%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : GEG006^1 : 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 : n027.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 168.92s 169.59s % Output : Proof 168.92s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : GEG006^1 : 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 % 0.17/0.34 % Computer : n027.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 : Mon Jun 1 23:02:51 EDT 2026 % 0.17/0.34 % CPUTime : % 0.33/0.51 %----Proving TH0 % 168.92/169.59 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 168.92/169.59 --- 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... % 168.92/169.59 --- 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... % 168.92/169.59 --- Run --ho-elim --full-saturate-quant at 18s... % 168.92/169.59 --- Run --ho-elim --no-e-matching --full-saturate-quant at 12s... % 168.92/169.59 % SZS status Theorem % 168.92/169.59 % SZS output start Proof % 168.92/169.59 ( % 168.92/169.59 (declare-sort tptp.reg 0) % 168.92/169.59 (declare-sort $$unsorted 0) % 168.92/169.59 (declare-sort tptp.mu 0) % 168.92/169.59 (declare-const tptp.c (-> tptp.reg tptp.reg Bool)) % 168.92/169.59 (declare-const tptp.france tptp.reg) % 168.92/169.59 (declare-const tptp.catalunya tptp.reg) % 168.92/169.59 (declare-const tptp.a (-> $$unsorted $$unsorted Bool)) % 168.92/169.59 (declare-const tptp.spain tptp.reg) % 168.92/169.59 (declare-const tptp.fool (-> $$unsorted $$unsorted Bool)) % 168.92/169.59 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 168.92/169.59 (declare-const tptp.paris tptp.reg) % 168.92/169.59 (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" $$unsorted)) (= _let_2 _let_1))))) % 168.92/169.59 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$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))))))) % 168.92/169.59 (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)))))) % 168.92/169.59 (define tptp.mor () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 168.92/169.59 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 168.92/169.59 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 168.92/169.59 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 168.92/169.59 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimplies _let_2) _let_3)) (_ (_ tptp.mimplies _let_3) _let_2)) _let_1)))))) % 168.92/169.59 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 168.92/169.59 (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))))))) % 168.92/169.59 (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))))))) % 168.92/169.59 (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)))))) % 168.92/169.59 (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)))))) % 168.92/169.59 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 168.92/169.59 (define tptp.mbox () (let ((_let_1 (@var "V" $$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))))))))) % 168.92/169.59 (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)))))) % 168.92/169.59 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 168.92/169.59 (define tptp.msymmetric () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 168.92/169.59 (define tptp.mserial () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 168.92/169.59 (define tptp.mtransitive () (let ((_let_1 (@var "U" $$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)))))))))) % 168.92/169.59 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (_ (_ _let_3 _let_2) _let_1)))))))))) % 168.92/169.59 (define tptp.mpartially_functional () (let ((_let_1 (@var "U" $$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)))))))))) % 168.92/169.59 (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 $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3) (exists (@list _let_2) (and (_ _let_5 _let_2) (forall (@list _let_1) (=> (_ _let_5 _let_1) (= _let_2 _let_1))))))))))))) % 168.92/169.59 (define tptp.mweakly_dense () (let ((_let_1 (@var "T" $$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)))))))))))) % 168.92/169.59 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_1) (_ _let_5 _let_2)) (or (_ (_ _let_3 _let_1) _let_2) (= _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1))))))))))) % 168.92/169.59 (define tptp.mweakly_directed () (let ((_let_1 (@var "V" $$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" $$unsorted))) (let ((_let_6 (_ _let_3 _let_5))) (lambda (@list _let_3) (forall (@list _let_5 _let_4 _let_2) (=> (and (_ _let_6 _let_4) (_ _let_6 _let_2)) (exists (@list _let_1) (and (_ (_ _let_3 _let_4) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))))))) % 168.92/169.59 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 168.92/169.59 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 168.92/169.59 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 168.92/169.59 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 168.92/169.59 (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)))))) % 168.92/169.59 (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))))))))) % 168.92/169.59 (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)))))) % 168.92/169.59 (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))))))))) % 168.92/169.59 (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))))))) % 168.92/169.59 (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))))))) % 168.92/169.59 (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))))))) % 168.92/169.59 (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)))))))))) % 168.92/169.59 (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))))))))))) % 168.92/169.59 (define @t1 () (@var "X" tptp.reg)) % 168.92/169.59 (define @t2 () (_ tptp.c @t1)) % 168.92/169.59 (define @t3 () (@var "Y" tptp.reg)) % 168.92/169.59 (define @t4 () (_ @t2 @t3)) % 168.92/169.59 (define @t5 () (@list @t1 @t3)) % 168.92/169.59 (define @t6 () (@var "__flatten_var_0" $$unsorted)) % 168.92/169.59 (define @t7 () (@var "A" (-> $$unsorted Bool))) % 168.92/169.59 (define @t8 () (_ tptp.mbox tptp.fool)) % 168.92/169.59 (define @t9 () (_ @t8 @t7)) % 168.92/169.59 (define @t10 () (_ tptp.mimplies @t9)) % 168.92/169.59 (define @t11 () (@list @t7 @t6)) % 168.92/169.59 (define @t12 () (@var "Phi" (-> $$unsorted Bool))) % 168.92/169.59 (define @t13 () (_ tptp.mbox tptp.a)) % 168.92/169.59 (define @t14 () (@list (@var "X" $$unsorted))) % 168.92/169.59 (define @t15 () (lambda @t14 (_ (_ tptp.tpp tptp.catalunya) tptp.spain))) % 168.92/169.59 (define @t16 () (lambda @t14 (_ (_ tptp.ntpp tptp.paris) tptp.france))) % 168.92/169.59 (define @t17 () (and (_ (_ tptp.o tptp.catalunya) tptp.spain) (_ (_ tptp.o tptp.france) tptp.paris))) % 168.92/169.59 (define @t18 () (lambda @t14 @t17)) % 168.92/169.59 (define @t19 () (not (_ tptp.mvalid (_ @t13 @t18)))) % 168.92/169.59 (define @t20 () (@var "Y" tptp.mu)) % 168.92/169.59 (define @t21 () (@var "X" tptp.mu)) % 168.92/169.59 (define @t22 () (@var "W" $$unsorted)) % 168.92/169.59 (define @t23 () (lambda (@list @t21 @t20 @t22) (= @t21 @t20))) % 168.92/169.59 (define @t24 () (@var "Y" (-> $$unsorted Bool))) % 168.92/169.59 (define @t25 () (@var "X" (-> $$unsorted Bool))) % 168.92/169.59 (define @t26 () (lambda (@list @t25 @t24 @t22) (= (_ @t25 @t22) (_ @t24 @t22)))) % 168.92/169.59 (define @t27 () (_ @t12 @t22)) % 168.92/169.59 (define @t28 () (not @t27)) % 168.92/169.59 (define @t29 () (@list @t12 @t22)) % 168.92/169.59 (define @t30 () (lambda @t29 @t28)) % 168.92/169.59 (define @t31 () (@var "Psi" (-> $$unsorted Bool))) % 168.92/169.59 (define @t32 () (lambda (@list @t12 @t31 @t22) (or @t27 (_ @t31 @t22)))) % 168.92/169.59 (define @t33 () (_ tptp.mnot @t31)) % 168.92/169.59 (define @t34 () (_ tptp.mnot @t12)) % 168.92/169.59 (define @t35 () (_ tptp.mor @t34)) % 168.92/169.59 (define @t36 () (@list @t12 @t31 @t6)) % 168.92/169.59 (define @t37 () (lambda @t36 (_ (_ tptp.mnot (_ @t35 @t33)) @t6))) % 168.92/169.59 (define @t38 () (lambda @t36 (_ (_ @t35 @t31) @t6))) % 168.92/169.59 (define @t39 () (lambda @t36 (_ (_ (_ tptp.mor @t33) @t12) @t6))) % 168.92/169.59 (define @t40 () (lambda @t36 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t12) @t31)) (_ (_ tptp.mimplies @t31) @t12)) @t6))) % 168.92/169.59 (define @t41 () (lambda @t36 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t12) @t31)) @t6))) % 168.92/169.59 (define @t42 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 168.92/169.59 (define @t43 () (_ @t42 @t21)) % 168.92/169.59 (define @t44 () (lambda (@list @t42 @t22) (forall (@list @t21) (_ @t43 @t22)))) % 168.92/169.59 (define @t45 () (@var "P" (-> $$unsorted Bool))) % 168.92/169.59 (define @t46 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 168.92/169.59 (define @t47 () (_ @t46 @t45)) % 168.92/169.59 (define @t48 () (lambda (@list @t46 @t22) (forall (@list @t45) (_ @t47 @t22)))) % 168.92/169.59 (define @t49 () (lambda (@list @t42 @t6) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list @t21 @t6) (_ (_ tptp.mnot @t43) @t6)))) @t6))) % 168.92/169.59 (define @t50 () (lambda (@list @t46 @t6) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t45 @t6) (_ (_ tptp.mnot @t47) @t6)))) @t6))) % 168.92/169.59 (define @t51 () (@list @t22)) % 168.92/169.59 (define @t52 () (lambda @t51 true)) % 168.92/169.59 (define @t53 () (@var "V" $$unsorted)) % 168.92/169.59 (define @t54 () (_ @t12 @t53)) % 168.92/169.59 (define @t55 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 168.92/169.59 (define @t56 () (_ (_ @t55 @t22) @t53)) % 168.92/169.59 (define @t57 () (not @t56)) % 168.92/169.59 (define @t58 () (or @t57 @t54)) % 168.92/169.59 (define @t59 () (@list @t53)) % 168.92/169.59 (define @t60 () (forall @t59 @t58)) % 168.92/169.59 (define @t61 () (@list @t55 @t12 @t22)) % 168.92/169.59 (define @t62 () (lambda @t61 @t60)) % 168.92/169.59 (define @t63 () (lambda (@list @t55 @t12 @t6) (_ (_ tptp.mnot (_ (_ tptp.mbox @t55) @t34)) @t6))) % 168.92/169.59 (define @t64 () (@var "S" $$unsorted)) % 168.92/169.59 (define @t65 () (_ @t55 @t64)) % 168.92/169.59 (define @t66 () (@list @t64)) % 168.92/169.59 (define @t67 () (@list @t55)) % 168.92/169.59 (define @t68 () (lambda @t67 (forall @t66 (_ @t65 @t64)))) % 168.92/169.59 (define @t69 () (@var "T" $$unsorted)) % 168.92/169.59 (define @t70 () (_ @t55 @t69)) % 168.92/169.59 (define @t71 () (_ @t65 @t69)) % 168.92/169.59 (define @t72 () (lambda @t67 (forall (@list @t64 @t69) (=> @t71 (_ @t70 @t64))))) % 168.92/169.59 (define @t73 () (@list @t69)) % 168.92/169.59 (define @t74 () (lambda @t67 (forall @t66 (exists @t73 @t71)))) % 168.92/169.59 (define @t75 () (@var "U" $$unsorted)) % 168.92/169.59 (define @t76 () (_ @t65 @t75)) % 168.92/169.59 (define @t77 () (_ @t70 @t75)) % 168.92/169.59 (define @t78 () (@list @t64 @t69 @t75)) % 168.92/169.59 (define @t79 () (lambda @t67 (forall @t78 (=> (and @t71 @t77) @t76)))) % 168.92/169.59 (define @t80 () (and @t71 @t76)) % 168.92/169.59 (define @t81 () (lambda @t67 (forall @t78 (=> @t80 @t77)))) % 168.92/169.59 (define @t82 () (= @t69 @t75)) % 168.92/169.59 (define @t83 () (lambda @t67 (forall @t78 (=> @t80 @t82)))) % 168.92/169.59 (define @t84 () (@list @t75)) % 168.92/169.59 (define @t85 () (lambda @t67 (forall @t66 (exists @t73 (and @t71 (forall @t84 (=> @t76 @t82))))))) % 168.92/169.59 (define @t86 () (_ @t55 @t75)) % 168.92/169.59 (define @t87 () (_ @t86 @t69)) % 168.92/169.59 (define @t88 () (lambda @t67 (forall @t78 (=> @t71 (exists @t84 (and @t76 @t87)))))) % 168.92/169.59 (define @t89 () (lambda @t67 (forall @t78 (=> @t80 (or @t77 @t82 @t87))))) % 168.92/169.59 (define @t90 () (lambda @t67 (forall @t78 (=> @t80 (exists @t59 (and (_ @t70 @t53) (_ @t86 @t53))))))) % 168.92/169.59 (define @t91 () (forall @t51 @t27)) % 168.92/169.59 (define @t92 () (@list @t12)) % 168.92/169.59 (define @t93 () (lambda @t92 @t91)) % 168.92/169.59 (define @t94 () (lambda @t92 (forall @t51 @t28))) % 168.92/169.59 (define @t95 () (lambda @t92 (exists @t51 @t27))) % 168.92/169.59 (define @t96 () (lambda @t92 (exists @t51 @t28))) % 168.92/169.59 (define @t97 () (lambda @t5 (not @t4))) % 168.92/169.59 (define @t98 () (@var "Z" tptp.reg)) % 168.92/169.59 (define @t99 () (_ tptp.c @t98)) % 168.92/169.59 (define @t100 () (_ @t99 @t3)) % 168.92/169.59 (define @t101 () (_ @t99 @t1)) % 168.92/169.59 (define @t102 () (@list @t98)) % 168.92/169.59 (define @t103 () (forall @t102 (=> @t101 @t100))) % 168.92/169.59 (define @t104 () (lambda @t5 @t103)) % 168.92/169.59 (define @t105 () (_ (_ tptp.p @t3) @t1)) % 168.92/169.59 (define @t106 () (_ (_ tptp.p @t1) @t3)) % 168.92/169.59 (define @t107 () (lambda @t5 (and @t106 @t105))) % 168.92/169.59 (define @t108 () (_ tptp.p @t98)) % 168.92/169.59 (define @t109 () (and (_ @t108 @t1) (_ @t108 @t3))) % 168.92/169.59 (define @t110 () (exists @t102 @t109)) % 168.92/169.59 (define @t111 () (lambda @t5 @t110)) % 168.92/169.59 (define @t112 () (not @t105)) % 168.92/169.59 (define @t113 () (_ (_ tptp.o @t1) @t3)) % 168.92/169.59 (define @t114 () (lambda @t5 (and @t113 (not @t106) @t112))) % 168.92/169.59 (define @t115 () (not @t113)) % 168.92/169.59 (define @t116 () (and @t4 @t115)) % 168.92/169.59 (define @t117 () (lambda @t5 @t116)) % 168.92/169.59 (define @t118 () (and @t106 @t112)) % 168.92/169.59 (define @t119 () (lambda @t5 @t118)) % 168.92/169.59 (define @t120 () (_ tptp.ec @t98)) % 168.92/169.59 (define @t121 () (and (_ @t120 @t1) (_ @t120 @t3))) % 168.92/169.59 (define @t122 () (exists @t102 @t121)) % 168.92/169.59 (define @t123 () (_ (_ tptp.pp @t1) @t3)) % 168.92/169.59 (define @t124 () (and @t123 @t122)) % 168.92/169.59 (define @t125 () (lambda @t5 @t124)) % 168.92/169.59 (define @t126 () (not @t122)) % 168.92/169.59 (define @t127 () (and @t123 @t126)) % 168.92/169.59 (define @t128 () (lambda @t5 @t127)) % 168.92/169.59 (define @t129 () (@list @t22 @t53)) % 168.92/169.59 (define @t130 () (forall @t129 (not (_ (@const 2 (-> (@ho-elim-sort (-> $$unsorted Bool)) $$unsorted Bool)) (_ (@const 1 (-> (@ho-elim-sort (-> $$unsorted $$unsorted Bool)) $$unsorted (@ho-elim-sort (-> $$unsorted Bool)))) (@const 0 (@ho-elim-sort (-> $$unsorted $$unsorted Bool))) @t22) @t53)))) % 168.92/169.59 (define @t131 () (@var "BOUND_VARIABLE_8328" tptp.reg)) % 168.92/169.59 (define @t132 () (@const 3 (@ho-elim-sort (-> tptp.reg tptp.reg Bool)))) % 168.92/169.59 (define @t133 () (@const 4 (-> (@ho-elim-sort (-> tptp.reg tptp.reg Bool)) tptp.reg (@ho-elim-sort (-> tptp.reg Bool))))) % 168.92/169.59 (define @t134 () (_ @t133 @t132 @t131)) % 168.92/169.59 (define @t135 () (@const 5 (-> (@ho-elim-sort (-> tptp.reg Bool)) tptp.reg Bool))) % 168.92/169.59 (define @t136 () (_ @t135 @t134 tptp.paris)) % 168.92/169.59 (define @t137 () (_ @t135 @t134 @t98)) % 168.92/169.59 (define @t138 () (not @t137)) % 168.92/169.59 (define @t139 () (@list @t131)) % 168.92/169.59 (define @t140 () (_ @t135 @t134 tptp.france)) % 168.92/169.59 (define @t141 () (forall @t102 (or (not (forall @t139 (or @t138 @t140))) (not (forall @t139 (or @t138 @t136)))))) % 168.92/169.59 (define @t142 () (not @t141)) % 168.92/169.59 (define @t143 () (_ @t135 @t134 tptp.spain)) % 168.92/169.59 (define @t144 () (_ @t135 @t134 tptp.catalunya)) % 168.92/169.59 (define @t145 () (forall @t102 (or (not (forall @t139 (or @t138 @t144))) (not (forall @t139 (or @t138 @t143)))))) % 168.92/169.59 (define @t146 () (not @t145)) % 168.92/169.59 (define @t147 () (not (tptp.a @t22 @t53))) % 168.92/169.59 (define @t148 () (forall @t129 @t147)) % 168.92/169.59 (define @t149 () (tptp.c @t131 tptp.paris)) % 168.92/169.59 (define @t150 () (tptp.c @t131 @t98)) % 168.92/169.59 (define @t151 () (not @t150)) % 168.92/169.59 (define @t152 () (tptp.c @t131 tptp.france)) % 168.92/169.59 (define @t153 () (not (forall @t139 (or @t151 @t152)))) % 168.92/169.59 (define @t154 () (not (forall @t102 (or @t153 (not (forall @t139 (or @t151 @t149))))))) % 168.92/169.59 (define @t155 () (tptp.c @t131 tptp.spain)) % 168.92/169.59 (define @t156 () (tptp.c @t131 tptp.catalunya)) % 168.92/169.59 (define @t157 () (not (forall @t139 (or @t151 @t156)))) % 168.92/169.59 (define @t158 () (not (forall @t102 (or @t157 (not (forall @t139 (or @t151 @t155))))))) % 168.92/169.59 (define @t159 () (and @t158 @t154)) % 168.92/169.59 (define @t160 () (forall @t59 @t147)) % 168.92/169.59 (define @t161 () (forall @t51 @t160)) % 168.92/169.59 (define @t162 () (or @t159 @t161)) % 168.92/169.59 (define @t163 () (or @t159 @t160)) % 168.92/169.59 (define @t164 () (lambda @t51 @t163)) % 168.92/169.59 (define @t165 () (_ @t164 @t22)) % 168.92/169.59 (define @t166 () (forall @t51 @t165)) % 168.92/169.59 (define @t167 () (_ @t12 @t22)) % 168.92/169.59 (define @t168 () (lambda @t92 (forall @t51 @t167))) % 168.92/169.59 (define @t169 () (or @t159 @t147)) % 168.92/169.59 (define @t170 () (or @t147 @t159)) % 168.92/169.59 (define @t171 () (lambda @t14 @t159)) % 168.92/169.59 (define @t172 () (_ @t171 @t53)) % 168.92/169.59 (define @t173 () (or @t147 @t172)) % 168.92/169.59 (define @t174 () (forall @t59 @t173)) % 168.92/169.59 (define @t175 () (lambda @t51 @t174)) % 168.92/169.59 (define @t176 () (_ @t12 @t53)) % 168.92/169.59 (define @t177 () (lambda @t29 (forall @t59 (or @t147 @t176)))) % 168.92/169.59 (define @t178 () (tptp.c @t131 @t3)) % 168.92/169.59 (define @t179 () (forall @t139 (or @t151 @t178))) % 168.92/169.59 (define @t180 () (not @t179)) % 168.92/169.59 (define @t181 () (@list @t3)) % 168.92/169.59 (define @t182 () (lambda @t181 (not (forall @t102 (or @t153 @t180))))) % 168.92/169.59 (define @t183 () (tptp.c @t131 @t1)) % 168.92/169.59 (define @t184 () (forall @t139 (or @t151 @t183))) % 168.92/169.59 (define @t185 () (forall @t102 (or (not @t184) @t180))) % 168.92/169.59 (define @t186 () (not @t185)) % 168.92/169.59 (define @t187 () (lambda @t5 @t186)) % 168.92/169.59 (define @t188 () (_ @t187 tptp.france)) % 168.92/169.59 (define @t189 () (lambda @t181 (not (forall @t102 (or @t157 @t180))))) % 168.92/169.59 (define @t190 () (_ @t187 tptp.catalunya)) % 168.92/169.59 (define @t191 () (and (_ @t190 tptp.spain) (_ @t188 tptp.paris))) % 168.92/169.59 (define @t192 () (lambda @t14 @t191)) % 168.92/169.59 (define @t193 () (_ @t55 @t22 @t53)) % 168.92/169.59 (define @t194 () (_ (lambda @t61 (forall @t59 (or (not @t193) @t176))) tptp.a)) % 168.92/169.59 (define @t195 () (and @t184 @t179)) % 168.92/169.59 (define @t196 () (forall @t102 (not @t195))) % 168.92/169.59 (define @t197 () (not @t196)) % 168.92/169.59 (define @t198 () (lambda @t181 @t179)) % 168.92/169.59 (define @t199 () (tptp.c @t98 @t3)) % 168.92/169.59 (define @t200 () (tptp.c @t98 @t1)) % 168.92/169.59 (define @t201 () (not @t200)) % 168.92/169.59 (define @t202 () (forall @t102 (or @t201 @t199))) % 168.92/169.59 (define @t203 () (@list @t98)) % 168.92/169.59 (define @t204 () (@list @t131)) % 168.92/169.59 (define @t205 () (lambda @t5 @t202)) % 168.92/169.59 (define @t206 () (_ @t205 @t98)) % 168.92/169.59 (define @t207 () (and (_ @t206 @t1) (_ @t206 @t3))) % 168.92/169.59 (define @t208 () (not @t101)) % 168.92/169.59 (define @t209 () (or @t208 @t100)) % 168.92/169.59 (define @t210 () (_ @t133 @t132 @t98)) % 168.92/169.59 (define @t211 () (_ @t135 @t210 tptp.catalunya)) % 168.92/169.59 (define @t212 () (_ @t135 @t210 tptp.spain)) % 168.92/169.59 (define @t213 () (not @t212)) % 168.92/169.59 (define @t214 () (not @t211)) % 168.92/169.59 (define @t215 () (forall @t102 (or @t214 @t212))) % 168.92/169.59 (define @t216 () (@var "BOUND_VARIABLE_8441" tptp.reg)) % 168.92/169.59 (define @t217 () (not (_ @t135 @t134 @t216))) % 168.92/169.59 (define @t218 () (not (forall @t139 (or @t217 @t137)))) % 168.92/169.59 (define @t219 () (@list @t216)) % 168.92/169.59 (define @t220 () (and (not (forall @t102 (or @t214 (not (forall @t219 (or @t218 (not (forall @t139 (or @t217 @t144)))))) @t213 (not (forall @t219 (or @t218 (not (forall @t139 (or @t217 @t143))))))))) @t215 (not (forall @t102 (or @t213 @t211))))) % 168.92/169.59 (define @t221 () (tptp.c @t98 tptp.catalunya)) % 168.92/169.59 (define @t222 () (tptp.c @t98 tptp.spain)) % 168.92/169.59 (define @t223 () (not @t222)) % 168.92/169.59 (define @t224 () (not @t221)) % 168.92/169.59 (define @t225 () (not (tptp.c @t131 @t216))) % 168.92/169.59 (define @t226 () (not (forall @t139 (or @t225 @t150)))) % 168.92/169.59 (define @t227 () (not (forall @t219 (or @t226 (not (forall @t139 (or @t225 @t156))))))) % 168.92/169.59 (define @t228 () (and (not (forall @t102 (or @t224 @t227 @t223 (not (forall @t219 (or @t226 (not (forall @t139 (or @t225 @t155))))))))) (forall @t102 (or @t224 @t222)) (not (forall @t102 (or @t223 @t221))))) % 168.92/169.59 (define @t229 () (or @t228 @t161)) % 168.92/169.59 (define @t230 () (or @t228 @t160)) % 168.92/169.59 (define @t231 () (lambda @t51 @t230)) % 168.92/169.59 (define @t232 () (_ @t231 @t22)) % 168.92/169.59 (define @t233 () (forall @t51 @t232)) % 168.92/169.59 (define @t234 () (or @t228 @t147)) % 168.92/169.59 (define @t235 () (or @t147 @t228)) % 168.92/169.59 (define @t236 () (lambda @t14 @t228)) % 168.92/169.59 (define @t237 () (_ @t236 @t53)) % 168.92/169.59 (define @t238 () (or @t147 @t237)) % 168.92/169.59 (define @t239 () (forall @t59 @t238)) % 168.92/169.59 (define @t240 () (lambda @t51 @t239)) % 168.92/169.59 (define @t241 () (not @t199)) % 168.92/169.59 (define @t242 () (not (forall @t139 (or @t225 @t178)))) % 168.92/169.59 (define @t243 () (forall @t219 (or @t226 @t242))) % 168.92/169.59 (define @t244 () (not @t243)) % 168.92/169.59 (define @t245 () (lambda @t181 (and (not (forall @t102 (or @t224 @t227 @t241 @t244))) (forall @t102 (or @t224 @t199)) (not (forall @t102 (or @t241 @t221)))))) % 168.92/169.59 (define @t246 () (forall @t102 (or @t241 @t200))) % 168.92/169.59 (define @t247 () (not @t246)) % 168.92/169.59 (define @t248 () (not (forall @t139 (or @t225 @t183)))) % 168.92/169.59 (define @t249 () (forall @t219 (or @t226 @t248))) % 168.92/169.59 (define @t250 () (not @t249)) % 168.92/169.59 (define @t251 () (forall @t102 (or @t201 @t250 @t241 @t244))) % 168.92/169.59 (define @t252 () (not @t251)) % 168.92/169.59 (define @t253 () (and @t252 @t202 @t247)) % 168.92/169.59 (define @t254 () (_ (lambda @t5 @t253) tptp.catalunya)) % 168.92/169.59 (define @t255 () (and @t202 @t247)) % 168.92/169.59 (define @t256 () (not @t100)) % 168.92/169.59 (define @t257 () (or @t208 @t250 @t256 @t244)) % 168.92/169.59 (define @t258 () (and @t100 @t243)) % 168.92/169.59 (define @t259 () (and @t101 @t249 @t100 @t243)) % 168.92/169.59 (define @t260 () (forall @t102 (not @t259))) % 168.92/169.59 (define @t261 () (not @t260)) % 168.92/169.59 (define @t262 () (and @t101 @t249)) % 168.92/169.59 (define @t263 () (lambda @t181 @t258)) % 168.92/169.59 (define @t264 () (and @t4 @t185)) % 168.92/169.59 (define @t265 () (lambda @t5 @t264)) % 168.92/169.59 (define @t266 () (_ @t265 @t98)) % 168.92/169.59 (define @t267 () (and (_ @t266 @t1) (_ @t266 @t3))) % 168.92/169.59 (define @t268 () (exists @t102 @t267)) % 168.92/169.59 (define @t269 () (lambda @t181 @t255)) % 168.92/169.59 (define @t270 () (_ (lambda @t5 @t255) @t1)) % 168.92/169.59 (define @t271 () (_ @t270 @t3)) % 168.92/169.59 (define @t272 () (lambda @t181 @t186)) % 168.92/169.59 (define @t273 () (_ @t187 @t1)) % 168.92/169.59 (define @t274 () (not (_ @t273 @t3))) % 168.92/169.59 (define @t275 () (@var "BOUND_VARIABLE_8290" tptp.reg)) % 168.92/169.59 (define @t276 () (tptp.c @t98 @t275)) % 168.92/169.59 (define @t277 () (lambda (@list @t275) (forall @t102 (or @t241 @t276)))) % 168.92/169.59 (define @t278 () (not (_ (_ @t205 @t3) @t1))) % 168.92/169.59 (define @t279 () (lambda @t181 @t202)) % 168.92/169.59 (define @t280 () (_ @t205 @t1)) % 168.92/169.59 (define @t281 () (@list true)) % 168.92/169.59 (define @t282 () (@list @t130)) % 168.92/169.59 (define @t283 () (@list false)) % 168.92/169.59 (define @t284 () (not @t144)) % 168.92/169.59 (define @t285 () (forall @t139 (or @t284 @t143))) % 168.92/169.59 (define @t286 () (not @t285)) % 168.92/169.59 (define @t287 () (forall @t139 (or @t284 @t144))) % 168.92/169.59 (define @t288 () (not @t287)) % 168.92/169.59 (define @t289 () (or @t288 @t286)) % 168.92/169.59 (define @t290 () (_ @t135 @t210 tptp.paris)) % 168.92/169.59 (define @t291 () (_ @t135 @t210 tptp.france)) % 168.92/169.59 (define @t292 () (not @t291)) % 168.92/169.59 (define @t293 () (not @t290)) % 168.92/169.59 (define @t294 () (forall @t102 (or @t293 @t291))) % 168.92/169.59 (define @t295 () (and (forall @t102 (or @t293 (not (forall @t219 (or @t218 (not (forall @t139 (or @t217 @t136)))))) @t292 (not (forall @t219 (or @t218 (not (forall @t139 (or @t217 @t140)))))))) @t294 (not (forall @t102 (or @t292 @t290))))) % 168.92/169.59 (define @t296 () (tptp.c @t98 tptp.paris)) % 168.92/169.59 (define @t297 () (tptp.c @t98 tptp.france)) % 168.92/169.59 (define @t298 () (not @t297)) % 168.92/169.59 (define @t299 () (not @t296)) % 168.92/169.59 (define @t300 () (not (forall @t219 (or @t226 (not (forall @t139 (or @t225 @t149))))))) % 168.92/169.59 (define @t301 () (and (forall @t102 (or @t299 @t300 @t298 (not (forall @t219 (or @t226 (not (forall @t139 (or @t225 @t152)))))))) (forall @t102 (or @t299 @t297)) (not (forall @t102 (or @t298 @t296))))) % 168.92/169.59 (define @t302 () (or @t301 @t161)) % 168.92/169.59 (define @t303 () (or @t301 @t160)) % 168.92/169.59 (define @t304 () (lambda @t51 @t303)) % 168.92/169.59 (define @t305 () (_ @t304 @t22)) % 168.92/169.59 (define @t306 () (forall @t51 @t305)) % 168.92/169.59 (define @t307 () (or @t301 @t147)) % 168.92/169.59 (define @t308 () (or @t147 @t301)) % 168.92/169.59 (define @t309 () (lambda @t14 @t301)) % 168.92/169.59 (define @t310 () (_ @t309 @t53)) % 168.92/169.59 (define @t311 () (or @t147 @t310)) % 168.92/169.59 (define @t312 () (forall @t59 @t311)) % 168.92/169.59 (define @t313 () (lambda @t51 @t312)) % 168.92/169.59 (define @t314 () (lambda @t181 (and (forall @t102 (or @t299 @t300 @t241 @t244)) (forall @t102 (or @t299 @t199)) (not (forall @t102 (or @t241 @t296)))))) % 168.92/169.59 (define @t315 () (and @t251 @t202 @t247)) % 168.92/169.59 (define @t316 () (_ (lambda @t5 @t315) tptp.paris)) % 168.92/169.59 (define @t317 () (not @t268)) % 168.92/169.59 (define @t318 () (not @t136)) % 168.92/169.59 (define @t319 () (forall @t139 (or @t318 @t140))) % 168.92/169.59 (define @t320 () (not @t319)) % 168.92/169.59 (define @t321 () (forall @t139 (or @t318 @t136))) % 168.92/169.59 (define @t322 () (not @t321)) % 168.92/169.59 (define @t323 () (or @t320 @t322)) % 168.92/169.59 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 168.92/169.59 (assume @p2 (forall (@list @t1) (_ @t2 @t1))) % 168.92/169.59 (assume @p3 (forall @t5 (=> @t4 (_ (_ tptp.c @t3) @t1)))) % 168.92/169.59 (assume @p4 (_ tptp.mvalid (_ tptp.mforall_prop (lambda @t11 (_ (_ @t10 @t7) @t6))))) % 168.92/169.59 (assume @p5 (_ tptp.mvalid (_ tptp.mforall_prop (lambda @t11 (_ (_ @t10 (_ @t8 @t9)) @t6))))) % 168.92/169.59 (assume @p6 (_ tptp.mvalid (_ tptp.mforall_prop (lambda (@list @t12 @t6) (_ (_ (_ tptp.mimplies (_ @t8 @t12)) (_ @t13 @t12)) @t6))))) % 168.92/169.59 (assume @p7 (_ tptp.mvalid (_ @t13 @t15))) % 168.92/169.59 (assume @p8 (_ tptp.mvalid (_ @t8 (lambda @t14 (_ (_ tptp.ec tptp.spain) tptp.france))))) % 168.92/169.59 (assume @p9 (_ tptp.mvalid (_ @t13 @t16))) % 168.92/169.59 (assume @p10 @t19) % 168.92/169.59 (assume @p11 true) % 168.92/169.59 (step @p12 (= tptp.meq_ind @t23) :rule refl :args (@t23)) % 168.92/169.59 (step @p13 (= tptp.meq_prop @t26) :rule refl :args (@t26)) % 168.92/169.59 (step @p14 (= tptp.mnot @t30) :rule refl :args (@t30)) % 168.92/169.59 (step @p15 (= tptp.mor @t32) :rule refl :args (@t32)) % 168.92/169.59 (step @p16 (= tptp.mand @t37) :rule refl :args (@t37)) % 168.92/169.59 (step @p17 (= tptp.mimplies @t38) :rule refl :args (@t38)) % 168.92/169.59 (step @p18 (= tptp.mimplied @t39) :rule refl :args (@t39)) % 168.92/169.59 (step @p19 (= tptp.mequiv @t40) :rule refl :args (@t40)) % 168.92/169.59 (step @p20 (= tptp.mxor @t41) :rule refl :args (@t41)) % 168.92/169.59 (step @p21 (= tptp.mforall_ind @t44) :rule refl :args (@t44)) % 168.92/169.59 (step @p22 (= tptp.mforall_prop @t48) :rule refl :args (@t48)) % 168.92/169.59 (step @p23 (= tptp.mexists_ind @t49) :rule refl :args (@t49)) % 168.92/169.59 (step @p24 (= tptp.mexists_prop @t50) :rule refl :args (@t50)) % 168.92/169.59 (step @p25 (= tptp.mtrue @t52) :rule refl :args (@t52)) % 168.92/169.59 (step @p26 (= tptp.mbox @t62) :rule refl :args (@t62)) % 168.92/169.59 (step @p27 (= tptp.mdia @t63) :rule refl :args (@t63)) % 168.92/169.59 (step @p28 (= tptp.mreflexive @t68) :rule refl :args (@t68)) % 168.92/169.59 (step @p29 (= tptp.msymmetric @t72) :rule refl :args (@t72)) % 168.92/169.59 (step @p30 (= tptp.mserial @t74) :rule refl :args (@t74)) % 168.92/169.59 (step @p31 (= tptp.mtransitive @t79) :rule refl :args (@t79)) % 168.92/169.59 (step @p32 (= tptp.meuclidean @t81) :rule refl :args (@t81)) % 168.92/169.59 (step @p33 (= tptp.mpartially_functional @t83) :rule refl :args (@t83)) % 168.92/169.59 (step @p34 (= tptp.mfunctional @t85) :rule refl :args (@t85)) % 168.92/169.59 (step @p35 (= tptp.mweakly_dense @t88) :rule refl :args (@t88)) % 168.92/169.59 (step @p36 (= tptp.mweakly_connected @t89) :rule refl :args (@t89)) % 168.92/169.59 (step @p37 (= tptp.mweakly_directed @t90) :rule refl :args (@t90)) % 168.92/169.59 (step @p38 (= tptp.mvalid @t93) :rule refl :args (@t93)) % 168.92/169.59 (step @p39 (= tptp.minvalid @t94) :rule refl :args (@t94)) % 168.92/169.59 (step @p40 (= tptp.msatisfiable @t95) :rule refl :args (@t95)) % 168.92/169.59 (step @p41 (= tptp.mcountersatisfiable @t96) :rule refl :args (@t96)) % 168.92/169.59 (step @p42 (= tptp.dc @t97) :rule refl :args (@t97)) % 168.92/169.59 (step @p43 (= tptp.p @t104) :rule refl :args (@t104)) % 168.92/169.59 (step @p44 (= tptp.eq @t107) :rule refl :args (@t107)) % 168.92/169.59 (step @p45 (= tptp.o @t111) :rule refl :args (@t111)) % 168.92/169.59 (step @p46 (= tptp.po @t114) :rule refl :args (@t114)) % 168.92/169.59 (step @p47 (= tptp.ec @t117) :rule refl :args (@t117)) % 168.92/169.59 (step @p48 (= tptp.pp @t119) :rule refl :args (@t119)) % 168.92/169.59 (step @p49 (= tptp.tpp @t125) :rule refl :args (@t125)) % 168.92/169.59 (step @p50 (= tptp.ntpp @t128) :rule refl :args (@t128)) % 168.92/169.59 ; WARNING: add trust step for TRUST % 168.92/169.59 ; trust TRUST PREPROCESS_HO_ELIM % 168.92/169.59 (step @p51 :rule trust :premises () :args ((= (not (or @t159 @t148)) (not (or (and @t146 @t142) @t130))))) % 168.92/169.59 (step @p52 :rule quant-merge-prenex :args ((= @t161 @t148))) % 168.92/169.59 (step @p53 :rule refl :args (@t159)) % 168.92/169.59 (step @p54 :rule nary_cong :premises (@p53 @p52) :args (@t162)) % 168.92/169.59 (step @p55 :rule quant-miniscope-or :args ((= (forall @t51 @t163) @t162))) % 168.92/169.59 (step @p56 :rule trans :premises (@p55 @p54)) % 168.92/169.59 (step @p57 :rule beta-reduce :args ((= @t165 @t163))) % 168.92/169.59 (step @p58 :rule cong :premises (@p57) :args (@t166)) % 168.92/169.59 (step @p59 :rule trans :premises (@p58 @p56)) % 168.92/169.59 (step @p60 :rule beta-reduce :args ((= (_ @t168 @t164) @t166))) % 168.92/169.59 (step @p61 :rule trans :premises (@p60 @p59)) % 168.92/169.59 (step @p62 :rule quant-miniscope-or :args ((= (forall @t59 @t169) @t163))) % 168.92/169.59 (step @p63 :rule aci_norm :args ((= @t170 @t169))) % 168.92/169.59 (step @p64 :rule cong :premises (@p63) :args ((forall @t59 @t170))) % 168.92/169.59 (step @p65 :rule trans :premises (@p64 @p62)) % 168.92/169.59 (step @p66 :rule beta-reduce :args ((= @t172 @t159))) % 168.92/169.59 (step @p67 :rule refl :args (@t147)) % 168.92/169.59 (step @p68 :rule nary_cong :premises (@p67 @p66) :args (@t173)) % 168.92/169.59 (step @p69 :rule cong :premises (@p68) :args (@t174)) % 168.92/169.59 (step @p70 :rule trans :premises (@p69 @p65)) % 168.92/169.59 (step @p71 :rule cong :premises (@p70) :args (@t175)) % 168.92/169.59 (step @p72 :rule beta-reduce :args ((= (_ @t177 @t171) @t175))) % 168.92/169.59 (step @p73 :rule trans :premises (@p72 @p71)) % 168.92/169.59 (step @p74 :rule beta-reduce :args ((= (_ @t182 tptp.paris) @t154))) % 168.92/169.59 (step @p75 :rule refl :args (tptp.paris)) % 168.92/169.59 (step @p76 :rule beta-reduce :args ((= @t188 @t182))) % 168.92/169.59 (step @p77 :rule ho_cong :premises (@p76 @p75)) % 168.92/169.59 (step @p78 :rule trans :premises (@p77 @p74)) % 168.92/169.59 (step @p79 :rule beta-reduce :args ((= (_ @t189 tptp.spain) @t158))) % 168.92/169.59 (step @p80 :rule refl :args (tptp.spain)) % 168.92/169.59 (step @p81 :rule beta-reduce :args ((= @t190 @t189))) % 168.92/169.59 (step @p82 :rule ho_cong :premises (@p81 @p80)) % 168.92/169.59 (step @p83 :rule trans :premises (@p82 @p79)) % 168.92/169.59 (step @p84 :rule nary_cong :premises (@p83 @p78) :args (@t191)) % 168.92/169.59 (step @p85 :rule cong :premises (@p84) :args (@t192)) % 168.92/169.59 (step @p86 :rule beta-reduce :args ((= @t194 @t177))) % 168.92/169.59 (step @p87 :rule ho_cong :premises (@p86 @p85)) % 168.92/169.59 (step @p88 :rule trans :premises (@p87 @p73)) % 168.92/169.59 (step @p89 :rule refl :args (@t168)) % 168.92/169.59 (step @p90 :rule ho_cong :premises (@p89 @p88)) % 168.92/169.59 (step @p91 :rule trans :premises (@p90 @p61)) % 168.92/169.59 (step @p92 :rule cong :premises (@p91) :args ((not (_ @t168 (_ @t194 @t192))))) % 168.92/169.59 (step @p93 :rule refl :args (tptp.france)) % 168.92/169.59 (step @p94 :rule bool-and-de-morgan :args (@t184 @t179 true)) % 168.92/169.59 (step @p95 :rule cong :premises (@p94) :args (@t196)) % 168.92/169.59 (step @p96 :rule cong :premises (@p95) :args (@t197)) % 168.92/169.59 (step @p97 :rule exists-elim :args ((= (exists @t102 @t195) @t197))) % 168.92/169.59 (step @p98 :rule trans :premises (@p97 @p96)) % 168.92/169.59 (step @p99 :rule beta-reduce :args ((= (_ @t198 @t3) @t179))) % 168.92/169.59 (step @p100 :rule refl :args (@t3)) % 168.92/169.59 (step @p101 :rule beta-reduce :args ((= (_ (lambda @t5 (forall @t139 (or (not @t183) @t178))) @t98) @t198))) % 168.92/169.59 (step @p102 :rule refl :args (@t98)) % 168.92/169.59 (step @p103 :rule alpha_equiv :args (@t202 @t203 @t204)) % 168.92/169.59 (step @p104 :rule cong :premises (@p103) :args (@t205)) % 168.92/169.59 (step @p105 :rule ho_cong :premises (@p104 @p102)) % 168.92/169.59 (step @p106 :rule trans :premises (@p105 @p101)) % 168.92/169.59 (step @p107 :rule ho_cong :premises (@p106 @p100)) % 168.92/169.59 (step @p108 :rule trans :premises (@p107 @p99)) % 168.92/169.59 (step @p109 :rule beta-reduce :args ((= (_ @t198 @t1) @t184))) % 168.92/169.59 (step @p110 :rule refl :args (@t1)) % 168.92/169.59 (step @p111 :rule ho_cong :premises (@p106 @p110)) % 168.92/169.59 (step @p112 :rule trans :premises (@p111 @p109)) % 168.92/169.59 (step @p113 :rule nary_cong :premises (@p112 @p108) :args (@t207)) % 168.92/169.59 (step @p114 :rule cong :premises (@p113) :args ((exists @t102 @t207))) % 168.92/169.59 (step @p115 :rule trans :premises (@p114 @p98)) % 168.92/169.59 (step @p116 :rule refl :args (@t98)) % 168.92/169.59 (step @p117 :rule refl :args (@t199)) % 168.92/169.59 (step @p118 :rule refl :args (@t100)) % 168.92/169.59 (step @p119 :rule cong :premises (@p118 @p117) :args ((= @t100 @t199))) % 168.92/169.59 (step @p120 :rule symm :premises (@p119)) % 168.92/169.59 (step @p121 :rule eq_resolve :premises (@p118 @p120)) % 168.92/169.59 (step @p122 :rule refl :args (@t200)) % 168.92/169.59 (step @p123 :rule refl :args (@t101)) % 168.92/169.59 (step @p124 :rule cong :premises (@p123 @p122) :args ((= @t101 @t200))) % 168.92/169.59 (step @p125 :rule symm :premises (@p124)) % 168.92/169.59 (step @p126 :rule eq_resolve :premises (@p123 @p125)) % 168.92/169.59 (step @p127 :rule cong :premises (@p126) :args (@t208)) % 168.92/169.59 (step @p128 :rule nary_cong :premises (@p127 @p121) :args (@t209)) % 168.92/169.59 (step @p129 :rule cong :premises (@p128) :args ((forall @t102 @t209))) % 168.92/169.59 (step @p130 :rule bool-impl-elim :args (@t101 @t100)) % 168.92/169.59 (step @p131 :rule cong :premises (@p130) :args (@t103)) % 168.92/169.59 (step @p132 :rule trans :premises (@p131 @p129)) % 168.92/169.59 (step @p133 :rule cong :premises (@p132) :args (@t104)) % 168.92/169.59 (step @p134 :rule trans :premises (@p43 @p133)) % 168.92/169.59 (step @p135 :rule ho_cong :premises (@p134 @p116)) % 168.92/169.59 (step @p136 :rule ho_cong :premises (@p135 @p100)) % 168.92/169.59 (step @p137 :rule ho_cong :premises (@p135 @p110)) % 168.92/169.59 (step @p138 :rule nary_cong :premises (@p137 @p136) :args (@t109)) % 168.92/169.59 (step @p139 :rule cong :premises (@p138) :args (@t110)) % 168.92/169.59 (step @p140 :rule trans :premises (@p139 @p115)) % 168.92/169.59 (step @p141 :rule cong :premises (@p140) :args (@t111)) % 168.92/169.59 (step @p142 :rule trans :premises (@p45 @p141)) % 168.92/169.59 (step @p143 :rule ho_cong :premises (@p142 @p93)) % 168.92/169.59 (step @p144 :rule ho_cong :premises (@p143 @p75)) % 168.92/169.59 (step @p145 :rule refl :args (tptp.catalunya)) % 168.92/169.59 (step @p146 :rule ho_cong :premises (@p142 @p145)) % 168.92/169.59 (step @p147 :rule ho_cong :premises (@p146 @p80)) % 168.92/169.59 (step @p148 :rule nary_cong :premises (@p147 @p144) :args (@t17)) % 168.92/169.59 (step @p149 :rule cong :premises (@p148) :args (@t18)) % 168.92/169.59 (step @p150 :rule refl :args (tptp.a)) % 168.92/169.59 (step @p151 :rule refl :args (@t176)) % 168.92/169.59 (step @p152 :rule refl :args (@t54)) % 168.92/169.59 (step @p153 :rule cong :premises (@p152 @p151) :args ((= @t54 @t176))) % 168.92/169.59 (step @p154 :rule symm :premises (@p153)) % 168.92/169.59 (step @p155 :rule eq_resolve :premises (@p152 @p154)) % 168.92/169.59 (step @p156 :rule refl :args (@t193)) % 168.92/169.59 (step @p157 :rule refl :args (@t56)) % 168.92/169.59 (step @p158 :rule cong :premises (@p157 @p156) :args ((= @t56 @t193))) % 168.92/169.59 (step @p159 :rule symm :premises (@p158)) % 168.92/169.59 (step @p160 :rule eq_resolve :premises (@p157 @p159)) % 168.92/169.59 (step @p161 :rule cong :premises (@p160) :args (@t57)) % 168.92/169.59 (step @p162 :rule nary_cong :premises (@p161 @p155) :args (@t58)) % 168.92/169.59 (step @p163 :rule cong :premises (@p162) :args (@t60)) % 168.92/169.59 (step @p164 :rule cong :premises (@p163) :args (@t62)) % 168.92/169.59 (step @p165 :rule trans :premises (@p26 @p164)) % 168.92/169.59 (step @p166 :rule ho_cong :premises (@p165 @p150)) % 168.92/169.59 (step @p167 :rule ho_cong :premises (@p166 @p149)) % 168.92/169.59 (step @p168 :rule refl :args (@t167)) % 168.92/169.59 (step @p169 :rule refl :args (@t27)) % 168.92/169.59 (step @p170 :rule cong :premises (@p169 @p168) :args ((= @t27 @t167))) % 168.92/169.59 (step @p171 :rule symm :premises (@p170)) % 168.92/169.59 (step @p172 :rule eq_resolve :premises (@p169 @p171)) % 168.92/169.59 (step @p173 :rule cong :premises (@p172) :args (@t91)) % 168.92/169.59 (step @p174 :rule cong :premises (@p173) :args (@t93)) % 168.92/169.59 (step @p175 :rule trans :premises (@p38 @p174)) % 168.92/169.59 (step @p176 :rule ho_cong :premises (@p175 @p167)) % 168.92/169.59 (step @p177 :rule cong :premises (@p176) :args (@t19)) % 168.92/169.59 (step @p178 :rule trans :premises (@p177 @p92)) % 168.92/169.59 (step @p179 :rule trans :premises (@p178 @p51)) % 168.92/169.59 (step @p180 :rule eq_resolve :premises (@p10 @p179)) % 168.92/169.59 (step @p181 :rule not_or_elim :premises (@p180) :args (1)) % 168.92/169.59 ; trust TRUST PREPROCESS_HO_ELIM % 168.92/169.59 (step @p182 :rule trust :premises () :args ((= (or @t228 @t148) (or @t220 @t130)))) % 168.92/169.59 (step @p183 :rule refl :args (@t228)) % 168.92/169.59 (step @p184 :rule nary_cong :premises (@p183 @p52) :args (@t229)) % 168.92/169.59 (step @p185 :rule quant-miniscope-or :args ((= (forall @t51 @t230) @t229))) % 168.92/169.59 (step @p186 :rule trans :premises (@p185 @p184)) % 168.92/169.59 (step @p187 :rule beta-reduce :args ((= @t232 @t230))) % 168.92/169.59 (step @p188 :rule cong :premises (@p187) :args (@t233)) % 168.92/169.59 (step @p189 :rule trans :premises (@p188 @p186)) % 168.92/169.59 (step @p190 :rule beta-reduce :args ((= (_ @t168 @t231) @t233))) % 168.92/169.59 (step @p191 :rule trans :premises (@p190 @p189)) % 168.92/169.59 (step @p192 :rule quant-miniscope-or :args ((= (forall @t59 @t234) @t230))) % 168.92/169.59 (step @p193 :rule aci_norm :args ((= @t235 @t234))) % 168.92/169.59 (step @p194 :rule cong :premises (@p193) :args ((forall @t59 @t235))) % 168.92/169.59 (step @p195 :rule trans :premises (@p194 @p192)) % 168.92/169.59 (step @p196 :rule beta-reduce :args ((= @t237 @t228))) % 168.92/169.59 (step @p197 :rule nary_cong :premises (@p67 @p196) :args (@t238)) % 168.92/169.59 (step @p198 :rule cong :premises (@p197) :args (@t239)) % 168.92/169.59 (step @p199 :rule trans :premises (@p198 @p195)) % 168.92/169.59 (step @p200 :rule cong :premises (@p199) :args (@t240)) % 168.92/169.59 (step @p201 :rule beta-reduce :args ((= (_ @t177 @t236) @t240))) % 168.92/169.59 (step @p202 :rule trans :premises (@p201 @p200)) % 168.92/169.59 (step @p203 :rule beta-reduce :args ((= (_ @t245 tptp.spain) @t228))) % 168.92/169.59 (step @p204 :rule beta-reduce :args ((= @t254 @t245))) % 168.92/169.59 (step @p205 :rule ho_cong :premises (@p204 @p80)) % 168.92/169.59 (step @p206 :rule trans :premises (@p205 @p203)) % 168.92/169.59 (step @p207 :rule cong :premises (@p206) :args ((lambda @t14 (_ @t254 tptp.spain)))) % 168.92/169.59 (step @p208 :rule ho_cong :premises (@p86 @p207)) % 168.92/169.59 (step @p209 :rule trans :premises (@p208 @p202)) % 168.92/169.59 (step @p210 :rule ho_cong :premises (@p89 @p209)) % 168.92/169.59 (step @p211 :rule trans :premises (@p210 @p191)) % 168.92/169.59 (step @p212 :rule aci_norm :args ((= (and @t255 @t252) @t253))) % 168.92/169.59 (step @p213 :rule refl :args (@t244)) % 168.92/169.59 (step @p214 :rule cong :premises (@p121) :args (@t256)) % 168.92/169.59 (step @p215 :rule refl :args (@t250)) % 168.92/169.59 (step @p216 :rule nary_cong :premises (@p127 @p215 @p214 @p213) :args (@t257)) % 168.92/169.59 (step @p217 :rule cong :premises (@p216) :args ((forall @t102 @t257))) % 168.92/169.59 (step @p218 :rule aci_norm :args ((= (or @t208 (or @t250 (or @t256 @t244))) @t257))) % 168.92/169.59 (step @p219 :rule bool-and-de-morgan :args (@t100 @t243 true)) % 168.92/169.59 (step @p220 :rule nary_cong :premises (@p215 @p219) :args ((or @t250 (not @t258)))) % 168.92/169.59 (step @p221 :rule bool-and-de-morgan :args (@t249 @t100 (and @t243))) % 168.92/169.59 (step @p222 :rule trans :premises (@p221 @p220)) % 168.92/169.59 (step @p223 :rule refl :args (@t208)) % 168.92/169.59 (step @p224 :rule nary_cong :premises (@p223 @p222) :args ((or @t208 (not (and @t249 @t100 @t243))))) % 168.92/169.59 (step @p225 :rule bool-and-de-morgan :args (@t101 @t249 (and @t100 @t243))) % 168.92/169.59 (step @p226 :rule trans :premises (@p225 @p224)) % 168.92/169.59 (step @p227 :rule trans :premises (@p226 @p218)) % 168.92/169.59 (step @p228 :rule cong :premises (@p227) :args (@t260)) % 168.92/169.59 (step @p229 :rule trans :premises (@p228 @p217)) % 168.92/169.59 (step @p230 :rule cong :premises (@p229) :args (@t261)) % 168.92/169.59 (step @p231 :rule exists-elim :args ((= (exists @t102 @t259) @t261))) % 168.92/169.59 (step @p232 :rule trans :premises (@p231 @p230)) % 168.92/169.59 (step @p233 :rule aci_norm :args ((= (and @t262 @t258) @t259))) % 168.92/169.59 (step @p234 :rule beta-reduce :args ((= (_ @t263 @t3) @t258))) % 168.92/169.59 (step @p235 :rule beta-reduce :args ((= (_ (lambda @t5 (and @t4 (forall @t219 (or @t248 @t242)))) @t98) @t263))) % 168.92/169.59 (step @p236 :rule alpha_equiv :args (@t185 @t203 (@list @t216))) % 168.92/169.59 (step @p237 :rule refl :args (@t4)) % 168.92/169.59 (step @p238 :rule nary_cong :premises (@p237 @p236) :args (@t264)) % 168.92/169.59 (step @p239 :rule cong :premises (@p238) :args (@t265)) % 168.92/169.59 (step @p240 :rule ho_cong :premises (@p239 @p102)) % 168.92/169.59 (step @p241 :rule trans :premises (@p240 @p235)) % 168.92/169.59 (step @p242 :rule ho_cong :premises (@p241 @p100)) % 168.92/169.59 (step @p243 :rule trans :premises (@p242 @p234)) % 168.92/169.59 (step @p244 :rule beta-reduce :args ((= (_ @t263 @t1) @t262))) % 168.92/169.59 (step @p245 :rule ho_cong :premises (@p241 @p110)) % 168.92/169.59 (step @p246 :rule trans :premises (@p245 @p244)) % 168.92/169.59 (step @p247 :rule nary_cong :premises (@p246 @p243) :args (@t267)) % 168.92/169.59 (step @p248 :rule trans :premises (@p247 @p233)) % 168.92/169.59 (step @p249 :rule cong :premises (@p248) :args (@t268)) % 168.92/169.59 (step @p250 :rule trans :premises (@p249 @p232)) % 168.92/169.59 (step @p251 :rule beta-reduce :args ((= (_ @t269 @t3) @t255))) % 168.92/169.59 (step @p252 :rule beta-reduce :args ((= @t270 @t269))) % 168.92/169.59 (step @p253 :rule ho_cong :premises (@p252 @p100)) % 168.92/169.59 (step @p254 :rule trans :premises (@p253 @p251)) % 168.92/169.59 (step @p255 :rule nary_cong :premises (@p254 @p250) :args ((and @t271 @t268))) % 168.92/169.59 (step @p256 :rule trans :premises (@p255 @p212)) % 168.92/169.59 (step @p257 :rule bool-double-not-elim :args (@t185)) % 168.92/169.59 (step @p258 :rule beta-reduce :args ((= (_ @t272 @t3) @t186))) % 168.92/169.59 (step @p259 :rule beta-reduce :args ((= @t273 @t272))) % 168.92/169.59 (step @p260 :rule ho_cong :premises (@p259 @p100)) % 168.92/169.59 (step @p261 :rule trans :premises (@p260 @p258)) % 168.92/169.59 (step @p262 :rule cong :premises (@p261) :args (@t274)) % 168.92/169.59 (step @p263 :rule trans :premises (@p262 @p257)) % 168.92/169.59 (step @p264 :rule refl :args (@t4)) % 168.92/169.59 (step @p265 :rule nary_cong :premises (@p264 @p263) :args ((and @t4 @t274))) % 168.92/169.59 (step @p266 :rule ho_cong :premises (@p142 @p110)) % 168.92/169.59 (step @p267 :rule ho_cong :premises (@p266 @p100)) % 168.92/169.59 (step @p268 :rule cong :premises (@p267) :args (@t115)) % 168.92/169.59 (step @p269 :rule nary_cong :premises (@p264 @p268) :args (@t116)) % 168.92/169.59 (step @p270 :rule trans :premises (@p269 @p265)) % 168.92/169.59 (step @p271 :rule cong :premises (@p270) :args (@t117)) % 168.92/169.59 (step @p272 :rule trans :premises (@p47 @p271)) % 168.92/169.59 (step @p273 :rule ho_cong :premises (@p272 @p116)) % 168.92/169.59 (step @p274 :rule ho_cong :premises (@p273 @p100)) % 168.92/169.59 (step @p275 :rule ho_cong :premises (@p273 @p110)) % 168.92/169.59 (step @p276 :rule nary_cong :premises (@p275 @p274) :args (@t121)) % 168.92/169.59 (step @p277 :rule cong :premises (@p276) :args (@t122)) % 168.92/169.59 (step @p278 :rule beta-reduce :args ((= (_ @t277 @t1) @t246))) % 168.92/169.59 (step @p279 :rule beta-reduce :args ((= (_ (lambda (@list @t1 @t275) (forall @t102 (or @t201 @t276))) @t3) @t277))) % 168.92/169.59 (step @p280 :rule refl :args (@t3)) % 168.92/169.59 (step @p281 :rule alpha_equiv :args (@t205 (@list @t3) (@list @t275))) % 168.92/169.59 (step @p282 :rule ho_cong :premises (@p281 @p280)) % 168.92/169.59 (step @p283 :rule trans :premises (@p282 @p279)) % 168.92/169.59 (step @p284 :rule ho_cong :premises (@p283 @p110)) % 168.92/169.59 (step @p285 :rule trans :premises (@p284 @p278)) % 168.92/169.59 (step @p286 :rule cong :premises (@p285) :args (@t278)) % 168.92/169.59 (step @p287 :rule beta-reduce :args ((= (_ @t279 @t3) @t202))) % 168.92/169.59 (step @p288 :rule beta-reduce :args ((= @t280 @t279))) % 168.92/169.59 (step @p289 :rule ho_cong :premises (@p288 @p100)) % 168.92/169.59 (step @p290 :rule trans :premises (@p289 @p287)) % 168.92/169.59 (step @p291 :rule nary_cong :premises (@p290 @p286) :args ((and (_ @t280 @t3) @t278))) % 168.92/169.59 (step @p292 :rule ho_cong :premises (@p134 @p100)) % 168.92/169.59 (step @p293 :rule ho_cong :premises (@p292 @p110)) % 168.92/169.59 (step @p294 :rule cong :premises (@p293) :args (@t112)) % 168.92/169.59 (step @p295 :rule ho_cong :premises (@p134 @p110)) % 168.92/169.59 (step @p296 :rule ho_cong :premises (@p295 @p100)) % 168.92/169.59 (step @p297 :rule nary_cong :premises (@p296 @p294) :args (@t118)) % 168.92/169.59 (step @p298 :rule trans :premises (@p297 @p291)) % 168.92/169.59 (step @p299 :rule cong :premises (@p298) :args (@t119)) % 168.92/169.59 (step @p300 :rule trans :premises (@p48 @p299)) % 168.92/169.59 (step @p301 :rule ho_cong :premises (@p300 @p110)) % 168.92/169.59 (step @p302 :rule ho_cong :premises (@p301 @p100)) % 168.92/169.59 (step @p303 :rule nary_cong :premises (@p302 @p277) :args (@t124)) % 168.92/169.59 (step @p304 :rule trans :premises (@p303 @p256)) % 168.92/169.59 (step @p305 :rule cong :premises (@p304) :args (@t125)) % 168.92/169.59 (step @p306 :rule trans :premises (@p49 @p305)) % 168.92/169.59 (step @p307 :rule ho_cong :premises (@p306 @p145)) % 168.92/169.59 (step @p308 :rule ho_cong :premises (@p307 @p80)) % 168.92/169.59 (step @p309 :rule cong :premises (@p308) :args (@t15)) % 168.92/169.59 (step @p310 :rule ho_cong :premises (@p166 @p309)) % 168.92/169.59 (step @p311 :rule ho_cong :premises (@p175 @p310)) % 168.92/169.59 (step @p312 :rule trans :premises (@p311 @p211)) % 168.92/169.59 (step @p313 :rule trans :premises (@p312 @p182)) % 168.92/169.59 (step @p314 :rule eq_resolve :premises (@p7 @p313)) % 168.92/169.59 (step @p315 :rule reordering :premises (@p314) :args ((or @t130 @t220))) % 168.92/169.59 (step @p316 :rule chain_m_resolution :premises (@p315 @p181) :args (@t220 @t281 @t282)) % 168.92/169.59 (step @p317 :rule cnf_and_pos :args (@t220 1)) % 168.92/169.59 (step @p318 :rule reordering :premises (@p317) :args ((or @t215 (not @t220)))) % 168.92/169.59 (step @p319 :rule chain_m_resolution :premises (@p318 @p316) :args (@t215 @t283 (@list @t220))) % 168.92/169.59 (step @p320 :rule alpha_equiv :args (@t215 @t203 @t204)) % 168.92/169.59 (step @p321 :rule equiv_elim1 :premises (@p320)) % 168.92/169.59 (step @p322 :rule chain_m_resolution :premises (@p321 @p319) :args (@t285 @t283 (@list @t215))) % 168.92/169.59 (step @p323 :rule aci_norm :args ((= (or false @t286) @t286))) % 168.92/169.59 (step @p324 :rule refl :args (@t286)) % 168.92/169.59 (step @p325 :rule evaluate :args ((not true))) % 168.92/169.59 (step @p326 :rule quant-unused-vars :args ((= (forall @t139 true) true))) % 168.92/169.59 (step @p327 :rule bool-or-taut2 :args (false @t144 false false)) % 168.92/169.59 (step @p328 :rule cong :premises (@p327) :args (@t287)) % 168.92/169.59 (step @p329 :rule trans :premises (@p328 @p326)) % 168.92/169.59 (step @p330 :rule cong :premises (@p329) :args (@t288)) % 168.92/169.59 (step @p331 :rule trans :premises (@p330 @p325)) % 168.92/169.59 (step @p332 :rule nary_cong :premises (@p331 @p324) :args (@t289)) % 168.92/169.59 (step @p333 :rule trans :premises (@p332 @p323)) % 168.92/169.59 (step @p334 :rule refl :args (@t145)) % 168.92/169.59 (step @p335 :rule cong :premises (@p334 @p333) :args ((=> @t145 @t289))) % 168.92/169.59 (assume-push @p426 @t145) % 168.92/169.59 (step @p337 :rule instantiate :premises (@p426) :args ((@list tptp.catalunya))) % 168.92/169.59 (step-pop @p427 :rule scope :premises (@p337)) % 168.92/169.59 (step @p338 :rule process_scope :premises (@p427) :args (@t289)) % 168.92/169.59 (step @p340 :rule eq_resolve :premises (@p338 @p335)) % 168.92/169.59 (step @p341 :rule implies_elim :premises (@p340)) % 168.92/169.59 (step @p342 :rule chain_m_resolution :premises (@p341 @p322) :args (@t146 @t283 (@list @t285))) % 168.92/169.59 (step @p343 :rule bool-double-not-elim :args (@t141)) % 168.92/169.59 (step @p344 :rule bool-double-not-elim :args (@t145)) % 168.92/169.59 (step @p345 :rule nary_cong :premises (@p344 @p343) :args ((or (not @t146) (not @t142)))) % 168.92/169.59 (step @p346 :rule not_or_elim :premises (@p180) :args (0)) % 168.92/169.59 (step @p347 :rule not_and :premises (@p346)) % 168.92/169.59 (step @p348 :rule eq_resolve :premises (@p347 @p345)) % 168.92/169.59 (step @p349 :rule reordering :premises (@p348) :args ((or @t141 @t145))) % 168.92/169.59 (step @p350 :rule chain_m_resolution :premises (@p349 @p342) :args (@t141 @t281 (@list @t145))) % 168.92/169.59 ; trust TRUST PREPROCESS_HO_ELIM % 168.92/169.59 (step @p351 :rule trust :premises () :args ((= (or @t301 @t148) (or @t295 @t130)))) % 168.92/169.59 (step @p352 :rule refl :args (@t301)) % 168.92/169.59 (step @p353 :rule nary_cong :premises (@p352 @p52) :args (@t302)) % 168.92/169.59 (step @p354 :rule quant-miniscope-or :args ((= (forall @t51 @t303) @t302))) % 168.92/169.59 (step @p355 :rule trans :premises (@p354 @p353)) % 168.92/169.59 (step @p356 :rule beta-reduce :args ((= @t305 @t303))) % 168.92/169.59 (step @p357 :rule cong :premises (@p356) :args (@t306)) % 168.92/169.59 (step @p358 :rule trans :premises (@p357 @p355)) % 168.92/169.59 (step @p359 :rule beta-reduce :args ((= (_ @t168 @t304) @t306))) % 168.92/169.59 (step @p360 :rule trans :premises (@p359 @p358)) % 168.92/169.59 (step @p361 :rule quant-miniscope-or :args ((= (forall @t59 @t307) @t303))) % 168.92/169.59 (step @p362 :rule aci_norm :args ((= @t308 @t307))) % 168.92/169.59 (step @p363 :rule cong :premises (@p362) :args ((forall @t59 @t308))) % 168.92/169.59 (step @p364 :rule trans :premises (@p363 @p361)) % 168.92/169.59 (step @p365 :rule beta-reduce :args ((= @t310 @t301))) % 168.92/169.59 (step @p366 :rule nary_cong :premises (@p67 @p365) :args (@t311)) % 168.92/169.59 (step @p367 :rule cong :premises (@p366) :args (@t312)) % 168.92/169.59 (step @p368 :rule trans :premises (@p367 @p364)) % 168.92/169.59 (step @p369 :rule cong :premises (@p368) :args (@t313)) % 168.92/169.59 (step @p370 :rule beta-reduce :args ((= (_ @t177 @t309) @t313))) % 168.92/169.59 (step @p371 :rule trans :premises (@p370 @p369)) % 168.92/169.59 (step @p372 :rule beta-reduce :args ((= (_ @t314 tptp.france) @t301))) % 168.92/169.59 (step @p373 :rule beta-reduce :args ((= @t316 @t314))) % 168.92/169.59 (step @p374 :rule ho_cong :premises (@p373 @p93)) % 168.92/169.59 (step @p375 :rule trans :premises (@p374 @p372)) % 168.92/169.59 (step @p376 :rule cong :premises (@p375) :args ((lambda @t14 (_ @t316 tptp.france)))) % 168.92/169.59 (step @p377 :rule ho_cong :premises (@p86 @p376)) % 168.92/169.59 (step @p378 :rule trans :premises (@p377 @p371)) % 168.92/169.59 (step @p379 :rule ho_cong :premises (@p89 @p378)) % 168.92/169.59 (step @p380 :rule trans :premises (@p379 @p360)) % 168.92/169.59 (step @p381 :rule aci_norm :args ((= (and @t255 @t251) @t315))) % 168.92/169.59 (step @p382 :rule bool-double-not-elim :args (@t251)) % 168.92/169.59 (step @p383 :rule cong :premises (@p250) :args (@t317)) % 168.92/169.59 (step @p384 :rule trans :premises (@p383 @p382)) % 168.92/169.59 (step @p385 :rule nary_cong :premises (@p254 @p384) :args ((and @t271 @t317))) % 168.92/169.59 (step @p386 :rule trans :premises (@p385 @p381)) % 168.92/169.59 (step @p387 :rule cong :premises (@p277) :args (@t126)) % 168.92/169.59 (step @p388 :rule nary_cong :premises (@p302 @p387) :args (@t127)) % 168.92/169.59 (step @p389 :rule trans :premises (@p388 @p386)) % 168.92/169.59 (step @p390 :rule cong :premises (@p389) :args (@t128)) % 168.92/169.59 (step @p391 :rule trans :premises (@p50 @p390)) % 168.92/169.59 (step @p392 :rule ho_cong :premises (@p391 @p75)) % 168.92/169.59 (step @p393 :rule ho_cong :premises (@p392 @p93)) % 168.92/169.59 (step @p394 :rule cong :premises (@p393) :args (@t16)) % 168.92/169.59 (step @p395 :rule ho_cong :premises (@p166 @p394)) % 168.92/169.59 (step @p396 :rule ho_cong :premises (@p175 @p395)) % 168.92/169.59 (step @p397 :rule trans :premises (@p396 @p380)) % 168.92/169.59 (step @p398 :rule trans :premises (@p397 @p351)) % 168.92/169.59 (step @p399 :rule eq_resolve :premises (@p9 @p398)) % 168.92/169.59 (step @p400 :rule reordering :premises (@p399) :args ((or @t130 @t295))) % 168.92/169.59 (step @p401 :rule chain_m_resolution :premises (@p400 @p181) :args (@t295 @t281 @t282)) % 168.92/169.59 (step @p402 :rule cnf_and_pos :args (@t295 1)) % 168.92/169.59 (step @p403 :rule reordering :premises (@p402) :args ((or @t294 (not @t295)))) % 168.92/169.59 (step @p404 :rule chain_m_resolution :premises (@p403 @p401) :args (@t294 @t283 (@list @t295))) % 168.92/169.59 (step @p405 :rule alpha_equiv :args (@t294 @t203 @t204)) % 168.92/169.59 (step @p406 :rule equiv_elim1 :premises (@p405)) % 168.92/169.59 (step @p407 :rule chain_m_resolution :premises (@p406 @p404) :args (@t319 @t283 (@list @t294))) % 168.92/169.59 (step @p408 :rule aci_norm :args ((= (or @t320 false) @t320))) % 168.92/169.59 (step @p409 :rule bool-or-taut2 :args (false @t136 false false)) % 168.92/169.59 (step @p410 :rule cong :premises (@p409) :args (@t321)) % 168.92/169.59 (step @p411 :rule trans :premises (@p410 @p326)) % 168.92/169.59 (step @p412 :rule cong :premises (@p411) :args (@t322)) % 168.92/169.59 (step @p413 :rule trans :premises (@p412 @p325)) % 168.92/169.59 (step @p414 :rule refl :args (@t320)) % 168.92/169.59 (step @p415 :rule nary_cong :premises (@p414 @p413) :args (@t323)) % 168.92/169.59 (step @p416 :rule trans :premises (@p415 @p408)) % 168.92/169.59 (step @p417 :rule refl :args (@t141)) % 168.92/169.59 (step @p418 :rule cong :premises (@p417 @p416) :args ((=> @t141 @t323))) % 168.92/169.59 (assume-push @p428 @t141) % 168.92/169.59 (step @p420 :rule instantiate :premises (@p428) :args ((@list tptp.paris))) % 168.92/169.59 (step-pop @p429 :rule scope :premises (@p420)) % 168.92/169.59 (step @p421 :rule process_scope :premises (@p429) :args (@t323)) % 168.92/169.59 (step @p423 :rule eq_resolve :premises (@p421 @p418)) % 168.92/169.59 (step @p424 :rule implies_elim :premises (@p423)) % 168.92/169.59 (step @p425 false :rule chain_m_resolution :premises (@p424 @p407 @p350) :args (false (@list false false) (@list @t319 @t141))) % 168.92/169.59 ) % 168.92/169.59 % SZS output end Proof % 168.92/169.59 % cvc5 exiting %------------------------------------------------------------------------------