define @t285 () (not @t284)) % 182.18/182.45 (define @t286 () (not @t283)) % 182.18/182.45 (define @t287 () (not (tptp.c @t152 @t278))) % 182.18/182.45 (define @t288 () (not (forall @t157 (or @t287 @t170)))) % 182.18/182.45 (define @t289 () (not (forall @t281 (or @t288 (not (forall @t157 (or @t287 (tptp.c @t152 tptp.catalunya)))))))) % 182.18/182.45 (define @t290 () (and (not (forall @t111 (or @t286 @t289 @t285 (not (forall @t281 (or @t288 (not (forall @t157 (or @t287 (tptp.c @t152 tptp.spain)))))))))) (forall @t111 (or @t286 @t284)) (not (forall @t111 (or @t285 @t283))))) % 182.18/182.45 (define @t291 () (or @t290 @t178)) % 182.18/182.45 (define @t292 () (or @t290 @t177)) % 182.18/182.45 (define @t293 () (lambda @t60 @t292)) % 182.18/182.45 (define @t294 () (_ @t293 @t31)) % 182.18/182.45 (define @t295 () (forall @t60 @t294)) % 182.18/182.45 (define @t296 () (or @t290 @t165)) % 182.18/182.45 (define @t297 () (or @t165 @t290)) % 182.18/182.45 (define @t298 () (lambda @t19 @t290)) % 182.18/182.45 (define @t299 () (_ @t298 @t62)) % 182.18/182.45 (define @t300 () (or @t165 @t299)) % 182.18/182.45 (define @t301 () (forall @t68 @t300)) % 182.18/182.45 (define @t302 () (lambda @t60 @t301)) % 182.18/182.45 (define @t303 () (not (forall @t157 (or @t287 @t232)))) % 182.18/182.45 (define @t304 () (forall @t281 (or @t288 @t303))) % 182.18/182.45 (define @t305 () (not @t304)) % 182.18/182.45 (define @t306 () (lambda @t234 (and (not (forall @t111 (or @t286 @t289 @t247 @t305))) (forall @t111 (or @t286 @t246)) (not (forall @t111 (or @t247 @t283)))))) % 182.18/182.45 (define @t307 () (not @t248)) % 182.18/182.45 (define @t308 () (not (forall @t157 (or @t287 @t236)))) % 182.18/182.45 (define @t309 () (forall @t281 (or @t288 @t308))) % 182.18/182.45 (define @t310 () (not @t309)) % 182.18/182.45 (define @t311 () (not (forall @t111 (or @t249 @t310 @t247 @t305)))) % 182.18/182.45 (define @t312 () (and @t311 @t250 @t307)) % 182.18/182.45 (define @t313 () (_ (lambda @t9 @t312) tptp.catalunya)) % 182.18/182.45 (define @t314 () (and @t250 @t307)) % 182.18/182.45 (define @t315 () (not @t109)) % 182.18/182.45 (define @t316 () (or @t267 @t310 @t315 @t305)) % 182.18/182.45 (define @t317 () (and @t109 @t304)) % 182.18/182.45 (define @t318 () (and @t110 @t309 @t109 @t304)) % 182.18/182.45 (define @t319 () (forall @t111 (not @t318))) % 182.18/182.45 (define @t320 () (not @t319)) % 182.18/182.45 (define @t321 () (and @t110 @t309)) % 182.18/182.45 (define @t322 () (lambda @t234 @t317)) % 182.18/182.45 (define @t323 () (and @t8 @t240)) % 182.18/182.45 (define @t324 () (lambda @t9 @t323)) % 182.18/182.45 (define @t325 () (_ @t324 @t21)) % 182.18/182.45 (define @t326 () (and (_ @t325 @t1) (_ @t325 @t6))) % 182.18/182.45 (define @t327 () (exists @t111 @t326)) % 182.18/182.45 (define @t328 () (lambda @t234 @t314)) % 182.18/182.45 (define @t329 () (_ (lambda @t9 @t314) @t1)) % 182.18/182.45 (define @t330 () (lambda @t234 @t242)) % 182.18/182.45 (define @t331 () (_ @t243 @t1)) % 182.18/182.45 (define @t332 () (not (_ @t331 @t6))) % 182.18/182.45 (define @t333 () (not @t274)) % 182.18/182.45 (define @t334 () (@list true)) % 182.18/182.45 (define @t335 () (@list false)) % 182.18/182.45 (define @t336 () (_ @t138 @t137 @t149)) % 182.18/182.45 (define @t337 () (_ @t139 @t336 tptp.catalunya)) % 182.18/182.45 (define @t338 () (or (not (_ @t139 @t336 tptp.spain)) @t337)) % 182.18/182.45 (define @t339 () (_ @t138 @t137 tptp.catalunya)) % 182.18/182.45 (define @t340 () (_ @t139 @t339 @t149)) % 182.18/182.45 (define @t341 () (not @t340)) % 182.18/182.45 (define @t342 () (or @t341 @t337)) % 182.18/182.45 (define @t343 () (_ @t139 @t339 tptp.france)) % 182.18/182.45 (define @t344 () (_ @t139 @t339 tptp.catalunya)) % 182.18/182.45 (define @t345 () (not @t344)) % 182.18/182.45 (define @t346 () (or @t345 @t343)) % 182.18/182.45 (define @t347 () (not @t343)) % 182.18/182.45 (define @t348 () (and (or @t347 @t344) @t346)) % 182.18/182.45 (define @t349 () (forall @t157 (or (not @t154) @t154))) % 182.18/182.45 (define @t350 () (not @t349)) % 182.18/182.45 (define @t351 () (or @t348 @t350 @t350)) % 182.18/182.45 (define @t352 () (@list @t164)) % 182.18/182.45 (define @t353 () (tptp.c @t1 @t1)) % 182.18/182.45 (define @t354 () (or @t347 @t340)) % 182.18/182.45 (define @t355 () (not @t354)) % 182.18/182.45 (define @t356 () (@list false true)) % 182.18/182.45 (define @t357 () (and @t354 (or @t341 @t343))) % 182.18/182.45 (define @t358 () (or @t357 @t350 @t350)) % 182.18/182.45 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 182.18/182.45 (assume @p2 @t5) % 182.18/182.45 (assume @p3 @t10) % 182.18/182.45 (assume @p4 (_ tptp.mvalid (_ tptp.mforall_prop (lambda @t16 (_ (_ @t15 @t12) @t11))))) % 182.18/182.45 (assume @p5 (_ tptp.mvalid (_ tptp.mforall_prop (lambda @t16 (_ (_ @t15 (_ @t13 @t14)) @t11))))) % 182.18/182.45 (assume @p6 (_ tptp.mvalid (_ tptp.mforall_prop (lambda (@list @t17 @t11) (_ (_ (_ tptp.mimplies (_ @t13 @t17)) (_ @t18 @t17)) @t11))))) % 182.18/182.45 (assume @p7 (_ tptp.mvalid (_ @t18 @t20))) % 182.18/182.45 (assume @p8 (_ tptp.mvalid (_ @t13 (lambda @t19 (_ (_ tptp.ec tptp.spain) tptp.france))))) % 182.18/182.45 (assume @p9 (_ tptp.mvalid (_ @t18 (lambda @t19 (_ (_ tptp.ntpp tptp.paris) tptp.france))))) % 182.18/182.45 (assume @p10 @t28) % 182.18/182.45 (assume @p11 true) % 182.18/182.45 (step @p12 (= tptp.meq_ind @t32) :rule refl :args (@t32)) % 182.18/182.45 (step @p13 (= tptp.meq_prop @t35) :rule refl :args (@t35)) % 182.18/182.45 (step @p14 (= tptp.mnot @t39) :rule refl :args (@t39)) % 182.18/182.45 (step @p15 (= tptp.mor @t41) :rule refl :args (@t41)) % 182.18/182.45 (step @p16 (= tptp.mand @t46) :rule refl :args (@t46)) % 182.18/182.45 (step @p17 (= tptp.mimplies @t47) :rule refl :args (@t47)) % 182.18/182.45 (step @p18 (= tptp.mimplied @t48) :rule refl :args (@t48)) % 182.18/182.45 (step @p19 (= tptp.mequiv @t49) :rule refl :args (@t49)) % 182.18/182.45 (step @p20 (= tptp.mxor @t50) :rule refl :args (@t50)) % 182.18/182.45 (step @p21 (= tptp.mforall_ind @t53) :rule refl :args (@t53)) % 182.18/182.45 (step @p22 (= tptp.mforall_prop @t57) :rule refl :args (@t57)) % 182.18/182.45 (step @p23 (= tptp.mexists_ind @t58) :rule refl :args (@t58)) % 182.18/182.45 (step @p24 (= tptp.mexists_prop @t59) :rule refl :args (@t59)) % 182.18/182.45 (step @p25 (= tptp.mtrue @t61) :rule refl :args (@t61)) % 182.18/182.45 (step @p26 (= tptp.mbox @t71) :rule refl :args (@t71)) % 182.18/182.45 (step @p27 (= tptp.mdia @t72) :rule refl :args (@t72)) % 182.18/182.45 (step @p28 (= tptp.mreflexive @t77) :rule refl :args (@t77)) % 182.18/182.45 (step @p29 (= tptp.msymmetric @t81) :rule refl :args (@t81)) % 182.18/182.45 (step @p30 (= tptp.mserial @t83) :rule refl :args (@t83)) % 182.18/182.45 (step @p31 (= tptp.mtransitive @t88) :rule refl :args (@t88)) % 182.18/182.45 (step @p32 (= tptp.meuclidean @t90) :rule refl :args (@t90)) % 182.18/182.45 (step @p33 (= tptp.mpartially_functional @t92) :rule refl :args (@t92)) % 182.18/182.45 (step @p34 (= tptp.mfunctional @t94) :rule refl :args (@t94)) % 182.18/182.45 (step @p35 (= tptp.mweakly_dense @t97) :rule refl :args (@t97)) % 182.18/182.45 (step @p36 (= tptp.mweakly_connected @t98) :rule refl :args (@t98)) % 182.18/182.45 (step @p37 (= tptp.mweakly_directed @t99) :rule refl :args (@t99)) % 182.18/182.45 (step @p38 (= tptp.mvalid @t102) :rule refl :args (@t102)) % 182.18/182.45 (step @p39 (= tptp.minvalid @t103) :rule refl :args (@t103)) % 182.18/182.45 (step @p40 (= tptp.msatisfiable @t104) :rule refl :args (@t104)) % 182.18/182.45 (step @p41 (= tptp.mcountersatisfiable @t105) :rule refl :args (@t105)) % 182.18/182.45 (step @p42 (= tptp.dc @t107) :rule refl :args (@t107)) % 182.18/182.45 (step @p43 (= tptp.p @t113) :rule refl :args (@t113)) % 182.18/182.45 (step @p44 (= tptp.eq @t117) :rule refl :args (@t117)) % 182.18/182.45 (step @p45 (= tptp.o @t121) :rule refl :args (@t121)) % 182.18/182.45 (step @p46 (= tptp.po @t124) :rule refl :args (@t124)) % 182.18/182.45 (step @p47 (= tptp.ec @t127) :rule refl :args (@t127)) % 182.18/182.45 (step @p48 (= tptp.pp @t129) :rule refl :args (@t129)) % 182.18/182.45 (step @p49 (= tptp.tpp @t135) :rule refl :args (@t135)) % 182.18/182.45 (step @p50 (= tptp.ntpp @t136) :rule refl :args (@t136)) % 182.18/182.45 ; WARNING: add trust step for TRUST % 182.18/182.45 ; trust TRUST PREPROCESS_HO_ELIM % 182.18/182.45 (step @p51 :rule trust :premises () :args ((= (forall @t9 (or (not @t142) @t141)) (forall @t9 (or (not (_ @t139 @t140 @t6)) (_ @t139 (_ @t138 @t137 @t6) @t1)))))) % 182.18/182.45 (step @p52 :rule refl :args (@t141)) % 182.18/182.45 (step @p53 :rule refl :args (@t7)) % 182.18/182.45 (step @p54 :rule cong :premises (@p53 @p52) :args ((= @t7 @t141))) % 182.18/182.45 (step @p55 :rule symm :premises (@p54)) % 182.18/182.45 (step @p56 :rule eq_resolve :premises (@p53 @p55)) % 182.18/182.45 (step @p57 :rule refl :args (@t142)) % 182.18/182.45 (step @p58 :rule refl :args (@t8)) % 182.18/182.45 (step @p59 :rule cong :premises (@p58 @p57) :args ((= @t8 @t142))) % 182.18/182.45 (step @p60 :rule symm :premises (@p59)) % 182.18/182.45 (step @p61 :rule eq_resolve :premises (@p58 @p60)) % 182.18/182.45 (step @p62 :rule cong :premises (@p61) :args (@t106)) % 182.18/182.45 (step @p63 :rule nary_cong :premises (@p62 @p56) :args (@t143)) % 182.18/182.45 (step @p64 :rule cong :premises (@p63) :args ((forall @t9 @t143))) % 182.18/182.45 (step @p65 :rule bool-impl-elim :args (@t8 @t7)) % 182.18/182.45 (step @p66 :rule cong :premises (@p65) :args (@t10)) % 182.18/182.45 (step @p67 :rule trans :premises (@p66 @p64)) % 182.18/182.45 (step @p68 :rule trans :premises (@p67 @p51)) % 182.18/182.45 (step @p69 :rule eq_resolve :premises (@p3 @p68)) % 182.18/182.45 (step @p70 :rule instantiate :premises (@p69) :args ((@list tptp.catalunya @t149))) % 182.18/182.45 ; trust TRUST PREPROCESS_HO_ELIM % 182.18/182.45 (step @p71 :rule trust :premises () :args ((= (not (or @t176 @t166)) (not (or (not @t164) @t151))))) % 182.18/182.45 (step @p72 :rule quant-merge-prenex :args ((= @t178 @t166))) % 182.18/182.45 (step @p73 :rule refl :args (@t176)) % 182.18/182.45 (step @p74 :rule nary_cong :premises (@p73 @p72) :args (@t179)) % 182.18/182.45 (step @p75 :rule quant-miniscope-or :args ((= (forall @t60 @t180) @t179))) % 182.18/182.45 (step @p76 :rule trans :premises (@p75 @p74)) % 182.18/182.45 (step @p77 :rule beta-reduce :args ((= @t182 @t180))) % 182.18/182.45 (step @p78 :rule cong :premises (@p77) :args (@t183)) % 182.18/182.45 (step @p79 :rule trans :premises (@p78 @p76)) % 182.18/182.45 (step @p80 :rule beta-reduce :args ((= (_ @t185 @t181) @t183))) % 182.18/182.45 (step @p81 :rule trans :premises (@p80 @p79)) % 182.18/182.45 (step @p82 :rule quant-miniscope-or :args ((= (forall @t68 @t186) @t180))) % 182.18/182.45 (step @p83 :rule aci_norm :args ((= @t187 @t186))) % 182.18/182.45 (step @p84 :rule cong :premises (@p83) :args ((forall @t68 @t187))) % 182.18/182.45 (step @p85 :rule trans :premises (@p84 @p82)) % 182.18/182.45 (step @p86 :rule beta-reduce :args ((= @t189 @t176))) % 182.18/182.45 (step @p87 :rule refl :args (@t165)) % 182.18/182.45 (step @p88 :rule nary_cong :premises (@p87 @p86) :args (@t190)) % 182.18/182.45 (step @p89 :rule cong :premises (@p88) :args (@t191)) % 182.18/182.45 (step @p90 :rule trans :premises (@p89 @p85)) % 182.18/182.45 (step @p91 :rule cong :premises (@p90) :args (@t192)) % 182.18/182.45 (step @p92 :rule beta-reduce :args ((= (_ @t194 @t188) @t192))) % 182.18/182.45 (step @p93 :rule trans :premises (@p92 @p91)) % 182.18/182.45 (step @p94 :rule aci_norm :args ((= @t196 @t175))) % 182.18/182.45 (step @p95 :rule cong :premises (@p94) :args (@t197)) % 182.18/182.45 (step @p96 :rule quant-merge-prenex :args ((= (forall @t25 @t198) @t197))) % 182.18/182.45 (step @p97 :rule alpha_equiv :args (@t199 (@list @t155) @t201)) % 182.18/182.45 (step @p98 :rule alpha_equiv :args (@t202 (@list @t159) @t204)) % 182.18/182.45 (step @p99 :rule quant-unused-vars :args ((= @t206 @t202))) % 182.18/182.45 (step @p100 :rule trans :premises (@p99 @p98)) % 182.18/182.45 (step @p101 :rule alpha_equiv :args (@t207 (@list @t161) @t209)) % 182.18/182.45 (step @p102 :rule quant-unused-vars :args ((= @t210 @t207))) % 182.18/182.45 (step @p103 :rule trans :premises (@p102 @p101)) % 182.18/182.45 (step @p104 :rule nary_cong :premises (@p103 @p100) :args (@t211)) % 182.18/182.45 (step @p105 :rule quant-miniscope-and :args ((= @t212 @t211))) % 182.18/182.45 (step @p106 :rule trans :premises (@p105 @p104)) % 182.18/182.45 (step @p107 :rule nary_cong :premises (@p106 @p97) :args (@t213)) % 182.18/182.45 (step @p108 :rule quant-miniscope-or :args ((= @t198 @t213))) % 182.18/182.45 (step @p109 :rule trans :premises (@p108 @p107)) % 182.18/182.45 (step @p110 :rule symm :premises (@p109)) % 182.18/182.45 (step @p111 :rule cong :premises (@p110) :args ((forall @t25 @t223))) % 182.18/182.45 (step @p112 :rule trans :premises (@p111 @p96)) % 182.18/182.45 (step @p113 :rule trans :premises (@p112 @p95)) % 182.18/182.45 (step @p114 :rule aci_norm :args ((= (or @t222 @t217 @t217) @t223))) % 182.18/182.45 (step @p115 :rule bool-double-not-elim :args (@t217)) % 182.18/182.45 (step @p116 :rule bool-double-not-elim :args (@t222)) % 182.18/182.45 (step @p117 :rule nary_cong :premises (@p116 @p115 @p115) :args (@t228)) % 182.18/182.45 (step @p118 :rule aci_norm :args ((= (or @t227 (or @t225 @t225)) @t228))) % 182.18/182.45 (step @p119 :rule trans :premises (@p118 @p117)) % 182.18/182.45 (step @p120 :rule bool-and-de-morgan :args (@t224 @t224 true)) % 182.18/182.45 (step @p121 :rule refl :args (@t227)) % 182.18/182.45 (step @p122 :rule nary_cong :premises (@p121 @p120) :args ((or @t227 (not (and @t224 @t224))))) % 182.18/182.45 (step @p123 :rule bool-and-de-morgan :args (@t226 @t224 (and @t224))) % 182.18/182.45 (step @p124 :rule trans :premises (@p123 @p122)) % 182.18/182.45 (step @p125 :rule trans :premises (@p124 @p119)) % 182.18/182.45 (step @p126 :rule trans :premises (@p125 @p114)) % 182.18/182.45 (step @p127 :rule cong :premises (@p126) :args (@t230)) % 182.18/182.45 (step @p128 :rule trans :premises (@p127 @p113)) % 182.18/182.45 (step @p129 :rule cong :premises (@p128) :args (@t231)) % 182.18/182.45 (step @p130 :rule exists-elim :args ((= (exists @t25 @t229) @t231))) % 182.18/182.45 (step @p131 :rule trans :premises (@p130 @p129)) % 182.18/182.45 (step @p132 :rule beta-reduce :args ((= (_ @t235 tptp.france) @t224))) % 182.18/182.45 (step @p133 :rule refl :args (tptp.france)) % 182.18/182.45 (step @p134 :rule beta-reduce :args ((= (_ (lambda @t9 (not (forall @t216 (or (not (forall @t157 (or @t214 @t236))) @t233)))) @t21) @t235))) % 182.18/182.45 (step @p135 :rule refl :args (@t21)) % 182.18/182.45 (step @p136 :rule alpha_equiv :args (@t240 @t241 @t201)) % 182.18/182.45 (step @p137 :rule cong :premises (@p136) :args (@t242)) % 182.18/182.45 (step @p138 :rule cong :premises (@p137) :args (@t243)) % 182.18/182.45 (step @p139 :rule ho_cong :premises (@p138 @p135)) % 182.18/182.45 (step @p140 :rule trans :premises (@p139 @p134)) % 182.18/182.45 (step @p141 :rule ho_cong :premises (@p140 @p133)) % 182.18/182.45 (step @p142 :rule trans :premises (@p141 @p132)) % 182.18/182.45 (step @p143 :rule beta-reduce :args ((= (_ @t244 @t6) @t222))) % 182.18/182.45 (step @p144 :rule refl :args (@t6)) % 182.18/182.45 (step @p145 :rule beta-reduce :args ((= (_ (lambda @t9 (and (forall @t221 (or (not (tptp.c @t208 @t1)) @t220)) (forall @t219 (or @t218 (tptp.c @t203 @t1))))) @t21) @t244))) % 182.18/182.45 (step @p146 :rule alpha_equiv :args (@t248 @t241 @t204)) % 182.18/182.45 (step @p147 :rule alpha_equiv :args (@t250 @t241 @t209)) % 182.18/182.45 (step @p148 :rule nary_cong :premises (@p147 @p146) :args (@t251)) % 182.18/182.45 (step @p149 :rule cong :premises (@p148) :args (@t252)) % 182.18/182.45 (step @p150 :rule ho_cong :premises (@p149 @p135)) % 182.18/182.45 (step @p151 :rule trans :premises (@p150 @p145)) % 182.18/182.45 (step @p152 :rule ho_cong :premises (@p151 @p144)) % 182.18/182.45 (step @p153 :rule trans :premises (@p152 @p143)) % 182.18/182.45 (step @p154 :rule cong :premises (@p153) :args (@t253)) % 182.18/182.45 (step @p155 :rule nary_cong :premises (@p154 @p142 @p142) :args (@t255)) % 182.18/182.45 (step @p156 :rule cong :premises (@p155) :args (@t256)) % 182.18/182.45 (step @p157 :rule trans :premises (@p156 @p131)) % 182.18/182.45 (step @p158 :rule cong :premises (@p157) :args (@t257)) % 182.18/182.45 (step @p159 :rule beta-reduce :args ((= @t259 @t194))) % 182.18/182.45 (step @p160 :rule ho_cong :premises (@p159 @p158)) % 182.18/182.45 (step @p161 :rule trans :premises (@p160 @p93)) % 182.18/182.45 (step @p162 :rule refl :args (@t185)) % 182.18/182.45 (step @p163 :rule ho_cong :premises (@p162 @p161)) % 182.18/182.45 (step @p164 :rule trans :premises (@p163 @p81)) % 182.18/182.45 (step @p165 :rule cong :premises (@p164) :args ((not (_ @t185 (_ @t259 @t257))))) % 182.18/182.45 (step @p166 :rule refl :args (@t21)) % 182.18/182.45 (step @p167 :rule bool-and-de-morgan :args (@t239 @t238 true)) % 182.18/182.45 (step @p168 :rule cong :premises (@p167) :args (@t261)) % 182.18/182.45 (step @p169 :rule cong :premises (@p168) :args (@t262)) % 182.18/182.45 (step @p170 :rule exists-elim :args ((= (exists @t111 @t260) @t262))) % 182.18/182.45 (step @p171 :rule trans :premises (@p170 @p169)) % 182.18/182.45 (step @p172 :rule beta-reduce :args ((= (_ @t263 @t6) @t238))) % 182.18/182.45 (step @p173 :rule beta-reduce :args ((= (_ (lambda @t9 (forall @t157 (or (not @t236) @t232))) @t21) @t263))) % 182.18/182.45 (step @p174 :rule alpha_equiv :args (@t250 @t241 (@list @t152))) % 182.18/182.45 (step @p175 :rule cong :premises (@p174) :args (@t264)) % 182.18/182.45 (step @p176 :rule ho_cong :premises (@p175 @p135)) % 182.18/182.45 (step @p177 :rule trans :premises (@p176 @p173)) % 182.18/182.45 (step @p178 :rule ho_cong :premises (@p177 @p144)) % 182.18/182.45 (step @p179 :rule trans :premises (@p178 @p172)) % 182.18/182.45 (step @p180 :rule beta-reduce :args ((= (_ @t263 @t1) @t239))) % 182.18/182.45 (step @p181 :rule refl :args (@t1)) % 182.18/182.45 (step @p182 :rule ho_cong :premises (@p177 @p181)) % 182.18/182.45 (step @p183 :rule trans :premises (@p182 @p180)) % 182.18/182.45 (step @p184 :rule nary_cong :premises (@p183 @p179) :args (@t266)) % 182.18/182.45 (step @p185 :rule cong :premises (@p184) :args ((exists @t111 @t266))) % 182.18/182.45 (step @p186 :rule trans :premises (@p185 @p171)) % 182.18/182.45 (step @p187 :rule refl :args (@t246)) % 182.18/182.45 (step @p188 :rule refl :args (@t109)) % 182.18/182.45 (step @p189 :rule cong :premises (@p188 @p187) :args ((= @t109 @t246))) % 182.18/182.45 (step @p190 :rule symm :premises (@p189)) % 182.18/182.45 (step @p191 :rule eq_resolve :premises (@p188 @p190)) % 182.18/182.45 (step @p192 :rule refl :args (@t245)) % 182.18/182.45 (step @p193 :rule refl :args (@t110)) % 182.18/182.45 (step @p194 :rule cong :premises (@p193 @p192) :args ((= @t110 @t245))) % 182.18/182.45 (step @p195 :rule symm :premises (@p194)) % 182.18/182.45 (step @p196 :rule eq_resolve :premises (@p193 @p195)) % 182.18/182.45 (step @p197 :rule cong :premises (@p196) :args (@t267)) % 182.18/182.45 (step @p198 :rule nary_cong :premises (@p197 @p191) :args (@t268)) % 182.18/182.45 (step @p199 :rule cong :premises (@p198) :args ((forall @t111 @t268))) % 182.18/182.45 (step @p200 :rule bool-impl-elim :args (@t110 @t109)) % 182.18/182.45 (step @p201 :rule cong :premises (@p200) :args (@t112)) % 182.18/182.45 (step @p202 :rule trans :premises (@p201 @p199)) % 182.18/182.45 (step @p203 :rule cong :premises (@p202) :args (@t113)) % 182.18/182.45 (step @p204 :rule trans :premises (@p43 @p203)) % 182.18/182.45 (step @p205 :rule ho_cong :premises (@p204 @p166)) % 182.18/182.45 (step @p206 :rule ho_cong :premises (@p205 @p144)) % 182.18/182.45 (step @p207 :rule ho_cong :premises (@p205 @p181)) % 182.18/182.45 (step @p208 :rule nary_cong :premises (@p207 @p206) :args (@t119)) % 182.18/182.45 (step @p209 :rule cong :premises (@p208) :args (@t120)) % 182.18/182.45 (step @p210 :rule trans :premises (@p209 @p186)) % 182.18/182.45 (step @p211 :rule cong :premises (@p210) :args (@t121)) % 182.18/182.45 (step @p212 :rule trans :premises (@p45 @p211)) % 182.18/182.45 (step @p213 :rule ho_cong :premises (@p212 @p166)) % 182.18/182.45 (step @p214 :rule ho_cong :premises (@p213 @p133)) % 182.18/182.45 (step @p215 :rule beta-reduce :args ((= (_ @t271 @t1) @t248))) % 182.18/182.45 (step @p216 :rule beta-reduce :args ((= (_ (lambda (@list @t1 @t269) (forall @t111 (or @t249 @t270))) @t6) @t271))) % 182.18/182.45 (step @p217 :rule refl :args (@t6)) % 182.18/182.45 (step @p218 :rule alpha_equiv :args (@t264 (@list @t6) (@list @t269))) % 182.18/182.45 (step @p219 :rule ho_cong :premises (@p218 @p217)) % 182.18/182.45 (step @p220 :rule trans :premises (@p219 @p216)) % 182.18/182.45 (step @p221 :rule ho_cong :premises (@p220 @p181)) % 182.18/182.45 (step @p222 :rule trans :premises (@p221 @p215)) % 182.18/182.45 (step @p223 :rule beta-reduce :args ((= (_ @t272 @t6) @t250))) % 182.18/182.45 (step @p224 :rule beta-reduce :args ((= @t273 @t272))) % 182.18/182.45 (step @p225 :rule ho_cong :premises (@p224 @p144)) % 182.18/182.45 (step @p226 :rule trans :premises (@p225 @p223)) % 182.18/182.45 (step @p227 :rule nary_cong :premises (@p226 @p222) :args ((and @t275 @t274))) % 182.18/182.45 (step @p228 :rule ho_cong :premises (@p204 @p144)) % 182.18/182.45 (step @p229 :rule ho_cong :premises (@p228 @p181)) % 182.18/182.45 (step @p230 :rule ho_cong :premises (@p204 @p181)) % 182.18/182.45 (step @p231 :rule ho_cong :premises (@p230 @p144)) % 182.18/182.45 (step @p232 :rule nary_cong :premises (@p231 @p229) :args (@t116)) % 182.18/182.45 (step @p233 :rule trans :premises (@p232 @p227)) % 182.18/182.45 (step @p234 :rule cong :premises (@p233) :args (@t117)) % 182.18/182.45 (step @p235 :rule trans :premises (@p44 @p234)) % 182.18/182.45 (step @p236 :rule ho_cong :premises (@p235 @p166)) % 182.18/182.45 (step @p237 :rule ho_cong :premises (@p236 @p144)) % 182.18/182.45 (step @p238 :rule cong :premises (@p237) :args (@t23)) % 182.18/182.45 (step @p239 :rule nary_cong :premises (@p238 @p214 @p214) :args (@t24)) % 182.18/182.45 (step @p240 :rule cong :premises (@p239) :args (@t26)) % 182.18/182.45 (step @p241 :rule cong :premises (@p240) :args (@t27)) % 182.18/182.45 (step @p242 :rule refl :args (tptp.a)) % 182.18/182.45 (step @p243 :rule refl :args (@t193)) % 182.18/182.45 (step @p244 :rule refl :args (@t63)) % 182.18/182.45 (step @p245 :rule cong :premises (@p244 @p243) :args ((= @t63 @t193))) % 182.18/182.45 (step @p246 :rule symm :premises (@p245)) % 182.18/182.45 (step @p247 :rule eq_resolve :premises (@p244 @p246)) % 182.18/182.45 (step @p248 :rule refl :args (@t258)) % 182.18/182.45 (step @p249 :rule refl :args (@t65)) % 182.18/182.45 (step @p250 :rule cong :premises (@p249 @p248) :args ((= @t65 @t258))) % 182.18/182.45 (step @p251 :rule symm :premises (@p250)) % 182.18/182.45 (step @p252 :rule eq_resolve :premises (@p249 @p251)) % 182.18/182.45 (step @p253 :rule cong :premises (@p252) :args (@t66)) % 182.18/182.45 (step @p254 :rule nary_cong :premises (@p253 @p247) :args (@t67)) % 182.18/182.45 (step @p255 :rule cong :premises (@p254) :args (@t69)) % 182.18/182.45 (step @p256 :rule cong :premises (@p255) :args (@t71)) % 182.18/182.45 (step @p257 :rule trans :premises (@p26 @p256)) % 182.18/182.45 (step @p258 :rule ho_cong :premises (@p257 @p242)) % 182.18/182.45 (step @p259 :rule ho_cong :premises (@p258 @p241)) % 182.18/182.45 (step @p260 :rule refl :args (@t184)) % 182.18/182.45 (step @p261 :rule refl :args (@t36)) % 182.18/182.45 (step @p262 :rule cong :premises (@p261 @p260) :args ((= @t36 @t184))) % 182.18/182.45 (step @p263 :rule symm :premises (@p262)) % 182.18/182.45 (step @p264 :rule eq_resolve :premises (@p261 @p263)) % 182.18/182.45 (step @p265 :rule cong :premises (@p264) :args (@t100)) % 182.18/182.45 (step @p266 :rule cong :premises (@p265) :args (@t102)) % 182.18/182.45 (step @p267 :rule trans :premises (@p38 @p266)) % 182.18/182.45 (step @p268 :rule ho_cong :premises (@p267 @p259)) % 182.18/182.45 (step @p269 :rule cong :premises (@p268) :args (@t28)) % 182.18/182.45 (step @p270 :rule trans :premises (@p269 @p165)) % 182.18/182.45 (step @p271 :rule trans :premises (@p270 @p71)) % 182.18/182.45 (step @p272 :rule eq_resolve :premises (@p10 @p271)) % 182.18/182.45 (step @p273 :rule not_or_elim :premises (@p272) :args (1)) % 182.18/182.45 ; trust TRUST PREPROCESS_HO_ELIM % 182.18/182.45 (step @p274 :rule trust :premises () :args ((= (or @t290 @t166) (or @t282 @t151)))) % 182.18/182.45 (step @p275 :rule refl :args (@t290)) % 182.18/182.45 (step @p276 :rule nary_cong :premises (@p275 @p72) :args (@t291)) % 182.18/182.45 (step @p277 :rule quant-miniscope-or :args ((= (forall @t60 @t292) @t291))) % 182.18/182.45 (step @p278 :rule trans :premises (@p277 @p276)) % 182.18/182.45 (step @p279 :rule beta-reduce :args ((= @t294 @t292))) % 182.18/182.45 (step @p280 :rule cong :premises (@p279) :args (@t295)) % 182.18/182.45 (step @p281 :rule trans :premises (@p280 @p278)) % 182.18/182.45 (step @p282 :rule beta-reduce :args ((= (_ @t185 @t293) @t295))) % 182.18/182.45 (step @p283 :rule trans :premises (@p282 @p281)) % 182.18/182.45 (step @p284 :rule quant-miniscope-or :args ((= (forall @t68 @t296) @t292))) % 182.18/182.45 (step @p285 :rule aci_norm :args ((= @t297 @t296))) % 182.18/182.45 (step @p286 :rule cong :premises (@p285) :args ((forall @t68 @t297))) % 182.18/182.45 (step @p287 :rule trans :premises (@p286 @p284)) % 182.18/182.45 (step @p288 :rule beta-reduce :args ((= @t299 @t290))) % 182.18/182.45 (step @p289 :rule nary_cong :premises (@p87 @p288) :args (@t300)) % 182.18/182.45 (step @p290 :rule cong :premises (@p289) :args (@t301)) % 182.18/182.45 (step @p291 :rule trans :premises (@p290 @p287)) % 182.18/182.45 (step @p292 :rule cong :premises (@p291) :args (@t302)) % 182.18/182.45 (step @p293 :rule beta-reduce :args ((= (_ @t194 @t298) @t302))) % 182.18/182.45 (step @p294 :rule trans :premises (@p293 @p292)) % 182.18/182.45 (step @p295 :rule beta-reduce :args ((= (_ @t306 tptp.spain) @t290))) % 182.18/182.45 (step @p296 :rule refl :args (tptp.spain)) % 182.18/182.45 (step @p297 :rule beta-reduce :args ((= @t313 @t306))) % 182.18/182.45 (step @p298 :rule ho_cong :premises (@p297 @p296)) % 182.18/182.45 (step @p299 :rule trans :premises (@p298 @p295)) % 182.18/182.45 (step @p300 :rule cong :premises (@p299) :args ((lambda @t19 (_ @t313 tptp.spain)))) % 182.18/182.45 (step @p301 :rule ho_cong :premises (@p159 @p300)) % 182.18/182.45 (step @p302 :rule trans :premises (@p301 @p294)) % 182.18/182.45 (step @p303 :rule ho_cong :premises (@p162 @p302)) % 182.18/182.45 (step @p304 :rule trans :premises (@p303 @p283)) % 182.18/182.45 (step @p305 :rule refl :args (tptp.catalunya)) % 182.18/182.45 (step @p306 :rule aci_norm :args ((= (and @t314 @t311) @t312))) % 182.18/182.45 (step @p307 :rule refl :args (@t305)) % 182.18/182.45 (step @p308 :rule cong :premises (@p191) :args (@t315)) % 182.18/182.45 (step @p309 :rule refl :args (@t310)) % 182.18/182.45 (step @p310 :rule nary_cong :premises (@p197 @p309 @p308 @p307) :args (@t316)) % 182.18/182.45 (step @p311 :rule cong :premises (@p310) :args ((forall @t111 @t316))) % 182.18/182.45 (step @p312 :rule aci_norm :args ((= (or @t267 (or @t310 (or @t315 @t305))) @t316))) % 182.18/182.45 (step @p313 :rule bool-and-de-morgan :args (@t109 @t304 true)) % 182.18/182.45 (step @p314 :rule nary_cong :premises (@p309 @p313) :args ((or @t310 (not @t317)))) % 182.18/182.45 (step @p315 :rule bool-and-de-morgan :args (@t309 @t109 (and @t304))) % 182.18/182.45 (step @p316 :rule trans :premises (@p315 @p314)) % 182.18/182.45 (step @p317 :rule refl :args (@t267)) % 182.18/182.45 (step @p318 :rule nary_cong :premises (@p317 @p316) :args ((or @t267 (not (and @t309 @t109 @t304))))) % 182.18/182.45 (step @p319 :rule bool-and-de-morgan :args (@t110 @t309 (and @t109 @t304))) % 182.18/182.45 (step @p320 :rule trans :premises (@p319 @p318)) % 182.18/182.45 (step @p321 :rule trans :premises (@p320 @p312)) % 182.18/182.45 (step @p322 :rule cong :premises (@p321) :args (@t319)) % 182.18/182.45 (step @p323 :rule trans :premises (@p322 @p311)) % 182.18/182.45 (step @p324 :rule cong :premises (@p323) :args (@t320)) % 182.18/182.45 (step @p325 :rule exists-elim :args ((= (exists @t111 @t318) @t320))) % 182.18/182.45 (step @p326 :rule trans :premises (@p325 @p324)) % 182.18/182.45 (step @p327 :rule aci_norm :args ((= (and @t321 @t317) @t318))) % 182.18/182.45 (step @p328 :rule beta-reduce :args ((= (_ @t322 @t6) @t317))) % 182.18/182.45 (step @p329 :rule beta-reduce :args ((= (_ (lambda @t9 (and @t8 (forall @t281 (or @t308 @t303)))) @t21) @t322))) % 182.18/182.45 (step @p330 :rule alpha_equiv :args (@t240 @t241 (@list @t278))) % 182.18/182.45 (step @p331 :rule nary_cong :premises (@p58 @p330) :args (@t323)) % 182.18/182.45 (step @p332 :rule cong :premises (@p331) :args (@t324)) % 182.18/182.45 (step @p333 :rule ho_cong :premises (@p332 @p135)) % 182.18/182.45 (step @p334 :rule trans :premises (@p333 @p329)) % 182.18/182.45 (step @p335 :rule ho_cong :premises (@p334 @p144)) % 182.18/182.45 (step @p336 :rule trans :premises (@p335 @p328)) % 182.18/182.45 (step @p337 :rule beta-reduce :args ((= (_ @t322 @t1) @t321))) % 182.18/182.45 (step @p338 :rule ho_cong :premises (@p334 @p181)) % 182.18/182.45 (step @p339 :rule trans :premises (@p338 @p337)) % 182.18/182.45 (step @p340 :rule nary_cong :premises (@p339 @p336) :args (@t326)) % 182.18/182.45 (step @p341 :rule trans :premises (@p340 @p327)) % 182.18/182.45 (step @p342 :rule cong :premises (@p341) :args (@t327)) % 182.18/182.45 (step @p343 :rule trans :premises (@p342 @p326)) % 182.18/182.45 (step @p344 :rule beta-reduce :args ((= (_ @t328 @t6) @t314))) % 182.18/182.45 (step @p345 :rule beta-reduce :args ((= @t329 @t328))) % 182.18/182.45 (step @p346 :rule ho_cong :premises (@p345 @p144)) % 182.18/182.45 (step @p347 :rule trans :premises (@p346 @p344)) % 182.18/182.45 (step @p348 :rule nary_cong :premises (@p347 @p343) :args ((and (_ @t329 @t6) @t327))) % 182.18/182.45 (step @p349 :rule trans :premises (@p348 @p306)) % 182.18/182.45 (step @p350 :rule bool-double-not-elim :args (@t240)) % 182.18/182.45 (step @p351 :rule beta-reduce :args ((= (_ @t330 @t6) @t242))) % 182.18/182.45 (step @p352 :rule beta-reduce :args ((= @t331 @t330))) % 182.18/182.45 (step @p353 :rule ho_cong :premises (@p352 @p144)) % 182.18/182.45 (step @p354 :rule trans :premises (@p353 @p351)) % 182.18/182.45 (step @p355 :rule cong :premises (@p354) :args (@t332)) % 182.18/182.45 (step @p356 :rule trans :premises (@p355 @p350)) % 182.18/182.45 (step @p357 :rule refl :args (@t8)) % 182.18/182.45 (step @p358 :rule nary_cong :premises (@p357 @p356) :args ((and @t8 @t332))) % 182.18/182.45 (step @p359 :rule ho_cong :premises (@p212 @p181)) % 182.18/182.45 (step @p360 :rule ho_cong :premises (@p359 @p144)) % 182.18/182.45 (step @p361 :rule cong :premises (@p360) :args (@t125)) % 182.18/182.45 (step @p362 :rule nary_cong :premises (@p357 @p361) :args (@t126)) % 182.18/182.45 (step @p363 :rule trans :premises (@p362 @p358)) % 182.18/182.45 (step @p364 :rule cong :premises (@p363) :args (@t127)) % 182.18/182.45 (step @p365 :rule trans :premises (@p47 @p364)) % 182.18/182.45 (step @p366 :rule ho_cong :premises (@p365 @p166)) % 182.18/182.45 (step @p367 :rule ho_cong :premises (@p366 @p144)) % 182.18/182.45 (step @p368 :rule ho_cong :premises (@p366 @p181)) % 182.18/182.45 (step @p369 :rule nary_cong :premises (@p368 @p367) :args (@t131)) % 182.18/182.45 (step @p370 :rule cong :premises (@p369) :args (@t132)) % 182.18/182.45 (step @p371 :rule cong :premises (@p222) :args (@t333)) % 182.18/182.45 (step @p372 :rule nary_cong :premises (@p226 @p371) :args ((and @t275 @t333))) % 182.18/182.45 (step @p373 :rule cong :premises (@p229) :args (@t122)) % 182.18/182.45 (step @p374 :rule nary_cong :premises (@p231 @p373) :args (@t128)) % 182.18/182.45 (step @p375 :rule trans :premises (@p374 @p372)) % 182.18/182.45 (step @p376 :rule cong :premises (@p375) :args (@t129)) % 182.18/182.45 (step @p377 :rule trans :premises (@p48 @p376)) % 182.18/182.45 (step @p378 :rule ho_cong :premises (@p377 @p181)) % 182.18/182.45 (step @p379 :rule ho_cong :premises (@p378 @p144)) % 182.18/182.45 (step @p380 :rule nary_cong :premises (@p379 @p370) :args (@t134)) % 182.18/182.45 (step @p381 :rule trans :premises (@p380 @p349)) % 182.18/182.45 (step @p382 :rule cong :premises (@p381) :args (@t135)) % 182.18/182.45 (step @p383 :rule trans :premises (@p49 @p382)) % 182.18/182.45 (step @p384 :rule ho_cong :premises (@p383 @p305)) % 182.18/182.45 (step @p385 :rule ho_cong :premises (@p384 @p296)) % 182.18/182.45 (step @p386 :rule cong :premises (@p385) :args (@t20)) % 182.18/182.45 (step @p387 :rule ho_cong :premises (@p258 @p386)) % 182.18/182.45 (step @p388 :rule ho_cong :premises (@p267 @p387)) % 182.18/182.45 (step @p389 :rule trans :premises (@p388 @p304)) % 182.18/182.45 (step @p390 :rule trans :premises (@p389 @p274)) % 182.18/182.45 (step @p391 :rule eq_resolve :premises (@p7 @p390)) % 182.18/182.45 (step @p392 :rule reordering :premises (@p391) :args ((or @t151 @t282))) % 182.18/182.45 (step @p393 :rule chain_m_resolution :premises (@p392 @p273) :args (@t282 @t334 (@list @t151))) % 182.18/182.45 (step @p394 :rule cnf_and_pos :args (@t282 2)) % 182.18/182.45 (step @p395 :rule reordering :premises (@p394) :args ((or @t276 (not @t282)))) % 182.18/182.45 (step @p396 :rule chain_m_resolution :premises (@p395 @p393) :args (@t276 @t335 (@list @t282))) % 182.18/182.45 (step @p397 :rule skolemize :premises (@p396)) % 182.18/182.45 (step @p398 :rule cnf_or_neg :args (@t338 1)) % 182.18/182.45 (step @p399 :rule chain_m_resolution :premises (@p398 @p397) :args ((not @t337) @t334 (@list @t338))) % 182.18/182.45 (step @p400 :rule cnf_or_pos :args (@t342)) % 182.18/182.45 (step @p401 :rule reordering :premises (@p400) :args ((or @t337 @t341 (not @t342)))) % 182.18/182.45 (step @p402 :rule chain_m_resolution :premises (@p401 @p399 @p70) :args (@t341 (@list true false) (@list @t337 @t342))) % 182.18/182.45 (step @p403 :rule not_or_elim :premises (@p272) :args (0)) % 182.18/182.45 (step @p404 :rule not_not_elim :premises (@p403)) % 182.18/182.45 (step @p405 :rule aci_norm :args ((= (or @t348 false false) @t348))) % 182.18/182.45 (step @p406 :rule evaluate :args ((not true))) % 182.18/182.45 (step @p407 :rule quant-unused-vars :args ((= (forall @t157 true) true))) % 182.18/182.45 (step @p408 :rule bool-or-taut2 :args (false @t154 false false)) % 182.18/182.45 (step @p409 :rule cong :premises (@p408) :args (@t349)) % 182.18/182.45 (step @p410 :rule trans :premises (@p409 @p407)) % 182.18/182.45 (step @p411 :rule cong :premises (@p410) :args (@t350)) % 182.18/182.45 (step @p412 :rule trans :premises (@p411 @p406)) % 182.18/182.45 (step @p413 :rule refl :args (@t348)) % 182.18/182.45 (step @p414 :rule nary_cong :premises (@p413 @p412 @p412) :args (@t351)) % 182.18/182.45 (step @p415 :rule trans :premises (@p414 @p405)) % 182.18/182.45 (step @p416 :rule refl :args (@t164)) % 182.18/182.45 (step @p417 :rule cong :premises (@p416 @p415) :args ((=> @t164 @t351))) % 182.18/182.45 (assume-push @p459 @t164) % 182.18/182.45 (step @p419 :rule instantiate :premises (@p404) :args ((@list tptp.france tptp.catalunya tptp.catalunya tptp.catalunya tptp.france))) % 182.18/182.45 (step-pop @p460 :rule scope :premises (@p419)) % 182.18/182.45 (step @p420 :rule process_scope :premises (@p460) :args (@t351)) % 182.18/182.45 (step @p422 :rule eq_resolve :premises (@p420 @p417)) % 182.18/182.45 (step @p423 :rule implies_elim :premises (@p422)) % 182.18/182.45 (step @p424 :rule chain_m_resolution :premises (@p423 @p404) :args (@t348 @t335 @t352)) % 182.18/182.45 (step @p425 :rule cnf_and_pos :args (@t348 1)) % 182.18/182.45 (step @p426 :rule reordering :premises (@p425) :args ((or @t346 (not @t348)))) % 182.18/182.46 (step @p427 :rule chain_m_resolution :premises (@p426 @p424) :args (@t346 @t335 (@list @t348))) % 182.18/182.46 ; trust TRUST PREPROCESS_HO_ELIM % 182.18/182.46 (step @p428 :rule trust :premises () :args ((= (forall @t4 @t353) (forall @t4 (_ @t139 @t140 @t1))))) % 182.18/182.46 (step @p429 :rule refl :args (@t353)) % 182.18/182.46 (step @p430 :rule refl :args (@t3)) % 182.18/182.46 (step @p431 :rule cong :premises (@p430 @p429) :args ((= @t3 @t353))) % 182.18/182.46 (step @p432 :rule symm :premises (@p431)) % 182.18/182.46 (step @p433 :rule eq_resolve :premises (@p430 @p432)) % 182.18/182.46 (step @p434 :rule cong :premises (@p433) :args (@t5)) % 182.18/182.46 (step @p435 :rule trans :premises (@p434 @p428)) % 182.18/182.46 (step @p436 :rule eq_resolve :premises (@p2 @p435)) % 182.18/182.46 (step @p437 :rule instantiate :premises (@p436) :args ((@list tptp.catalunya))) % 182.18/182.46 (step @p438 :rule cnf_or_pos :args (@t346)) % 182.18/182.46 (step @p439 :rule reordering :premises (@p438) :args ((or @t345 @t343 (not @t346)))) % 182.18/182.46 (step @p440 :rule chain_m_resolution :premises (@p439 @p437 @p427) :args (@t343 (@list false false) (@list @t344 @t346))) % 182.18/182.46 (step @p441 :rule cnf_or_pos :args (@t354)) % 182.18/182.46 (step @p442 :rule reordering :premises (@p441) :args ((or @t347 @t340 @t355))) % 182.18/182.46 (step @p443 :rule chain_m_resolution :premises (@p442 @p440 @p402) :args (@t355 @t356 (@list @t343 @t340))) % 182.18/182.46 (step @p444 :rule aci_norm :args ((= (or @t357 false false) @t357))) % 182.18/182.46 (step @p445 :rule refl :args (@t357)) % 182.18/182.46 (step @p446 :rule nary_cong :premises (@p445 @p412 @p412) :args (@t358)) % 182.18/182.46 (step @p447 :rule trans :premises (@p446 @p444)) % 182.18/182.46 (step @p448 :rule cong :premises (@p416 @p447) :args ((=> @t164 @t358))) % 182.18/182.46 (assume-push @p461 @t164) % 182.18/182.46 (step @p450 :rule instantiate :premises (@p404) :args ((@list tptp.france @t149 tptp.catalunya tptp.catalunya tptp.france))) % 182.18/182.46 (step-pop @p462 :rule scope :premises (@p450)) % 182.18/182.46 (step @p451 :rule process_scope :premises (@p462) :args (@t358)) % 182.18/182.46 (step @p453 :rule eq_resolve :premises (@p451 @p448)) % 182.18/182.46 (step @p454 :rule implies_elim :premises (@p453)) % 182.18/182.46 (step @p455 :rule chain_m_resolution :premises (@p454 @p404) :args (@t357 @t335 @t352)) % 182.18/182.46 (step @p456 :rule cnf_and_pos :args (@t357 0)) % 182.18/182.46 (step @p457 :rule reordering :premises (@p456) :args ((or @t354 (not @t357)))) % 182.18/182.46 (step @p458 false :rule chain_m_resolution :premises (@p457 @p455 @p443) :args (false @t356 (@list @t357 @t354))) % 182.18/182.46 ) % 182.18/182.46 % SZS output end Proof % 182.18/182.46 % cvc5 exiting %------------------------------------------------------------------------------