%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : GEG007^1 : 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 : n002.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 168.83s 169.83s % Output : Proof 168.83s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : GEG007^1 : 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 % 0.16/0.34 % Computer : n002.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Mon Jun 1 23:02:48 EDT 2026 % 0.16/0.34 % CPUTime : % 0.30/0.50 %----Proving TH0 % 168.83/169.83 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 168.83/169.83 --- 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... % 168.83/169.83 --- 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... % 168.83/169.83 --- Run --ho-elim --full-saturate-quant at 18s... % 168.83/169.83 --- Run --ho-elim --no-e-matching --full-saturate-quant at 12s... % 168.83/169.83 % SZS status Theorem % 168.83/169.83 % SZS output start Proof % 168.83/169.83 ( % 168.83/169.83 (declare-sort tptp.reg 0) % 168.83/169.83 (declare-sort $$unsorted 0) % 168.83/169.83 (declare-sort tptp.mu 0) % 168.83/169.83 (declare-const tptp.c (-> tptp.reg tptp.reg Bool)) % 168.83/169.83 (declare-const tptp.france tptp.reg) % 168.83/169.83 (declare-const tptp.catalunya tptp.reg) % 168.83/169.83 (declare-const tptp.a (-> $$unsorted $$unsorted Bool)) % 168.83/169.83 (declare-const tptp.spain tptp.reg) % 168.83/169.83 (declare-const tptp.fool (-> $$unsorted $$unsorted Bool)) % 168.83/169.83 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 168.83/169.83 (declare-const tptp.paris tptp.reg) % 168.83/169.83 (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" $$unsorted)) (= _let_2 _let_1))))) % 168.83/169.83 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$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))))))) % 168.83/169.83 (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)))))) % 168.83/169.83 (define tptp.mor () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 168.83/169.83 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 168.83/169.83 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 168.83/169.83 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 168.83/169.83 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimplies _let_2) _let_3)) (_ (_ tptp.mimplies _let_3) _let_2)) _let_1)))))) % 168.83/169.83 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 168.83/169.83 (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))))))) % 168.83/169.83 (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))))))) % 168.83/169.83 (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)))))) % 168.83/169.83 (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)))))) % 168.83/169.83 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 168.83/169.83 (define tptp.mbox () (let ((_let_1 (@var "V" $$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))))))))) % 168.83/169.83 (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)))))) % 168.83/169.83 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 168.83/169.83 (define tptp.msymmetric () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 168.83/169.83 (define tptp.mserial () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 168.83/169.83 (define tptp.mtransitive () (let ((_let_1 (@var "U" $$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)))))))))) % 168.83/169.83 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (_ (_ _let_3 _let_2) _let_1)))))))))) % 168.83/169.83 (define tptp.mpartially_functional () (let ((_let_1 (@var "U" $$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)))))))))) % 168.83/169.83 (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 $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3) (exists (@list _let_2) (and (_ _let_5 _let_2) (forall (@list _let_1) (=> (_ _let_5 _let_1) (= _let_2 _let_1))))))))))))) % 168.83/169.83 (define tptp.mweakly_dense () (let ((_let_1 (@var "T" $$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)))))))))))) % 168.83/169.83 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_1) (_ _let_5 _let_2)) (or (_ (_ _let_3 _let_1) _let_2) (= _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1))))))))))) % 168.83/169.83 (define tptp.mweakly_directed () (let ((_let_1 (@var "V" $$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" $$unsorted))) (let ((_let_6 (_ _let_3 _let_5))) (lambda (@list _let_3) (forall (@list _let_5 _let_4 _let_2) (=> (and (_ _let_6 _let_4) (_ _let_6 _let_2)) (exists (@list _let_1) (and (_ (_ _let_3 _let_4) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))))))) % 168.83/169.83 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 168.83/169.83 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 168.83/169.83 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 168.83/169.83 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 168.83/169.83 (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)))))) % 168.83/169.83 (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))))))))) % 168.83/169.83 (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)))))) % 168.83/169.83 (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))))))))) % 168.83/169.83 (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))))))) % 168.83/169.83 (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))))))) % 168.83/169.83 (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))))))) % 168.83/169.83 (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)))))))))) % 168.83/169.83 (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))))))))))) % 168.83/169.83 (define @t1 () (@var "X" tptp.reg)) % 168.83/169.83 (define @t2 () (_ tptp.c @t1)) % 168.83/169.83 (define @t3 () (@var "Y" tptp.reg)) % 168.83/169.83 (define @t4 () (_ @t2 @t3)) % 168.83/169.83 (define @t5 () (@list @t1 @t3)) % 168.83/169.83 (define @t6 () (@var "__flatten_var_0" $$unsorted)) % 168.83/169.83 (define @t7 () (@var "A" (-> $$unsorted Bool))) % 168.83/169.83 (define @t8 () (_ tptp.mbox tptp.fool)) % 168.83/169.83 (define @t9 () (_ @t8 @t7)) % 168.83/169.83 (define @t10 () (_ tptp.mimplies @t9)) % 168.83/169.83 (define @t11 () (@list @t7 @t6)) % 168.83/169.83 (define @t12 () (@var "Phi" (-> $$unsorted Bool))) % 168.83/169.83 (define @t13 () (_ tptp.mbox tptp.a)) % 168.83/169.83 (define @t14 () (@list @t12 @t6)) % 168.83/169.83 (define @t15 () (lambda @t14 (_ (_ (_ tptp.mimplies (_ @t8 @t12)) (_ @t13 @t12)) @t6))) % 168.83/169.83 (define @t16 () (@list (@var "X" $$unsorted))) % 168.83/169.83 (define @t17 () (lambda @t16 (_ (_ tptp.tpp tptp.catalunya) tptp.spain))) % 168.83/169.83 (define @t18 () (lambda @t16 (_ (_ tptp.ec tptp.spain) tptp.france))) % 168.83/169.83 (define @t19 () (lambda @t16 (_ (_ tptp.ntpp tptp.paris) tptp.france))) % 168.83/169.83 (define @t20 () (not (_ (_ tptp.eq tptp.catalunya) tptp.paris))) % 168.83/169.83 (define @t21 () (lambda @t16 @t20)) % 168.83/169.83 (define @t22 () (not (_ tptp.mvalid (_ @t13 @t21)))) % 168.83/169.83 (define @t23 () (@var "Y" tptp.mu)) % 168.83/169.83 (define @t24 () (@var "X" tptp.mu)) % 168.83/169.83 (define @t25 () (@var "W" $$unsorted)) % 168.83/169.83 (define @t26 () (lambda (@list @t24 @t23 @t25) (= @t24 @t23))) % 168.83/169.83 (define @t27 () (@var "Y" (-> $$unsorted Bool))) % 168.83/169.83 (define @t28 () (@var "X" (-> $$unsorted Bool))) % 168.83/169.83 (define @t29 () (lambda (@list @t28 @t27 @t25) (= (_ @t28 @t25) (_ @t27 @t25)))) % 168.83/169.83 (define @t30 () (_ @t12 @t25)) % 168.83/169.83 (define @t31 () (not @t30)) % 168.83/169.83 (define @t32 () (@list @t12 @t25)) % 168.83/169.83 (define @t33 () (lambda @t32 @t31)) % 168.83/169.83 (define @t34 () (@var "Psi" (-> $$unsorted Bool))) % 168.83/169.83 (define @t35 () (_ @t34 @t25)) % 168.83/169.83 (define @t36 () (lambda (@list @t12 @t34 @t25) (or @t30 @t35))) % 168.83/169.83 (define @t37 () (_ tptp.mnot @t34)) % 168.83/169.83 (define @t38 () (_ tptp.mnot @t12)) % 168.83/169.83 (define @t39 () (_ tptp.mor @t38)) % 168.83/169.83 (define @t40 () (@list @t12 @t34 @t6)) % 168.83/169.83 (define @t41 () (lambda @t40 (_ (_ tptp.mnot (_ @t39 @t37)) @t6))) % 168.83/169.83 (define @t42 () (lambda @t40 (_ (_ @t39 @t34) @t6))) % 168.83/169.83 (define @t43 () (lambda @t40 (_ (_ (_ tptp.mor @t37) @t12) @t6))) % 168.83/169.83 (define @t44 () (lambda @t40 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t12) @t34)) (_ (_ tptp.mimplies @t34) @t12)) @t6))) % 168.83/169.83 (define @t45 () (lambda @t40 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t12) @t34)) @t6))) % 168.83/169.83 (define @t46 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 168.83/169.83 (define @t47 () (_ @t46 @t24)) % 168.83/169.83 (define @t48 () (lambda (@list @t46 @t25) (forall (@list @t24) (_ @t47 @t25)))) % 168.83/169.83 (define @t49 () (@var "P" (-> $$unsorted Bool))) % 168.83/169.83 (define @t50 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 168.83/169.83 (define @t51 () (_ @t50 @t49)) % 168.83/169.83 (define @t52 () (_ @t51 @t25)) % 168.83/169.83 (define @t53 () (@list @t49)) % 168.83/169.83 (define @t54 () (forall @t53 @t52)) % 168.83/169.83 (define @t55 () (@list @t50 @t25)) % 168.83/169.83 (define @t56 () (lambda @t55 @t54)) % 168.83/169.83 (define @t57 () (lambda (@list @t46 @t6) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list @t24 @t6) (_ (_ tptp.mnot @t47) @t6)))) @t6))) % 168.83/169.83 (define @t58 () (lambda (@list @t50 @t6) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t49 @t6) (_ (_ tptp.mnot @t51) @t6)))) @t6))) % 168.83/169.83 (define @t59 () (@list @t25)) % 168.83/169.83 (define @t60 () (lambda @t59 true)) % 168.83/169.83 (define @t61 () (@var "V" $$unsorted)) % 168.83/169.83 (define @t62 () (_ @t12 @t61)) % 168.83/169.83 (define @t63 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 168.83/169.83 (define @t64 () (_ (_ @t63 @t25) @t61)) % 168.83/169.83 (define @t65 () (not @t64)) % 168.83/169.83 (define @t66 () (or @t65 @t62)) % 168.83/169.83 (define @t67 () (@list @t61)) % 168.83/169.83 (define @t68 () (forall @t67 @t66)) % 168.83/169.83 (define @t69 () (@list @t63 @t12 @t25)) % 168.83/169.83 (define @t70 () (lambda @t69 @t68)) % 168.83/169.83 (define @t71 () (lambda (@list @t63 @t12 @t6) (_ (_ tptp.mnot (_ (_ tptp.mbox @t63) @t38)) @t6))) % 168.83/169.83 (define @t72 () (@var "S" $$unsorted)) % 168.83/169.83 (define @t73 () (_ @t63 @t72)) % 168.83/169.83 (define @t74 () (@list @t72)) % 168.83/169.83 (define @t75 () (@list @t63)) % 168.83/169.83 (define @t76 () (lambda @t75 (forall @t74 (_ @t73 @t72)))) % 168.83/169.83 (define @t77 () (@var "T" $$unsorted)) % 168.83/169.83 (define @t78 () (_ @t63 @t77)) % 168.83/169.83 (define @t79 () (_ @t73 @t77)) % 168.83/169.83 (define @t80 () (lambda @t75 (forall (@list @t72 @t77) (=> @t79 (_ @t78 @t72))))) % 168.83/169.83 (define @t81 () (@list @t77)) % 168.83/169.83 (define @t82 () (lambda @t75 (forall @t74 (exists @t81 @t79)))) % 168.83/169.83 (define @t83 () (@var "U" $$unsorted)) % 168.83/169.83 (define @t84 () (_ @t73 @t83)) % 168.83/169.83 (define @t85 () (_ @t78 @t83)) % 168.83/169.83 (define @t86 () (@list @t72 @t77 @t83)) % 168.83/169.83 (define @t87 () (lambda @t75 (forall @t86 (=> (and @t79 @t85) @t84)))) % 168.83/169.83 (define @t88 () (and @t79 @t84)) % 168.83/169.83 (define @t89 () (lambda @t75 (forall @t86 (=> @t88 @t85)))) % 168.83/169.83 (define @t90 () (= @t77 @t83)) % 168.83/169.83 (define @t91 () (lambda @t75 (forall @t86 (=> @t88 @t90)))) % 168.83/169.83 (define @t92 () (@list @t83)) % 168.83/169.83 (define @t93 () (lambda @t75 (forall @t74 (exists @t81 (and @t79 (forall @t92 (=> @t84 @t90))))))) % 168.83/169.83 (define @t94 () (_ @t63 @t83)) % 168.83/169.83 (define @t95 () (_ @t94 @t77)) % 168.83/169.83 (define @t96 () (lambda @t75 (forall @t86 (=> @t79 (exists @t92 (and @t84 @t95)))))) % 168.83/169.83 (define @t97 () (lambda @t75 (forall @t86 (=> @t88 (or @t85 @t90 @t95))))) % 168.83/169.83 (define @t98 () (lambda @t75 (forall @t86 (=> @t88 (exists @t67 (and (_ @t78 @t61) (_ @t94 @t61))))))) % 168.83/169.83 (define @t99 () (forall @t59 @t30)) % 168.83/169.83 (define @t100 () (@list @t12)) % 168.83/169.83 (define @t101 () (lambda @t100 @t99)) % 168.83/169.83 (define @t102 () (lambda @t100 (forall @t59 @t31))) % 168.83/169.83 (define @t103 () (lambda @t100 (exists @t59 @t30))) % 168.83/169.83 (define @t104 () (lambda @t100 (exists @t59 @t31))) % 168.83/169.83 (define @t105 () (lambda @t5 (not @t4))) % 168.83/169.83 (define @t106 () (@var "Z" tptp.reg)) % 168.83/169.83 (define @t107 () (_ tptp.c @t106)) % 168.83/169.83 (define @t108 () (_ @t107 @t3)) % 168.83/169.83 (define @t109 () (_ @t107 @t1)) % 168.83/169.83 (define @t110 () (@list @t106)) % 168.83/169.83 (define @t111 () (forall @t110 (=> @t109 @t108))) % 168.83/169.83 (define @t112 () (lambda @t5 @t111)) % 168.83/169.83 (define @t113 () (_ (_ tptp.p @t3) @t1)) % 168.83/169.83 (define @t114 () (_ (_ tptp.p @t1) @t3)) % 168.83/169.83 (define @t115 () (and @t114 @t113)) % 168.83/169.83 (define @t116 () (lambda @t5 @t115)) % 168.83/169.83 (define @t117 () (_ tptp.p @t106)) % 168.83/169.83 (define @t118 () (and (_ @t117 @t1) (_ @t117 @t3))) % 168.83/169.83 (define @t119 () (exists @t110 @t118)) % 168.83/169.83 (define @t120 () (lambda @t5 @t119)) % 168.83/169.83 (define @t121 () (not @t113)) % 168.83/169.83 (define @t122 () (_ (_ tptp.o @t1) @t3)) % 168.83/169.83 (define @t123 () (lambda @t5 (and @t122 (not @t114) @t121))) % 168.83/169.83 (define @t124 () (not @t122)) % 168.83/169.83 (define @t125 () (and @t4 @t124)) % 168.83/169.83 (define @t126 () (lambda @t5 @t125)) % 168.83/169.83 (define @t127 () (and @t114 @t121)) % 168.83/169.83 (define @t128 () (lambda @t5 @t127)) % 168.83/169.83 (define @t129 () (_ tptp.ec @t106)) % 168.83/169.83 (define @t130 () (and (_ @t129 @t1) (_ @t129 @t3))) % 168.83/169.83 (define @t131 () (exists @t110 @t130)) % 168.83/169.83 (define @t132 () (_ (_ tptp.pp @t1) @t3)) % 168.83/169.83 (define @t133 () (and @t132 @t131)) % 168.83/169.83 (define @t134 () (lambda @t5 @t133)) % 168.83/169.83 (define @t135 () (not @t131)) % 168.83/169.83 (define @t136 () (and @t132 @t135)) % 168.83/169.83 (define @t137 () (lambda @t5 @t136)) % 168.83/169.83 (define @t138 () (@var "BOUND_VARIABLE_8895" $$unsorted)) % 168.83/169.83 (define @t139 () (@var "BOUND_VARIABLE_9160" (@ho-elim-sort (-> $$unsorted Bool)))) % 168.83/169.83 (define @t140 () (@const 0 (-> (@ho-elim-sort (-> $$unsorted Bool)) $$unsorted Bool))) % 168.83/169.83 (define @t141 () (@const 1 (@ho-elim-sort (-> $$unsorted $$unsorted Bool)))) % 168.83/169.83 (define @t142 () (@const 2 (-> (@ho-elim-sort (-> $$unsorted $$unsorted Bool)) $$unsorted (@ho-elim-sort (-> $$unsorted Bool))))) % 168.83/169.83 (define @t143 () (_ @t142 @t141 @t25)) % 168.83/169.83 (define @t144 () (@const 3 (@ho-elim-sort (-> $$unsorted $$unsorted Bool)))) % 168.83/169.83 (define @t145 () (not (_ @t140 (_ @t142 @t144 @t25) @t61))) % 168.83/169.83 (define @t146 () (forall (@list @t25 @t139 @t138) (or (not (forall @t67 (or @t145 (_ @t140 @t139 @t61)))) (not (_ @t140 @t143 @t138)) (_ @t140 @t139 @t138)))) % 168.83/169.83 (define @t147 () (_ @t49 @t138)) % 168.83/169.83 (define @t148 () (not (tptp.a @t25 @t138))) % 168.83/169.83 (define @t149 () (_ @t49 @t61)) % 168.83/169.83 (define @t150 () (not (tptp.fool @t25 @t61))) % 168.83/169.83 (define @t151 () (not (forall @t67 (or @t150 @t149)))) % 168.83/169.83 (define @t152 () (or @t151 @t148 @t147)) % 168.83/169.83 (define @t153 () (forall (@list @t25 @t49 @t138) @t152)) % 168.83/169.83 (define @t154 () (@list @t49 @t138)) % 168.83/169.83 (define @t155 () (forall @t154 @t152)) % 168.83/169.83 (define @t156 () (lambda @t59 @t155)) % 168.83/169.83 (define @t157 () (_ @t156 @t25)) % 168.83/169.83 (define @t158 () (forall @t59 @t157)) % 168.83/169.83 (define @t159 () (_ @t12 @t25)) % 168.83/169.83 (define @t160 () (lambda @t100 (forall @t59 @t159))) % 168.83/169.83 (define @t161 () (or @t148 @t147)) % 168.83/169.83 (define @t162 () (or @t151 @t161)) % 168.83/169.83 (define @t163 () (forall @t154 @t162)) % 168.83/169.83 (define @t164 () (@list @t138)) % 168.83/169.83 (define @t165 () (forall @t164 @t162)) % 168.83/169.83 (define @t166 () (forall @t164 @t161)) % 168.83/169.83 (define @t167 () (or @t151 @t166)) % 168.83/169.83 (define @t168 () (not (tptp.a @t25 @t61))) % 168.83/169.83 (define @t169 () (or @t151 (forall @t67 (or @t168 @t149)))) % 168.83/169.83 (define @t170 () (_ @t12 @t61)) % 168.83/169.83 (define @t171 () (forall @t67 (or (not (tptp.a @t6 @t61)) @t170))) % 168.83/169.83 (define @t172 () (forall @t67 (or (not (tptp.fool @t6 @t61)) @t170))) % 168.83/169.83 (define @t173 () (not @t172)) % 168.83/169.83 (define @t174 () (or @t173 @t171)) % 168.83/169.83 (define @t175 () (lambda @t14 @t174)) % 168.83/169.83 (define @t176 () (_ @t175 @t49 @t25)) % 168.83/169.83 (define @t177 () (forall @t53 @t176)) % 168.83/169.83 (define @t178 () (lambda @t59 @t177)) % 168.83/169.83 (define @t179 () (_ @t50 @t49 @t25)) % 168.83/169.83 (define @t180 () (lambda @t55 (forall @t53 @t179))) % 168.83/169.83 (define @t181 () (@list @t6)) % 168.83/169.83 (define @t182 () (forall @t67 (or @t168 @t170))) % 168.83/169.83 (define @t183 () (lambda @t59 @t182)) % 168.83/169.83 (define @t184 () (_ @t183 @t6)) % 168.83/169.83 (define @t185 () (or @t173 @t184)) % 168.83/169.83 (define @t186 () (lambda @t181 @t185)) % 168.83/169.83 (define @t187 () (_ @t34 @t6)) % 168.83/169.83 (define @t188 () (@list @t34 @t6)) % 168.83/169.83 (define @t189 () (lambda @t32 @t182)) % 168.83/169.83 (define @t190 () (_ @t63 @t25 @t61)) % 168.83/169.83 (define @t191 () (lambda @t69 (forall @t67 (or (not @t190) @t170)))) % 168.83/169.83 (define @t192 () (_ @t191 tptp.a)) % 168.83/169.83 (define @t193 () (forall @t67 (or @t150 @t170))) % 168.83/169.83 (define @t194 () (lambda @t59 @t193)) % 168.83/169.83 (define @t195 () (_ @t194 @t6)) % 168.83/169.83 (define @t196 () (not @t195)) % 168.83/169.83 (define @t197 () (or @t196 @t187)) % 168.83/169.83 (define @t198 () (lambda @t188 @t197)) % 168.83/169.83 (define @t199 () (or (not (_ @t12 @t6)) @t187)) % 168.83/169.83 (define @t200 () (lambda @t40 @t199)) % 168.83/169.83 (define @t201 () (lambda @t32 @t193)) % 168.83/169.83 (define @t202 () (_ @t191 tptp.fool)) % 168.83/169.83 (define @t203 () (or @t31 @t35)) % 168.83/169.83 (define @t204 () (lambda @t59 @t203)) % 168.83/169.83 (define @t205 () (@list @t34 @t25)) % 168.83/169.83 (define @t206 () (lambda @t59 @t31)) % 168.83/169.83 (define @t207 () (_ @t206 @t25)) % 168.83/169.83 (define @t208 () (or @t207 @t35)) % 168.83/169.83 (define @t209 () (lambda @t205 @t208)) % 168.83/169.83 (define @t210 () (@list @t25 @t61)) % 168.83/169.83 (define @t211 () (forall @t210 (not (_ @t140 @t143 @t61)))) % 168.83/169.83 (define @t212 () (@quantifiers_skolemize @t211 1)) % 168.83/169.83 (define @t213 () (@quantifiers_skolemize @t211 0)) % 168.83/169.83 (define @t214 () (_ @t142 @t144 @t213)) % 168.83/169.83 (define @t215 () (_ @t140 @t214 @t212)) % 168.83/169.83 (define @t216 () (_ @t140 (_ @t142 @t141 @t213) @t212)) % 168.83/169.83 (define @t217 () (not @t216)) % 168.83/169.83 (define @t218 () (or @t217 @t215)) % 168.83/169.83 (define @t219 () (_ @t140 @t214 @t61)) % 168.83/169.83 (define @t220 () (forall @t67 (or (not @t219) @t219))) % 168.83/169.83 (define @t221 () (not @t220)) % 168.83/169.83 (define @t222 () (or @t221 @t217 @t215)) % 168.83/169.83 (define @t223 () (@list false)) % 168.83/169.83 (define @t224 () (@const 4 (@ho-elim-sort (-> tptp.reg tptp.reg Bool)))) % 168.83/169.83 (define @t225 () (@const 5 (-> (@ho-elim-sort (-> tptp.reg tptp.reg Bool)) tptp.reg (@ho-elim-sort (-> tptp.reg Bool))))) % 168.83/169.83 (define @t226 () (_ @t225 @t224 @t106)) % 168.83/169.83 (define @t227 () (@const 6 (-> (@ho-elim-sort (-> tptp.reg Bool)) tptp.reg Bool))) % 168.83/169.83 (define @t228 () (_ @t227 @t226 tptp.catalunya)) % 168.83/169.83 (define @t229 () (_ @t227 @t226 tptp.paris)) % 168.83/169.83 (define @t230 () (not @t229)) % 168.83/169.83 (define @t231 () (not @t228)) % 168.83/169.83 (define @t232 () (forall @t210 @t168)) % 168.83/169.83 (define @t233 () (tptp.c @t106 tptp.catalunya)) % 168.83/169.83 (define @t234 () (tptp.c @t106 tptp.paris)) % 168.83/169.83 (define @t235 () (not @t234)) % 168.83/169.83 (define @t236 () (forall @t110 (or @t235 @t233))) % 168.83/169.83 (define @t237 () (not @t236)) % 168.83/169.83 (define @t238 () (not @t233)) % 168.83/169.83 (define @t239 () (forall @t110 (or @t238 @t234))) % 168.83/169.83 (define @t240 () (not @t239)) % 168.83/169.83 (define @t241 () (forall @t67 @t168)) % 168.83/169.83 (define @t242 () (forall @t59 @t241)) % 168.83/169.83 (define @t243 () (or @t240 @t237 @t242)) % 168.83/169.83 (define @t244 () (or @t240 @t237 @t241)) % 168.83/169.83 (define @t245 () (lambda @t59 @t244)) % 168.83/169.83 (define @t246 () (_ @t245 @t25)) % 168.83/169.83 (define @t247 () (forall @t59 @t246)) % 168.83/169.83 (define @t248 () (or @t240 @t237 @t168)) % 168.83/169.83 (define @t249 () (or @t168 @t240 @t237)) % 168.83/169.83 (define @t250 () (and @t239 @t236)) % 168.83/169.83 (define @t251 () (not @t250)) % 168.83/169.83 (define @t252 () (or @t168 @t251)) % 168.83/169.83 (define @t253 () (lambda @t16 @t251)) % 168.83/169.83 (define @t254 () (_ @t253 @t61)) % 168.83/169.83 (define @t255 () (or @t168 @t254)) % 168.83/169.83 (define @t256 () (forall @t67 @t255)) % 168.83/169.83 (define @t257 () (lambda @t59 @t256)) % 168.83/169.83 (define @t258 () (tptp.c @t106 @t3)) % 168.83/169.83 (define @t259 () (not @t258)) % 168.83/169.83 (define @t260 () (forall @t110 (or @t259 @t233))) % 168.83/169.83 (define @t261 () (forall @t110 (or @t238 @t258))) % 168.83/169.83 (define @t262 () (@list @t3)) % 168.83/169.83 (define @t263 () (lambda @t262 (and @t261 @t260))) % 168.83/169.83 (define @t264 () (tptp.c @t106 @t1)) % 168.83/169.83 (define @t265 () (forall @t110 (or @t259 @t264))) % 168.83/169.83 (define @t266 () (not @t264)) % 168.83/169.83 (define @t267 () (forall @t110 (or @t266 @t258))) % 168.83/169.83 (define @t268 () (_ (lambda @t5 (and @t267 @t265)) tptp.catalunya)) % 168.83/169.83 (define @t269 () (not (_ @t268 tptp.paris))) % 168.83/169.83 (define @t270 () (lambda @t16 @t269)) % 168.83/169.83 (define @t271 () (@var "BOUND_VARIABLE_8290" tptp.reg)) % 168.83/169.83 (define @t272 () (tptp.c @t106 @t271)) % 168.83/169.83 (define @t273 () (lambda (@list @t271) (forall @t110 (or @t259 @t272)))) % 168.83/169.83 (define @t274 () (lambda @t5 @t267)) % 168.83/169.83 (define @t275 () (lambda @t262 @t267)) % 168.83/169.83 (define @t276 () (_ @t274 @t1)) % 168.83/169.83 (define @t277 () (_ (_ @t274 @t3) @t1)) % 168.83/169.83 (define @t278 () (_ @t276 @t3)) % 168.83/169.83 (define @t279 () (not @t109)) % 168.83/169.83 (define @t280 () (or @t279 @t108)) % 168.83/169.83 (define @t281 () (not @t211)) % 168.83/169.83 (define @t282 () (not @t217)) % 168.83/169.83 (define @t283 () (@list true)) % 168.83/169.83 (define @t284 () (@list @t211)) % 168.83/169.83 (define @t285 () (@list false false)) % 168.83/169.83 (define @t286 () (@var "BOUND_VARIABLE_8328" tptp.reg)) % 168.83/169.83 (define @t287 () (_ @t225 @t224 @t286)) % 168.83/169.83 (define @t288 () (_ @t227 @t287 tptp.france)) % 168.83/169.83 (define @t289 () (_ @t227 @t287 tptp.catalunya)) % 168.83/169.83 (define @t290 () (not @t289)) % 168.83/169.83 (define @t291 () (@list @t286)) % 168.83/169.83 (define @t292 () (forall @t291 (or @t290 @t288))) % 168.83/169.83 (define @t293 () (@quantifiers_skolemize @t292 0)) % 168.83/169.83 (define @t294 () (_ @t225 @t224 @t293)) % 168.83/169.83 (define @t295 () (_ @t227 @t294 tptp.catalunya)) % 168.83/169.83 (define @t296 () (_ @t227 @t294 tptp.france)) % 168.83/169.83 (define @t297 () (not @t295)) % 168.83/169.83 (define @t298 () (or @t297 @t296)) % 168.83/169.83 (define @t299 () (@list @t293)) % 168.83/169.83 (define @t300 () (_ @t227 @t294 tptp.paris)) % 168.83/169.83 (define @t301 () (or @t297 @t300)) % 168.83/169.83 (define @t302 () (_ @t227 @t226 tptp.france)) % 168.83/169.83 (define @t303 () (not @t302)) % 168.83/169.83 (define @t304 () (forall @t110 (or @t230 @t302))) % 168.83/169.83 (define @t305 () (@var "BOUND_VARIABLE_8441" tptp.reg)) % 168.83/169.83 (define @t306 () (not (_ @t227 @t287 @t305))) % 168.83/169.83 (define @t307 () (_ @t227 @t287 @t106)) % 168.83/169.83 (define @t308 () (not (forall @t291 (or @t306 @t307)))) % 168.83/169.83 (define @t309 () (@list @t305)) % 168.83/169.83 (define @t310 () (and (forall @t110 (or @t230 (not (forall @t309 (or @t308 (not (forall @t291 (or @t306 (_ @t227 @t287 tptp.paris))))))) @t303 (not (forall @t309 (or @t308 (not (forall @t291 (or @t306 @t288)))))))) @t304 (not (forall @t110 (or @t303 @t229))))) % 168.83/169.83 (define @t311 () (tptp.c @t106 tptp.france)) % 168.83/169.83 (define @t312 () (not @t311)) % 168.83/169.83 (define @t313 () (tptp.c @t286 tptp.france)) % 168.83/169.83 (define @t314 () (not (tptp.c @t286 @t305))) % 168.83/169.83 (define @t315 () (tptp.c @t286 @t106)) % 168.83/169.83 (define @t316 () (not (forall @t291 (or @t314 @t315)))) % 168.83/169.83 (define @t317 () (not (forall @t309 (or @t316 (not (forall @t291 (or @t314 (tptp.c @t286 tptp.paris)))))))) % 168.83/169.83 (define @t318 () (and (forall @t110 (or @t235 @t317 @t312 (not (forall @t309 (or @t316 (not (forall @t291 (or @t314 @t313)))))))) (forall @t110 (or @t235 @t311)) (not (forall @t110 (or @t312 @t234))))) % 168.83/169.83 (define @t319 () (or @t318 @t242)) % 168.83/169.83 (define @t320 () (or @t318 @t241)) % 168.83/169.83 (define @t321 () (lambda @t59 @t320)) % 168.83/169.83 (define @t322 () (_ @t321 @t25)) % 168.83/169.83 (define @t323 () (forall @t59 @t322)) % 168.83/169.83 (define @t324 () (or @t318 @t168)) % 168.83/169.83 (define @t325 () (or @t168 @t318)) % 168.83/169.83 (define @t326 () (lambda @t16 @t318)) % 168.83/169.83 (define @t327 () (_ @t326 @t61)) % 168.83/169.83 (define @t328 () (or @t168 @t327)) % 168.83/169.83 (define @t329 () (forall @t67 @t328)) % 168.83/169.83 (define @t330 () (lambda @t59 @t329)) % 168.83/169.83 (define @t331 () (tptp.c @t286 @t3)) % 168.83/169.83 (define @t332 () (not (forall @t291 (or @t314 @t331)))) % 168.83/169.83 (define @t333 () (forall @t309 (or @t316 @t332))) % 168.83/169.83 (define @t334 () (not @t333)) % 168.83/169.83 (define @t335 () (lambda @t262 (and (forall @t110 (or @t235 @t317 @t259 @t334)) (forall @t110 (or @t235 @t258)) (not (forall @t110 (or @t259 @t234)))))) % 168.83/169.83 (define @t336 () (not @t265)) % 168.83/169.83 (define @t337 () (tptp.c @t286 @t1)) % 168.83/169.83 (define @t338 () (not (forall @t291 (or @t314 @t337)))) % 168.83/169.83 (define @t339 () (forall @t309 (or @t316 @t338))) % 168.83/169.83 (define @t340 () (not @t339)) % 168.83/169.83 (define @t341 () (forall @t110 (or @t266 @t340 @t259 @t334))) % 168.83/169.83 (define @t342 () (and @t341 @t267 @t336)) % 168.83/169.83 (define @t343 () (_ (lambda @t5 @t342) tptp.paris)) % 168.83/169.83 (define @t344 () (and @t267 @t336)) % 168.83/169.83 (define @t345 () (not @t108)) % 168.83/169.83 (define @t346 () (or @t279 @t340 @t345 @t334)) % 168.83/169.83 (define @t347 () (and @t108 @t333)) % 168.83/169.83 (define @t348 () (and @t109 @t339 @t108 @t333)) % 168.83/169.83 (define @t349 () (forall @t110 (not @t348))) % 168.83/169.83 (define @t350 () (not @t349)) % 168.83/169.83 (define @t351 () (and @t109 @t339)) % 168.83/169.83 (define @t352 () (lambda @t262 @t347)) % 168.83/169.83 (define @t353 () (not @t315)) % 168.83/169.83 (define @t354 () (forall @t291 (or @t353 @t331))) % 168.83/169.83 (define @t355 () (not @t354)) % 168.83/169.83 (define @t356 () (forall @t291 (or @t353 @t337))) % 168.83/169.83 (define @t357 () (forall @t110 (or (not @t356) @t355))) % 168.83/169.83 (define @t358 () (@list @t106)) % 168.83/169.83 (define @t359 () (and @t4 @t357)) % 168.83/169.83 (define @t360 () (lambda @t5 @t359)) % 168.83/169.83 (define @t361 () (_ @t360 @t106)) % 168.83/169.83 (define @t362 () (and (_ @t361 @t1) (_ @t361 @t3))) % 168.83/169.83 (define @t363 () (exists @t110 @t362)) % 168.83/169.83 (define @t364 () (not @t363)) % 168.83/169.83 (define @t365 () (lambda @t262 @t344)) % 168.83/169.83 (define @t366 () (_ (lambda @t5 @t344) @t1)) % 168.83/169.83 (define @t367 () (_ @t366 @t3)) % 168.83/169.83 (define @t368 () (not @t357)) % 168.83/169.83 (define @t369 () (lambda @t262 @t368)) % 168.83/169.83 (define @t370 () (_ (lambda @t5 @t368) @t1)) % 168.83/169.83 (define @t371 () (not (_ @t370 @t3))) % 168.83/169.83 (define @t372 () (and @t356 @t354)) % 168.83/169.83 (define @t373 () (forall @t110 (not @t372))) % 168.83/169.83 (define @t374 () (not @t373)) % 168.83/169.83 (define @t375 () (lambda @t262 @t354)) % 168.83/169.83 (define @t376 () (@list @t286)) % 168.83/169.83 (define @t377 () (_ @t274 @t106)) % 168.83/169.83 (define @t378 () (and (_ @t377 @t1) (_ @t377 @t3))) % 168.83/169.83 (define @t379 () (not @t277)) % 168.83/169.83 (define @t380 () (not @t300)) % 168.83/169.83 (define @t381 () (or @t380 @t296)) % 168.83/169.83 (define @t382 () (not @t298)) % 168.83/169.83 (define @t383 () (not @t292)) % 168.83/169.83 (define @t384 () (_ @t227 @t226 tptp.spain)) % 168.83/169.83 (define @t385 () (not @t384)) % 168.83/169.83 (define @t386 () (forall @t110 (or @t231 @t384))) % 168.83/169.83 (define @t387 () (_ @t227 @t287 tptp.spain)) % 168.83/169.83 (define @t388 () (and (not (forall @t110 (or @t231 (not (forall @t309 (or @t308 (not (forall @t291 (or @t306 @t289)))))) @t385 (not (forall @t309 (or @t308 (not (forall @t291 (or @t306 @t387))))))))) @t386 (not (forall @t110 (or @t385 @t228))))) % 168.83/169.83 (define @t389 () (tptp.c @t106 tptp.spain)) % 168.83/169.83 (define @t390 () (not @t389)) % 168.83/169.83 (define @t391 () (tptp.c @t286 tptp.spain)) % 168.83/169.83 (define @t392 () (not (forall @t309 (or @t316 (not (forall @t291 (or @t314 (tptp.c @t286 tptp.catalunya)))))))) % 168.83/169.83 (define @t393 () (and (not (forall @t110 (or @t238 @t392 @t390 (not (forall @t309 (or @t316 (not (forall @t291 (or @t314 @t391))))))))) (forall @t110 (or @t238 @t389)) (not (forall @t110 (or @t390 @t233))))) % 168.83/169.83 (define @t394 () (or @t393 @t242)) % 168.83/169.83 (define @t395 () (or @t393 @t241)) % 168.83/169.83 (define @t396 () (lambda @t59 @t395)) % 168.83/169.83 (define @t397 () (_ @t396 @t25)) % 168.83/169.83 (define @t398 () (forall @t59 @t397)) % 168.83/169.83 (define @t399 () (or @t393 @t168)) % 168.83/169.83 (define @t400 () (or @t168 @t393)) % 168.83/169.83 (define @t401 () (lambda @t16 @t393)) % 168.83/169.83 (define @t402 () (_ @t401 @t61)) % 168.83/169.83 (define @t403 () (or @t168 @t402)) % 168.83/169.83 (define @t404 () (forall @t67 @t403)) % 168.83/169.83 (define @t405 () (lambda @t59 @t404)) % 168.83/169.83 (define @t406 () (lambda @t262 (and (not (forall @t110 (or @t238 @t392 @t259 @t334))) @t261 (not @t260)))) % 168.83/169.83 (define @t407 () (not @t341)) % 168.83/169.83 (define @t408 () (and @t407 @t267 @t336)) % 168.83/169.83 (define @t409 () (_ (lambda @t5 @t408) tptp.catalunya)) % 168.83/169.83 (define @t410 () (forall @t291 (or @t290 @t387))) % 168.83/169.83 (define @t411 () (not @t410)) % 168.83/169.83 (define @t412 () (or @t411 @t383)) % 168.83/169.83 (define @t413 () (not @t412)) % 168.83/169.83 (define @t414 () (not @t307)) % 168.83/169.83 (define @t415 () (forall @t110 (or (not (forall @t291 (or @t414 @t387))) (not (forall @t291 (or @t414 @t288)))))) % 168.83/169.83 (define @t416 () (and (_ @t227 (_ @t225 @t224 tptp.spain) tptp.france) @t415)) % 168.83/169.83 (define @t417 () (not @t416)) % 168.83/169.83 (define @t418 () (forall @t210 @t145)) % 168.83/169.83 (define @t419 () (forall @t210 @t150)) % 168.83/169.83 (define @t420 () (not (forall @t291 (or @t353 @t391)))) % 168.83/169.83 (define @t421 () (_ tptp.c tptp.spain)) % 168.83/169.83 (define @t422 () (and (_ @t421 tptp.france) (forall @t110 (or @t420 (not (forall @t291 (or @t353 @t313))))))) % 168.83/169.83 (define @t423 () (forall @t67 @t150)) % 168.83/169.83 (define @t424 () (forall @t59 @t423)) % 168.83/169.83 (define @t425 () (or @t422 @t424)) % 168.83/169.83 (define @t426 () (or @t422 @t423)) % 168.83/169.83 (define @t427 () (lambda @t59 @t426)) % 168.83/169.83 (define @t428 () (_ @t427 @t25)) % 168.83/169.83 (define @t429 () (forall @t59 @t428)) % 168.83/169.83 (define @t430 () (or @t422 @t150)) % 168.83/169.83 (define @t431 () (or @t150 @t422)) % 168.83/169.83 (define @t432 () (lambda @t16 @t422)) % 168.83/169.83 (define @t433 () (_ @t432 @t61)) % 168.83/169.83 (define @t434 () (or @t150 @t433)) % 168.83/169.83 (define @t435 () (forall @t67 @t434)) % 168.83/169.83 (define @t436 () (lambda @t59 @t435)) % 168.83/169.83 (define @t437 () (lambda @t262 (and (_ @t421 @t3) (forall @t110 (or @t420 @t355))))) % 168.83/169.83 (define @t438 () (_ @t360 tptp.spain)) % 168.83/169.83 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 168.83/169.83 (assume @p2 (forall (@list @t1) (_ @t2 @t1))) % 168.83/169.83 (assume @p3 (forall @t5 (=> @t4 (_ (_ tptp.c @t3) @t1)))) % 168.83/169.83 (assume @p4 (_ tptp.mvalid (_ tptp.mforall_prop (lambda @t11 (_ (_ @t10 @t7) @t6))))) % 168.83/169.83 (assume @p5 (_ tptp.mvalid (_ tptp.mforall_prop (lambda @t11 (_ (_ @t10 (_ @t8 @t9)) @t6))))) % 168.83/169.83 (assume @p6 (_ tptp.mvalid (_ tptp.mforall_prop @t15))) % 168.83/169.83 (assume @p7 (_ tptp.mvalid (_ @t13 @t17))) % 168.83/169.83 (assume @p8 (_ tptp.mvalid (_ @t8 @t18))) % 168.83/169.83 (assume @p9 (_ tptp.mvalid (_ @t13 @t19))) % 168.83/169.83 (assume @p10 @t22) % 168.83/169.83 (assume @p11 true) % 168.83/169.83 (step @p12 (= tptp.meq_ind @t26) :rule refl :args (@t26)) % 168.83/169.83 (step @p13 (= tptp.meq_prop @t29) :rule refl :args (@t29)) % 168.83/169.83 (step @p14 (= tptp.mnot @t33) :rule refl :args (@t33)) % 168.83/169.83 (step @p15 (= tptp.mor @t36) :rule refl :args (@t36)) % 168.83/169.83 (step @p16 (= tptp.mand @t41) :rule refl :args (@t41)) % 168.83/169.83 (step @p17 (= tptp.mimplies @t42) :rule refl :args (@t42)) % 168.83/169.83 (step @p18 (= tptp.mimplied @t43) :rule refl :args (@t43)) % 168.83/169.83 (step @p19 (= tptp.mequiv @t44) :rule refl :args (@t44)) % 168.83/169.83 (step @p20 (= tptp.mxor @t45) :rule refl :args (@t45)) % 168.83/169.83 (step @p21 (= tptp.mforall_ind @t48) :rule refl :args (@t48)) % 168.83/169.83 (step @p22 (= tptp.mforall_prop @t56) :rule refl :args (@t56)) % 168.83/169.83 (step @p23 (= tptp.mexists_ind @t57) :rule refl :args (@t57)) % 168.83/169.83 (step @p24 (= tptp.mexists_prop @t58) :rule refl :args (@t58)) % 168.83/169.83 (step @p25 (= tptp.mtrue @t60) :rule refl :args (@t60)) % 168.83/169.83 (step @p26 (= tptp.mbox @t70) :rule refl :args (@t70)) % 168.83/169.83 (step @p27 (= tptp.mdia @t71) :rule refl :args (@t71)) % 168.83/169.83 (step @p28 (= tptp.mreflexive @t76) :rule refl :args (@t76)) % 168.83/169.83 (step @p29 (= tptp.msymmetric @t80) :rule refl :args (@t80)) % 168.83/169.83 (step @p30 (= tptp.mserial @t82) :rule refl :args (@t82)) % 168.83/169.83 (step @p31 (= tptp.mtransitive @t87) :rule refl :args (@t87)) % 168.83/169.83 (step @p32 (= tptp.meuclidean @t89) :rule refl :args (@t89)) % 168.83/169.83 (step @p33 (= tptp.mpartially_functional @t91) :rule refl :args (@t91)) % 168.83/169.83 (step @p34 (= tptp.mfunctional @t93) :rule refl :args (@t93)) % 168.83/169.83 (step @p35 (= tptp.mweakly_dense @t96) :rule refl :args (@t96)) % 168.83/169.83 (step @p36 (= tptp.mweakly_connected @t97) :rule refl :args (@t97)) % 168.83/169.83 (step @p37 (= tptp.mweakly_directed @t98) :rule refl :args (@t98)) % 168.83/169.83 (step @p38 (= tptp.mvalid @t101) :rule refl :args (@t101)) % 168.83/169.83 (step @p39 (= tptp.minvalid @t102) :rule refl :args (@t102)) % 168.83/169.83 (step @p40 (= tptp.msatisfiable @t103) :rule refl :args (@t103)) % 168.83/169.83 (step @p41 (= tptp.mcountersatisfiable @t104) :rule refl :args (@t104)) % 168.83/169.83 (step @p42 (= tptp.dc @t105) :rule refl :args (@t105)) % 168.83/169.83 (step @p43 (= tptp.p @t112) :rule refl :args (@t112)) % 168.83/169.83 (step @p44 (= tptp.eq @t116) :rule refl :args (@t116)) % 168.83/169.83 (step @p45 (= tptp.o @t120) :rule refl :args (@t120)) % 168.83/169.83 (step @p46 (= tptp.po @t123) :rule refl :args (@t123)) % 168.83/169.83 (step @p47 (= tptp.ec @t126) :rule refl :args (@t126)) % 168.83/169.83 (step @p48 (= tptp.pp @t128) :rule refl :args (@t128)) % 168.83/169.83 (step @p49 (= tptp.tpp @t134) :rule refl :args (@t134)) % 168.83/169.83 (step @p50 (= tptp.ntpp @t137) :rule refl :args (@t137)) % 168.83/169.83 ; WARNING: add trust step for TRUST % 168.83/169.83 ; trust TRUST PREPROCESS_HO_ELIM % 168.83/169.83 (step @p51 :rule trust :premises () :args ((= @t153 @t146))) % 168.83/169.83 (step @p52 :rule quant-merge-prenex :args ((= (forall @t59 @t155) @t153))) % 168.83/169.83 (step @p53 :rule beta-reduce :args ((= @t157 @t155))) % 168.83/169.83 (step @p54 :rule cong :premises (@p53) :args (@t158)) % 168.83/169.83 (step @p55 :rule trans :premises (@p54 @p52)) % 168.83/169.83 (step @p56 :rule beta-reduce :args ((= (_ @t160 @t156) @t158))) % 168.83/169.83 (step @p57 :rule trans :premises (@p56 @p55)) % 168.83/169.83 (step @p58 :rule aci_norm :args ((= @t162 @t152))) % 168.83/169.83 (step @p59 :rule cong :premises (@p58) :args (@t163)) % 168.83/169.83 (step @p60 :rule quant-merge-prenex :args ((= (forall @t53 @t165) @t163))) % 168.83/169.83 (step @p61 :rule alpha_equiv :args (@t166 (@list @t138) (@list @t61))) % 168.83/169.83 (step @p62 :rule refl :args (@t151)) % 168.83/169.83 (step @p63 :rule nary_cong :premises (@p62 @p61) :args (@t167)) % 168.83/169.83 (step @p64 :rule quant-miniscope-or :args ((= @t165 @t167))) % 168.83/169.83 (step @p65 :rule trans :premises (@p64 @p63)) % 168.83/169.83 (step @p66 :rule symm :premises (@p65)) % 168.83/169.83 (step @p67 :rule cong :premises (@p66) :args ((forall @t53 @t169))) % 168.83/169.83 (step @p68 :rule trans :premises (@p67 @p60)) % 168.83/169.83 (step @p69 :rule trans :premises (@p68 @p59)) % 168.83/169.83 (step @p70 :rule beta-reduce :args ((= @t176 @t169))) % 168.83/169.83 (step @p71 :rule cong :premises (@p70) :args (@t177)) % 168.83/169.83 (step @p72 :rule trans :premises (@p71 @p69)) % 168.83/169.83 (step @p73 :rule cong :premises (@p72) :args (@t178)) % 168.83/169.83 (step @p74 :rule beta-reduce :args ((= (_ @t180 @t175) @t178))) % 168.83/169.83 (step @p75 :rule trans :premises (@p74 @p73)) % 168.83/169.83 (step @p76 :rule beta-reduce :args ((= (_ (lambda @t181 @t174) @t6) @t174))) % 168.83/169.83 (step @p77 :rule refl :args (@t6)) % 168.83/169.83 (step @p78 :rule beta-reduce :args ((= @t184 @t171))) % 168.83/169.83 (step @p79 :rule refl :args (@t173)) % 168.83/169.83 (step @p80 :rule nary_cong :premises (@p79 @p78) :args (@t185)) % 168.83/169.83 (step @p81 :rule cong :premises (@p80) :args (@t186)) % 168.83/169.83 (step @p82 :rule beta-reduce :args ((= (_ (lambda @t188 (or @t173 @t187)) @t183) @t186))) % 168.83/169.83 (step @p83 :rule trans :premises (@p82 @p81)) % 168.83/169.83 (step @p84 :rule beta-reduce :args ((= (_ @t189 @t12) @t183))) % 168.83/169.83 (step @p85 :rule refl :args (@t12)) % 168.83/169.83 (step @p86 :rule beta-reduce :args ((= @t192 @t189))) % 168.83/169.83 (step @p87 :rule ho_cong :premises (@p86 @p85)) % 168.83/169.83 (step @p88 :rule trans :premises (@p87 @p84)) % 168.83/169.83 (step @p89 :rule refl :args (@t187)) % 168.83/169.83 (step @p90 :rule beta-reduce :args ((= @t195 @t172))) % 168.83/169.83 (step @p91 :rule cong :premises (@p90) :args (@t196)) % 168.83/169.83 (step @p92 :rule nary_cong :premises (@p91 @p89) :args (@t197)) % 168.83/169.83 (step @p93 :rule cong :premises (@p92) :args (@t198)) % 168.83/169.83 (step @p94 :rule beta-reduce :args ((= (_ @t200 @t194) @t198))) % 168.83/169.83 (step @p95 :rule trans :premises (@p94 @p93)) % 168.83/169.83 (step @p96 :rule beta-reduce :args ((= (_ @t201 @t12) @t194))) % 168.83/169.83 (step @p97 :rule beta-reduce :args ((= @t202 @t201))) % 168.83/169.83 (step @p98 :rule ho_cong :premises (@p97 @p85)) % 168.83/169.83 (step @p99 :rule trans :premises (@p98 @p96)) % 168.83/169.83 (step @p100 :rule refl :args (@t200)) % 168.83/169.83 (step @p101 :rule ho_cong :premises (@p100 @p99)) % 168.83/169.83 (step @p102 :rule trans :premises (@p101 @p95)) % 168.83/169.83 (step @p103 :rule ho_cong :premises (@p102 @p88)) % 168.83/169.83 (step @p104 :rule trans :premises (@p103 @p83)) % 168.83/169.83 (step @p105 :rule ho_cong :premises (@p104 @p77)) % 168.83/169.83 (step @p106 :rule trans :premises (@p105 @p76)) % 168.83/169.83 (step @p107 :rule cong :premises (@p106) :args ((lambda @t14 (_ (_ (_ @t200 (_ @t202 @t12)) (_ @t192 @t12)) @t6)))) % 168.83/169.83 (step @p108 :rule refl :args (@t180)) % 168.83/169.83 (step @p109 :rule ho_cong :premises (@p108 @p107)) % 168.83/169.83 (step @p110 :rule trans :premises (@p109 @p75)) % 168.83/169.83 (step @p111 :rule refl :args (@t160)) % 168.83/169.83 (step @p112 :rule ho_cong :premises (@p111 @p110)) % 168.83/169.83 (step @p113 :rule trans :premises (@p112 @p57)) % 168.83/169.83 (step @p114 :rule refl :args (tptp.a)) % 168.83/169.83 (step @p115 :rule refl :args (@t170)) % 168.83/169.83 (step @p116 :rule refl :args (@t62)) % 168.83/169.83 (step @p117 :rule cong :premises (@p116 @p115) :args ((= @t62 @t170))) % 168.83/169.83 (step @p118 :rule symm :premises (@p117)) % 168.83/169.83 (step @p119 :rule eq_resolve :premises (@p116 @p118)) % 168.83/169.83 (step @p120 :rule refl :args (@t190)) % 168.83/169.83 (step @p121 :rule refl :args (@t64)) % 168.83/169.83 (step @p122 :rule cong :premises (@p121 @p120) :args ((= @t64 @t190))) % 168.83/169.83 (step @p123 :rule symm :premises (@p122)) % 168.83/169.83 (step @p124 :rule eq_resolve :premises (@p121 @p123)) % 168.83/169.83 (step @p125 :rule cong :premises (@p124) :args (@t65)) % 168.83/169.83 (step @p126 :rule nary_cong :premises (@p125 @p119) :args (@t66)) % 168.83/169.83 (step @p127 :rule cong :premises (@p126) :args (@t68)) % 168.83/169.83 (step @p128 :rule cong :premises (@p127) :args (@t70)) % 168.83/169.83 (step @p129 :rule trans :premises (@p26 @p128)) % 168.83/169.83 (step @p130 :rule ho_cong :premises (@p129 @p114)) % 168.83/169.83 (step @p131 :rule ho_cong :premises (@p130 @p85)) % 168.83/169.83 (step @p132 :rule refl :args (tptp.fool)) % 168.83/169.83 (step @p133 :rule ho_cong :premises (@p129 @p132)) % 168.83/169.83 (step @p134 :rule ho_cong :premises (@p133 @p85)) % 168.83/169.83 (step @p135 :rule beta-reduce :args ((= (_ @t204 @t6) @t199))) % 168.83/169.83 (step @p136 :rule beta-reduce :args ((= (_ (lambda @t205 @t203) @t34) @t204))) % 168.83/169.83 (step @p137 :rule refl :args (@t34)) % 168.83/169.83 (step @p138 :rule refl :args (@t35)) % 168.83/169.83 (step @p139 :rule beta-reduce :args ((= @t207 @t31))) % 168.83/169.83 (step @p140 :rule nary_cong :premises (@p139 @p138) :args (@t208)) % 168.83/169.83 (step @p141 :rule cong :premises (@p140) :args (@t209)) % 168.83/169.83 (step @p142 :rule beta-reduce :args ((= (_ @t36 @t206) @t209))) % 168.83/169.83 (step @p143 :rule trans :premises (@p142 @p141)) % 168.83/169.83 (step @p144 :rule beta-reduce :args ((= (_ @t33 @t12) @t206))) % 168.83/169.83 (step @p145 :rule refl :args (@t36)) % 168.83/169.83 (step @p146 :rule ho_cong :premises (@p145 @p144)) % 168.83/169.83 (step @p147 :rule trans :premises (@p146 @p143)) % 168.83/169.83 (step @p148 :rule ho_cong :premises (@p147 @p137)) % 168.83/169.83 (step @p149 :rule trans :premises (@p148 @p136)) % 168.83/169.83 (step @p150 :rule ho_cong :premises (@p149 @p77)) % 168.83/169.83 (step @p151 :rule trans :premises (@p150 @p135)) % 168.83/169.83 (step @p152 :rule ho_cong :premises (@p14 @p85)) % 168.83/169.83 (step @p153 :rule ho_cong :premises (@p15 @p152)) % 168.83/169.83 (step @p154 :rule ho_cong :premises (@p153 @p137)) % 168.83/169.83 (step @p155 :rule ho_cong :premises (@p154 @p77)) % 168.83/169.83 (step @p156 :rule trans :premises (@p155 @p151)) % 168.83/169.83 (step @p157 :rule cong :premises (@p156) :args (@t42)) % 168.83/169.83 (step @p158 :rule trans :premises (@p17 @p157)) % 168.83/169.83 (step @p159 :rule ho_cong :premises (@p158 @p134)) % 168.83/169.83 (step @p160 :rule ho_cong :premises (@p159 @p131)) % 168.83/169.83 (step @p161 :rule ho_cong :premises (@p160 @p77)) % 168.83/169.83 (step @p162 :rule cong :premises (@p161) :args (@t15)) % 168.83/169.83 (step @p163 :rule refl :args (@t179)) % 168.83/169.83 (step @p164 :rule refl :args (@t52)) % 168.83/169.83 (step @p165 :rule cong :premises (@p164 @p163) :args ((= @t52 @t179))) % 168.83/169.83 (step @p166 :rule symm :premises (@p165)) % 168.83/169.83 (step @p167 :rule eq_resolve :premises (@p164 @p166)) % 168.83/169.83 (step @p168 :rule cong :premises (@p167) :args (@t54)) % 168.83/169.83 (step @p169 :rule cong :premises (@p168) :args (@t56)) % 168.83/169.83 (step @p170 :rule trans :premises (@p22 @p169)) % 168.83/169.83 (step @p171 :rule ho_cong :premises (@p170 @p162)) % 168.83/169.83 (step @p172 :rule refl :args (@t159)) % 168.83/169.83 (step @p173 :rule refl :args (@t30)) % 168.83/169.83 (step @p174 :rule cong :premises (@p173 @p172) :args ((= @t30 @t159))) % 168.83/169.83 (step @p175 :rule symm :premises (@p174)) % 168.83/169.83 (step @p176 :rule eq_resolve :premises (@p173 @p175)) % 168.83/169.83 (step @p177 :rule cong :premises (@p176) :args (@t99)) % 168.83/169.83 (step @p178 :rule cong :premises (@p177) :args (@t101)) % 168.83/169.83 (step @p179 :rule trans :premises (@p38 @p178)) % 168.83/169.83 (step @p180 :rule ho_cong :premises (@p179 @p171)) % 168.83/169.83 (step @p181 :rule trans :premises (@p180 @p113)) % 168.83/169.83 (step @p182 :rule trans :premises (@p181 @p51)) % 168.83/169.83 (step @p183 :rule eq_resolve :premises (@p6 @p182)) % 168.83/169.83 (step @p184 :rule aci_norm :args ((= (or false @t217 @t215) @t218))) % 168.83/169.83 (step @p185 :rule refl :args (@t215)) % 168.83/169.83 (step @p186 :rule refl :args (@t217)) % 168.83/169.83 (step @p187 :rule evaluate :args ((not true))) % 168.83/169.83 (step @p188 :rule quant-unused-vars :args ((= (forall @t67 true) true))) % 168.83/169.83 (step @p189 :rule bool-or-taut2 :args (false @t219 false false)) % 168.83/169.83 (step @p190 :rule cong :premises (@p189) :args (@t220)) % 168.83/169.83 (step @p191 :rule trans :premises (@p190 @p188)) % 168.83/169.83 (step @p192 :rule cong :premises (@p191) :args (@t221)) % 168.83/169.83 (step @p193 :rule trans :premises (@p192 @p187)) % 168.83/169.83 (step @p194 :rule nary_cong :premises (@p193 @p186 @p185) :args (@t222)) % 168.83/169.83 (step @p195 :rule trans :premises (@p194 @p184)) % 168.83/169.83 (step @p196 :rule refl :args (@t146)) % 168.83/169.83 (step @p197 :rule cong :premises (@p196 @p195) :args ((=> @t146 @t222))) % 168.83/169.83 (assume-push @p614 @t146) % 168.83/169.83 (step @p199 :rule instantiate :premises (@p183) :args ((@list @t213 @t214 @t212))) % 168.83/169.83 (step-pop @p615 :rule scope :premises (@p199)) % 168.83/169.83 (step @p200 :rule process_scope :premises (@p615) :args (@t222)) % 168.83/169.83 (step @p202 :rule eq_resolve :premises (@p200 @p197)) % 168.83/169.83 (step @p203 :rule implies_elim :premises (@p202)) % 168.83/169.83 (step @p204 :rule chain_m_resolution :premises (@p203 @p183) :args (@t218 @t223 (@list @t146))) % 168.83/169.83 ; trust TRUST PREPROCESS_HO_ELIM % 168.83/169.83 (step @p205 :rule trust :premises () :args ((= (not (or @t240 @t237 @t232)) (not (or (not (forall @t110 (or @t231 @t229))) (not (forall @t110 (or @t230 @t228))) @t211))))) % 168.83/169.83 (step @p206 :rule quant-merge-prenex :args ((= @t242 @t232))) % 168.83/169.83 (step @p207 :rule refl :args (@t237)) % 168.83/169.83 (step @p208 :rule refl :args (@t240)) % 168.83/169.83 (step @p209 :rule nary_cong :premises (@p208 @p207 @p206) :args (@t243)) % 168.83/169.83 (step @p210 :rule quant-miniscope-or :args ((= (forall @t59 @t244) @t243))) % 168.83/169.83 (step @p211 :rule trans :premises (@p210 @p209)) % 168.83/169.83 (step @p212 :rule beta-reduce :args ((= @t246 @t244))) % 168.83/169.83 (step @p213 :rule cong :premises (@p212) :args (@t247)) % 168.83/169.83 (step @p214 :rule trans :premises (@p213 @p211)) % 168.83/169.83 (step @p215 :rule beta-reduce :args ((= (_ @t160 @t245) @t247))) % 168.83/169.83 (step @p216 :rule trans :premises (@p215 @p214)) % 168.83/169.83 (step @p217 :rule quant-miniscope-or :args ((= (forall @t67 @t248) @t244))) % 168.83/169.83 (step @p218 :rule aci_norm :args ((= @t249 @t248))) % 168.83/169.83 (step @p219 :rule cong :premises (@p218) :args ((forall @t67 @t249))) % 168.83/169.83 (step @p220 :rule trans :premises (@p219 @p217)) % 168.83/169.83 (step @p221 :rule aci_norm :args ((= (or @t168 (or @t240 @t237)) @t249))) % 168.83/169.83 (step @p222 :rule bool-and-de-morgan :args (@t239 @t236 true)) % 168.83/169.83 (step @p223 :rule refl :args (@t168)) % 168.83/169.83 (step @p224 :rule nary_cong :premises (@p223 @p222) :args (@t252)) % 168.83/169.83 (step @p225 :rule trans :premises (@p224 @p221)) % 168.83/169.83 (step @p226 :rule cong :premises (@p225) :args ((forall @t67 @t252))) % 168.83/169.83 (step @p227 :rule trans :premises (@p226 @p220)) % 168.83/169.83 (step @p228 :rule beta-reduce :args ((= @t254 @t251))) % 168.83/169.83 (step @p229 :rule refl :args (@t168)) % 168.83/169.83 (step @p230 :rule nary_cong :premises (@p229 @p228) :args (@t255)) % 168.83/169.83 (step @p231 :rule cong :premises (@p230) :args (@t256)) % 168.83/169.83 (step @p232 :rule trans :premises (@p231 @p227)) % 168.83/169.83 (step @p233 :rule cong :premises (@p232) :args (@t257)) % 168.83/169.83 (step @p234 :rule beta-reduce :args ((= (_ @t189 @t253) @t257))) % 168.83/169.83 (step @p235 :rule trans :premises (@p234 @p233)) % 168.83/169.83 (step @p236 :rule beta-reduce :args ((= (_ @t263 tptp.paris) @t250))) % 168.83/169.83 (step @p237 :rule refl :args (tptp.paris)) % 168.83/169.83 (step @p238 :rule beta-reduce :args ((= @t268 @t263))) % 168.83/169.83 (step @p239 :rule ho_cong :premises (@p238 @p237)) % 168.83/169.83 (step @p240 :rule trans :premises (@p239 @p236)) % 168.83/169.83 (step @p241 :rule cong :premises (@p240) :args (@t269)) % 168.83/169.83 (step @p242 :rule cong :premises (@p241) :args (@t270)) % 168.83/169.83 (step @p243 :rule ho_cong :premises (@p86 @p242)) % 168.83/169.83 (step @p244 :rule trans :premises (@p243 @p235)) % 168.83/169.83 (step @p245 :rule ho_cong :premises (@p111 @p244)) % 168.83/169.83 (step @p246 :rule trans :premises (@p245 @p216)) % 168.83/169.83 (step @p247 :rule cong :premises (@p246) :args ((not (_ @t160 (_ @t192 @t270))))) % 168.83/169.83 (step @p248 :rule refl :args (tptp.catalunya)) % 168.83/169.83 (step @p249 :rule beta-reduce :args ((= (_ @t273 @t1) @t265))) % 168.83/169.83 (step @p250 :rule refl :args (@t1)) % 168.83/169.83 (step @p251 :rule beta-reduce :args ((= (_ (lambda (@list @t1 @t271) (forall @t110 (or @t266 @t272))) @t3) @t273))) % 168.83/169.83 (step @p252 :rule refl :args (@t3)) % 168.83/169.83 (step @p253 :rule alpha_equiv :args (@t274 (@list @t3) (@list @t271))) % 168.83/169.83 (step @p254 :rule ho_cong :premises (@p253 @p252)) % 168.83/169.83 (step @p255 :rule trans :premises (@p254 @p251)) % 168.83/169.83 (step @p256 :rule ho_cong :premises (@p255 @p250)) % 168.83/169.83 (step @p257 :rule trans :premises (@p256 @p249)) % 168.83/169.83 (step @p258 :rule beta-reduce :args ((= (_ @t275 @t3) @t267))) % 168.83/169.83 (step @p259 :rule refl :args (@t3)) % 168.83/169.83 (step @p260 :rule beta-reduce :args ((= @t276 @t275))) % 168.83/169.83 (step @p261 :rule ho_cong :premises (@p260 @p259)) % 168.83/169.83 (step @p262 :rule trans :premises (@p261 @p258)) % 168.83/169.83 (step @p263 :rule nary_cong :premises (@p262 @p257) :args ((and @t278 @t277))) % 168.83/169.83 (step @p264 :rule refl :args (@t258)) % 168.83/169.83 (step @p265 :rule refl :args (@t108)) % 168.83/169.83 (step @p266 :rule cong :premises (@p265 @p264) :args ((= @t108 @t258))) % 168.83/169.83 (step @p267 :rule symm :premises (@p266)) % 168.83/169.83 (step @p268 :rule eq_resolve :premises (@p265 @p267)) % 168.83/169.83 (step @p269 :rule refl :args (@t264)) % 168.83/169.83 (step @p270 :rule refl :args (@t109)) % 168.83/169.83 (step @p271 :rule cong :premises (@p270 @p269) :args ((= @t109 @t264))) % 168.83/169.83 (step @p272 :rule symm :premises (@p271)) % 168.83/169.83 (step @p273 :rule eq_resolve :premises (@p270 @p272)) % 168.83/169.83 (step @p274 :rule cong :premises (@p273) :args (@t279)) % 168.83/169.83 (step @p275 :rule nary_cong :premises (@p274 @p268) :args (@t280)) % 168.83/169.83 (step @p276 :rule cong :premises (@p275) :args ((forall @t110 @t280))) % 168.83/169.83 (step @p277 :rule bool-impl-elim :args (@t109 @t108)) % 168.83/169.83 (step @p278 :rule cong :premises (@p277) :args (@t111)) % 168.83/169.83 (step @p279 :rule trans :premises (@p278 @p276)) % 168.83/169.83 (step @p280 :rule cong :premises (@p279) :args (@t112)) % 168.83/169.83 (step @p281 :rule trans :premises (@p43 @p280)) % 168.83/169.83 (step @p282 :rule ho_cong :premises (@p281 @p259)) % 168.83/169.83 (step @p283 :rule ho_cong :premises (@p282 @p250)) % 168.83/169.83 (step @p284 :rule ho_cong :premises (@p281 @p250)) % 168.83/169.83 (step @p285 :rule ho_cong :premises (@p284 @p259)) % 168.83/169.83 (step @p286 :rule nary_cong :premises (@p285 @p283) :args (@t115)) % 168.83/169.83 (step @p287 :rule trans :premises (@p286 @p263)) % 168.83/169.83 (step @p288 :rule cong :premises (@p287) :args (@t116)) % 168.83/169.83 (step @p289 :rule trans :premises (@p44 @p288)) % 168.83/169.83 (step @p290 :rule ho_cong :premises (@p289 @p248)) % 168.83/169.83 (step @p291 :rule ho_cong :premises (@p290 @p237)) % 168.83/169.83 (step @p292 :rule cong :premises (@p291) :args (@t20)) % 168.83/169.83 (step @p293 :rule cong :premises (@p292) :args (@t21)) % 168.83/169.83 (step @p294 :rule ho_cong :premises (@p130 @p293)) % 168.83/169.83 (step @p295 :rule ho_cong :premises (@p179 @p294)) % 168.83/169.83 (step @p296 :rule cong :premises (@p295) :args (@t22)) % 168.83/169.83 (step @p297 :rule trans :premises (@p296 @p247)) % 168.83/169.83 (step @p298 :rule trans :premises (@p297 @p205)) % 168.83/169.83 (step @p299 :rule eq_resolve :premises (@p10 @p298)) % 168.83/169.83 (step @p300 :rule not_or_elim :premises (@p299) :args (2)) % 168.83/169.83 (step @p301 :rule refl :args (@t216)) % 168.83/169.83 (step @p302 :rule bool-double-not-elim :args (@t211)) % 168.83/169.83 (step @p303 :rule nary_cong :premises (@p302 @p301) :args ((or (not @t281) @t216))) % 168.83/169.83 (step @p304 :rule bool-double-not-elim :args (@t216)) % 168.83/169.83 (step @p305 :rule refl :args (@t281)) % 168.83/169.83 (step @p306 :rule cong :premises (@p305 @p304) :args ((=> @t281 @t282))) % 168.83/169.83 (assume-push @p616 @t281) % 168.83/169.83 (step @p308 :rule skolemize :premises (@p300)) % 168.83/169.83 (step-pop @p617 :rule scope :premises (@p308)) % 168.83/169.83 (step @p309 :rule process_scope :premises (@p617) :args (@t282)) % 168.83/169.83 (step @p311 :rule eq_resolve :premises (@p309 @p306)) % 168.83/169.83 (step @p312 :rule implies_elim :premises (@p311)) % 168.83/169.83 (step @p313 :rule eq_resolve :premises (@p312 @p303)) % 168.83/169.83 (step @p314 :rule chain_m_resolution :premises (@p313 @p300) :args (@t216 @t283 @t284)) % 168.83/169.83 (step @p315 :rule cnf_or_pos :args (@t218)) % 168.83/169.83 (step @p316 :rule reordering :premises (@p315) :args ((or @t217 @t215 (not @t218)))) % 168.83/169.83 (step @p317 :rule chain_m_resolution :premises (@p316 @p314 @p204) :args (@t215 @t285 (@list @t216 @t218))) % 168.83/169.83 (step @p318 :rule bool-double-not-elim :args (@t295)) % 168.83/169.83 (step @p319 :rule refl :args (@t298)) % 168.83/169.83 (step @p320 :rule nary_cong :premises (@p319 @p318) :args ((or @t298 (not @t297)))) % 168.83/169.83 (step @p321 :rule cnf_or_neg :args (@t298 0)) % 168.83/169.83 (step @p322 :rule eq_resolve :premises (@p321 @p320)) % 168.83/169.83 (step @p323 :rule reordering :premises (@p322) :args ((or @t295 @t298))) % 168.83/169.83 (step @p324 :rule cnf_or_neg :args (@t298 1)) % 168.83/169.83 (step @p325 :rule not_or_elim :premises (@p299) :args (0)) % 168.83/169.83 (step @p326 :rule not_not_elim :premises (@p325)) % 168.83/169.83 (step @p327 :rule instantiate :premises (@p326) :args (@t299)) % 168.83/169.83 (step @p328 :rule cnf_or_pos :args (@t301)) % 168.83/169.83 (step @p329 :rule reordering :premises (@p328) :args ((or @t297 @t300 (not @t301)))) % 168.83/169.83 ; trust TRUST PREPROCESS_HO_ELIM % 168.83/169.83 (step @p330 :rule trust :premises () :args ((= (or @t318 @t232) (or @t310 @t211)))) % 168.83/169.83 (step @p331 :rule refl :args (@t318)) % 168.83/169.83 (step @p332 :rule nary_cong :premises (@p331 @p206) :args (@t319)) % 168.83/169.83 (step @p333 :rule quant-miniscope-or :args ((= (forall @t59 @t320) @t319))) % 168.83/169.83 (step @p334 :rule trans :premises (@p333 @p332)) % 168.83/169.83 (step @p335 :rule beta-reduce :args ((= @t322 @t320))) % 168.83/169.83 (step @p336 :rule cong :premises (@p335) :args (@t323)) % 168.83/169.83 (step @p337 :rule trans :premises (@p336 @p334)) % 168.83/169.83 (step @p338 :rule beta-reduce :args ((= (_ @t160 @t321) @t323))) % 168.83/169.83 (step @p339 :rule trans :premises (@p338 @p337)) % 168.83/169.83 (step @p340 :rule quant-miniscope-or :args ((= (forall @t67 @t324) @t320))) % 168.83/169.83 (step @p341 :rule aci_norm :args ((= @t325 @t324))) % 168.83/169.83 (step @p342 :rule cong :premises (@p341) :args ((forall @t67 @t325))) % 168.83/169.83 (step @p343 :rule trans :premises (@p342 @p340)) % 168.83/169.83 (step @p344 :rule beta-reduce :args ((= @t327 @t318))) % 168.83/169.83 (step @p345 :rule nary_cong :premises (@p229 @p344) :args (@t328)) % 168.83/169.83 (step @p346 :rule cong :premises (@p345) :args (@t329)) % 168.83/169.83 (step @p347 :rule trans :premises (@p346 @p343)) % 168.83/169.83 (step @p348 :rule cong :premises (@p347) :args (@t330)) % 168.83/169.83 (step @p349 :rule beta-reduce :args ((= (_ @t189 @t326) @t330))) % 168.83/169.83 (step @p350 :rule trans :premises (@p349 @p348)) % 168.83/169.83 (step @p351 :rule beta-reduce :args ((= (_ @t335 tptp.france) @t318))) % 168.83/169.83 (step @p352 :rule refl :args (tptp.france)) % 168.83/169.83 (step @p353 :rule beta-reduce :args ((= @t343 @t335))) % 168.83/169.83 (step @p354 :rule ho_cong :premises (@p353 @p352)) % 168.83/169.83 (step @p355 :rule trans :premises (@p354 @p351)) % 168.83/169.83 (step @p356 :rule cong :premises (@p355) :args ((lambda @t16 (_ @t343 tptp.france)))) % 168.83/169.83 (step @p357 :rule ho_cong :premises (@p86 @p356)) % 168.83/169.83 (step @p358 :rule trans :premises (@p357 @p350)) % 168.83/169.83 (step @p359 :rule ho_cong :premises (@p111 @p358)) % 168.83/169.83 (step @p360 :rule trans :premises (@p359 @p339)) % 168.83/169.83 (step @p361 :rule aci_norm :args ((= (and @t344 @t341) @t342))) % 168.83/169.83 (step @p362 :rule bool-double-not-elim :args (@t341)) % 168.83/169.83 (step @p363 :rule refl :args (@t334)) % 168.83/169.83 (step @p364 :rule cong :premises (@p268) :args (@t345)) % 168.83/169.83 (step @p365 :rule refl :args (@t340)) % 168.83/169.83 (step @p366 :rule nary_cong :premises (@p274 @p365 @p364 @p363) :args (@t346)) % 168.83/169.83 (step @p367 :rule cong :premises (@p366) :args ((forall @t110 @t346))) % 168.83/169.83 (step @p368 :rule aci_norm :args ((= (or @t279 (or @t340 (or @t345 @t334))) @t346))) % 168.83/169.83 (step @p369 :rule bool-and-de-morgan :args (@t108 @t333 true)) % 168.83/169.83 (step @p370 :rule nary_cong :premises (@p365 @p369) :args ((or @t340 (not @t347)))) % 168.83/169.83 (step @p371 :rule bool-and-de-morgan :args (@t339 @t108 (and @t333))) % 168.83/169.83 (step @p372 :rule trans :premises (@p371 @p370)) % 168.83/169.83 (step @p373 :rule refl :args (@t279)) % 168.83/169.83 (step @p374 :rule nary_cong :premises (@p373 @p372) :args ((or @t279 (not (and @t339 @t108 @t333))))) % 168.83/169.83 (step @p375 :rule bool-and-de-morgan :args (@t109 @t339 (and @t108 @t333))) % 168.83/169.83 (step @p376 :rule trans :premises (@p375 @p374)) % 168.83/169.83 (step @p377 :rule trans :premises (@p376 @p368)) % 168.83/169.83 (step @p378 :rule cong :premises (@p377) :args (@t349)) % 168.83/169.83 (step @p379 :rule trans :premises (@p378 @p367)) % 168.83/169.83 (step @p380 :rule cong :premises (@p379) :args (@t350)) % 168.83/169.83 (step @p381 :rule exists-elim :args ((= (exists @t110 @t348) @t350))) % 168.83/169.83 (step @p382 :rule trans :premises (@p381 @p380)) % 168.83/169.83 (step @p383 :rule aci_norm :args ((= (and @t351 @t347) @t348))) % 168.83/169.83 (step @p384 :rule beta-reduce :args ((= (_ @t352 @t3) @t347))) % 168.83/169.83 (step @p385 :rule beta-reduce :args ((= (_ (lambda @t5 (and @t4 (forall @t309 (or @t338 @t332)))) @t106) @t352))) % 168.83/169.83 (step @p386 :rule refl :args (@t106)) % 168.83/169.83 (step @p387 :rule alpha_equiv :args (@t357 @t358 (@list @t305))) % 168.83/169.83 (step @p388 :rule refl :args (@t4)) % 168.83/169.83 (step @p389 :rule nary_cong :premises (@p388 @p387) :args (@t359)) % 168.83/169.83 (step @p390 :rule cong :premises (@p389) :args (@t360)) % 168.83/169.83 (step @p391 :rule ho_cong :premises (@p390 @p386)) % 168.83/169.83 (step @p392 :rule trans :premises (@p391 @p385)) % 168.83/169.83 (step @p393 :rule ho_cong :premises (@p392 @p259)) % 168.83/169.83 (step @p394 :rule trans :premises (@p393 @p384)) % 168.83/169.83 (step @p395 :rule beta-reduce :args ((= (_ @t352 @t1) @t351))) % 168.83/169.83 (step @p396 :rule ho_cong :premises (@p392 @p250)) % 168.83/169.83 (step @p397 :rule trans :premises (@p396 @p395)) % 168.83/169.83 (step @p398 :rule nary_cong :premises (@p397 @p394) :args (@t362)) % 168.83/169.83 (step @p399 :rule trans :premises (@p398 @p383)) % 168.83/169.83 (step @p400 :rule cong :premises (@p399) :args (@t363)) % 168.83/169.83 (step @p401 :rule trans :premises (@p400 @p382)) % 168.83/169.83 (step @p402 :rule cong :premises (@p401) :args (@t364)) % 168.83/169.83 (step @p403 :rule trans :premises (@p402 @p362)) % 168.83/169.83 (step @p404 :rule beta-reduce :args ((= (_ @t365 @t3) @t344))) % 168.83/169.83 (step @p405 :rule beta-reduce :args ((= @t366 @t365))) % 168.83/169.83 (step @p406 :rule ho_cong :premises (@p405 @p259)) % 168.83/169.83 (step @p407 :rule trans :premises (@p406 @p404)) % 168.83/169.83 (step @p408 :rule nary_cong :premises (@p407 @p403) :args ((and @t367 @t364))) % 168.83/169.83 (step @p409 :rule trans :premises (@p408 @p361)) % 168.83/169.83 (step @p410 :rule refl :args (@t106)) % 168.83/169.83 (step @p411 :rule bool-double-not-elim :args (@t357)) % 168.83/169.83 (step @p412 :rule beta-reduce :args ((= (_ @t369 @t3) @t368))) % 168.83/169.83 (step @p413 :rule beta-reduce :args ((= @t370 @t369))) % 168.83/169.83 (step @p414 :rule ho_cong :premises (@p413 @p259)) % 168.83/169.83 (step @p415 :rule trans :premises (@p414 @p412)) % 168.83/169.83 (step @p416 :rule cong :premises (@p415) :args (@t371)) % 168.83/169.83 (step @p417 :rule trans :premises (@p416 @p411)) % 168.83/169.83 (step @p418 :rule refl :args (@t4)) % 168.83/169.83 (step @p419 :rule nary_cong :premises (@p418 @p417) :args ((and @t4 @t371))) % 168.83/169.83 (step @p420 :rule bool-and-de-morgan :args (@t356 @t354 true)) % 168.83/169.83 (step @p421 :rule cong :premises (@p420) :args (@t373)) % 168.83/169.83 (step @p422 :rule cong :premises (@p421) :args (@t374)) % 168.83/169.83 (step @p423 :rule exists-elim :args ((= (exists @t110 @t372) @t374))) % 168.83/169.83 (step @p424 :rule trans :premises (@p423 @p422)) % 168.83/169.83 (step @p425 :rule beta-reduce :args ((= (_ @t375 @t3) @t354))) % 168.83/169.83 (step @p426 :rule beta-reduce :args ((= (_ (lambda @t5 (forall @t291 (or (not @t337) @t331))) @t106) @t375))) % 168.83/169.83 (step @p427 :rule alpha_equiv :args (@t267 @t358 @t376)) % 168.83/169.83 (step @p428 :rule cong :premises (@p427) :args (@t274)) % 168.83/169.83 (step @p429 :rule ho_cong :premises (@p428 @p386)) % 168.83/169.83 (step @p430 :rule trans :premises (@p429 @p426)) % 168.83/169.83 (step @p431 :rule ho_cong :premises (@p430 @p259)) % 168.83/169.83 (step @p432 :rule trans :premises (@p431 @p425)) % 168.83/169.83 (step @p433 :rule beta-reduce :args ((= (_ @t375 @t1) @t356))) % 168.83/169.83 (step @p434 :rule ho_cong :premises (@p430 @p250)) % 168.83/169.83 (step @p435 :rule trans :premises (@p434 @p433)) % 168.83/169.83 (step @p436 :rule nary_cong :premises (@p435 @p432) :args (@t378)) % 168.83/169.83 (step @p437 :rule cong :premises (@p436) :args ((exists @t110 @t378))) % 168.83/169.83 (step @p438 :rule trans :premises (@p437 @p424)) % 168.83/169.83 (step @p439 :rule ho_cong :premises (@p281 @p410)) % 168.83/169.83 (step @p440 :rule ho_cong :premises (@p439 @p259)) % 168.83/169.83 (step @p441 :rule ho_cong :premises (@p439 @p250)) % 168.83/169.83 (step @p442 :rule nary_cong :premises (@p441 @p440) :args (@t118)) % 168.83/169.83 (step @p443 :rule cong :premises (@p442) :args (@t119)) % 168.83/169.83 (step @p444 :rule trans :premises (@p443 @p438)) % 168.83/169.83 (step @p445 :rule cong :premises (@p444) :args (@t120)) % 168.83/169.83 (step @p446 :rule trans :premises (@p45 @p445)) % 168.83/169.83 (step @p447 :rule ho_cong :premises (@p446 @p250)) % 168.83/169.83 (step @p448 :rule ho_cong :premises (@p447 @p259)) % 168.83/169.83 (step @p449 :rule cong :premises (@p448) :args (@t124)) % 168.83/169.83 (step @p450 :rule nary_cong :premises (@p418 @p449) :args (@t125)) % 168.83/169.83 (step @p451 :rule trans :premises (@p450 @p419)) % 168.83/169.83 (step @p452 :rule cong :premises (@p451) :args (@t126)) % 168.83/169.83 (step @p453 :rule trans :premises (@p47 @p452)) % 168.83/169.83 (step @p454 :rule ho_cong :premises (@p453 @p410)) % 168.83/169.83 (step @p455 :rule ho_cong :premises (@p454 @p259)) % 168.83/169.83 (step @p456 :rule ho_cong :premises (@p454 @p250)) % 168.83/169.83 (step @p457 :rule nary_cong :premises (@p456 @p455) :args (@t130)) % 168.83/169.83 (step @p458 :rule cong :premises (@p457) :args (@t131)) % 168.83/169.83 (step @p459 :rule cong :premises (@p458) :args (@t135)) % 168.83/169.83 (step @p460 :rule cong :premises (@p257) :args (@t379)) % 168.83/169.83 (step @p461 :rule nary_cong :premises (@p262 @p460) :args ((and @t278 @t379))) % 168.83/169.83 (step @p462 :rule cong :premises (@p283) :args (@t121)) % 168.83/169.83 (step @p463 :rule nary_cong :premises (@p285 @p462) :args (@t127)) % 168.83/169.83 (step @p464 :rule trans :premises (@p463 @p461)) % 168.83/169.83 (step @p465 :rule cong :premises (@p464) :args (@t128)) % 168.83/169.83 (step @p466 :rule trans :premises (@p48 @p465)) % 168.83/169.83 (step @p467 :rule ho_cong :premises (@p466 @p250)) % 168.83/169.83 (step @p468 :rule ho_cong :premises (@p467 @p259)) % 168.83/169.83 (step @p469 :rule nary_cong :premises (@p468 @p459) :args (@t136)) % 168.83/169.83 (step @p470 :rule trans :premises (@p469 @p409)) % 168.83/169.83 (step @p471 :rule cong :premises (@p470) :args (@t137)) % 168.83/169.83 (step @p472 :rule trans :premises (@p50 @p471)) % 168.83/169.83 (step @p473 :rule ho_cong :premises (@p472 @p237)) % 168.83/169.83 (step @p474 :rule ho_cong :premises (@p473 @p352)) % 168.83/169.83 (step @p475 :rule cong :premises (@p474) :args (@t19)) % 168.83/169.83 (step @p476 :rule ho_cong :premises (@p130 @p475)) % 168.83/169.83 (step @p477 :rule ho_cong :premises (@p179 @p476)) % 168.83/169.83 (step @p478 :rule trans :premises (@p477 @p360)) % 168.83/169.83 (step @p479 :rule trans :premises (@p478 @p330)) % 168.83/169.83 (step @p480 :rule eq_resolve :premises (@p9 @p479)) % 168.83/169.83 (step @p481 :rule reordering :premises (@p480) :args ((or @t211 @t310))) % 168.83/169.83 (step @p482 :rule chain_m_resolution :premises (@p481 @p300) :args (@t310 @t283 @t284)) % 168.83/169.83 (step @p483 :rule cnf_and_pos :args (@t310 1)) % 168.83/169.83 (step @p484 :rule reordering :premises (@p483) :args ((or @t304 (not @t310)))) % 168.83/169.83 (step @p485 :rule chain_m_resolution :premises (@p484 @p482) :args (@t304 @t223 (@list @t310))) % 168.83/169.83 (step @p486 :rule instantiate :premises (@p485) :args (@t299)) % 168.83/169.83 (step @p487 :rule cnf_or_pos :args (@t381)) % 168.83/169.83 (step @p488 :rule reordering :premises (@p487) :args ((or @t296 @t380 (not @t381)))) % 168.83/169.83 (step @p489 :rule chain_m_resolution :premises (@p488 @p486 @p329 @p327 @p324 @p323) :args (@t298 (@list false false false true false) (@list @t381 @t300 @t301 @t296 @t295))) % 168.83/169.83 (step @p490 :rule refl :args (@t382)) % 168.83/169.83 (step @p491 :rule bool-double-not-elim :args (@t292)) % 168.83/169.83 (step @p492 :rule nary_cong :premises (@p491 @p490) :args ((or (not @t383) @t382))) % 168.83/169.83 (assume-push @p618 @t383) % 168.83/169.83 (step @p494 :rule skolemize :premises (@p618)) % 168.83/169.83 (step-pop @p619 :rule scope :premises (@p494)) % 168.83/169.83 (step @p495 :rule process_scope :premises (@p619) :args (@t382)) % 168.83/169.83 (step @p497 :rule implies_elim :premises (@p495)) % 168.83/169.83 (step @p498 :rule eq_resolve :premises (@p497 @p492)) % 168.83/169.83 (step @p499 :rule chain_m_resolution :premises (@p498 @p489) :args (@t292 @t223 (@list @t298))) % 168.83/169.83 ; trust TRUST PREPROCESS_HO_ELIM % 168.83/169.83 (step @p500 :rule trust :premises () :args ((= (or @t393 @t232) (or @t388 @t211)))) % 168.83/169.83 (step @p501 :rule refl :args (@t393)) % 168.83/169.83 (step @p502 :rule nary_cong :premises (@p501 @p206) :args (@t394)) % 168.83/169.83 (step @p503 :rule quant-miniscope-or :args ((= (forall @t59 @t395) @t394))) % 168.83/169.83 (step @p504 :rule trans :premises (@p503 @p502)) % 168.83/169.83 (step @p505 :rule beta-reduce :args ((= @t397 @t395))) % 168.83/169.83 (step @p506 :rule cong :premises (@p505) :args (@t398)) % 168.83/169.83 (step @p507 :rule trans :premises (@p506 @p504)) % 168.83/169.83 (step @p508 :rule beta-reduce :args ((= (_ @t160 @t396) @t398))) % 168.83/169.83 (step @p509 :rule trans :premises (@p508 @p507)) % 168.83/169.83 (step @p510 :rule quant-miniscope-or :args ((= (forall @t67 @t399) @t395))) % 168.83/169.83 (step @p511 :rule aci_norm :args ((= @t400 @t399))) % 168.83/169.83 (step @p512 :rule cong :premises (@p511) :args ((forall @t67 @t400))) % 168.83/169.83 (step @p513 :rule trans :premises (@p512 @p510)) % 168.83/169.83 (step @p514 :rule beta-reduce :args ((= @t402 @t393))) % 168.83/169.83 (step @p515 :rule nary_cong :premises (@p229 @p514) :args (@t403)) % 168.83/169.83 (step @p516 :rule cong :premises (@p515) :args (@t404)) % 168.83/169.83 (step @p517 :rule trans :premises (@p516 @p513)) % 168.83/169.83 (step @p518 :rule cong :premises (@p517) :args (@t405)) % 168.83/169.83 (step @p519 :rule beta-reduce :args ((= (_ @t189 @t401) @t405))) % 168.83/169.83 (step @p520 :rule trans :premises (@p519 @p518)) % 168.83/169.83 (step @p521 :rule beta-reduce :args ((= (_ @t406 tptp.spain) @t393))) % 168.83/169.83 (step @p522 :rule refl :args (tptp.spain)) % 168.83/169.83 (step @p523 :rule beta-reduce :args ((= @t409 @t406))) % 168.83/169.83 (step @p524 :rule ho_cong :premises (@p523 @p522)) % 168.83/169.83 (step @p525 :rule trans :premises (@p524 @p521)) % 168.83/169.83 (step @p526 :rule cong :premises (@p525) :args ((lambda @t16 (_ @t409 tptp.spain)))) % 168.83/169.83 (step @p527 :rule ho_cong :premises (@p86 @p526)) % 168.83/169.83 (step @p528 :rule trans :premises (@p527 @p520)) % 168.83/169.83 (step @p529 :rule ho_cong :premises (@p111 @p528)) % 168.83/169.83 (step @p530 :rule trans :premises (@p529 @p509)) % 168.83/169.83 (step @p531 :rule aci_norm :args ((= (and @t344 @t407) @t408))) % 168.83/169.83 (step @p532 :rule nary_cong :premises (@p407 @p401) :args ((and @t367 @t363))) % 168.83/169.83 (step @p533 :rule trans :premises (@p532 @p531)) % 168.83/169.83 (step @p534 :rule nary_cong :premises (@p468 @p458) :args (@t133)) % 168.83/169.83 (step @p535 :rule trans :premises (@p534 @p533)) % 168.83/169.83 (step @p536 :rule cong :premises (@p535) :args (@t134)) % 168.83/169.83 (step @p537 :rule trans :premises (@p49 @p536)) % 168.83/169.83 (step @p538 :rule ho_cong :premises (@p537 @p248)) % 168.83/169.83 (step @p539 :rule ho_cong :premises (@p538 @p522)) % 168.83/169.83 (step @p540 :rule cong :premises (@p539) :args (@t17)) % 168.83/169.83 (step @p541 :rule ho_cong :premises (@p130 @p540)) % 168.83/169.83 (step @p542 :rule ho_cong :premises (@p179 @p541)) % 168.83/169.83 (step @p543 :rule trans :premises (@p542 @p530)) % 168.83/169.83 (step @p544 :rule trans :premises (@p543 @p500)) % 168.83/169.83 (step @p545 :rule eq_resolve :premises (@p7 @p544)) % 168.83/169.83 (step @p546 :rule reordering :premises (@p545) :args ((or @t211 @t388))) % 168.83/169.83 (step @p547 :rule chain_m_resolution :premises (@p546 @p300) :args (@t388 @t283 @t284)) % 168.83/169.83 (step @p548 :rule cnf_and_pos :args (@t388 1)) % 168.83/169.83 (step @p549 :rule reordering :premises (@p548) :args ((or @t386 (not @t388)))) % 168.83/169.83 (step @p550 :rule chain_m_resolution :premises (@p549 @p547) :args (@t386 @t223 (@list @t388))) % 168.83/169.83 (step @p551 :rule alpha_equiv :args (@t386 @t358 @t376)) % 168.83/169.83 (step @p552 :rule equiv_elim1 :premises (@p551)) % 168.83/169.83 (step @p553 :rule chain_m_resolution :premises (@p552 @p550) :args (@t410 @t223 (@list @t386))) % 168.83/169.83 (step @p554 :rule cnf_or_pos :args (@t412)) % 168.83/169.83 (step @p555 :rule reordering :premises (@p554) :args ((or @t411 @t383 @t413))) % 168.83/169.83 (step @p556 :rule chain_m_resolution :premises (@p555 @p553 @p499) :args (@t413 @t285 (@list @t410 @t292))) % 168.83/169.83 (assume-push @p620 @t415) % 168.83/169.83 (step @p558 :rule instantiate :premises (@p620) :args ((@list tptp.catalunya))) % 168.83/169.83 (step-pop @p621 :rule scope :premises (@p558)) % 168.83/169.83 (step @p559 :rule process_scope :premises (@p621) :args (@t412)) % 168.83/169.83 (step @p561 :rule implies_elim :premises (@p559)) % 168.83/169.83 (step @p562 :rule chain_m_resolution :premises (@p561 @p556) :args ((not @t415) @t283 (@list @t412))) % 168.83/169.83 (step @p563 :rule cnf_and_pos :args (@t416 1)) % 168.83/169.83 (step @p564 :rule reordering :premises (@p563) :args ((or @t415 @t417))) % 168.83/169.83 (step @p565 :rule chain_m_resolution :premises (@p564 @p562) :args (@t417 @t283 (@list @t415))) % 168.83/169.83 ; trust TRUST PREPROCESS_HO_ELIM % 168.83/169.83 (step @p566 :rule trust :premises () :args ((= (or @t422 @t419) (or @t416 @t418)))) % 168.83/169.83 (step @p567 :rule quant-merge-prenex :args ((= @t424 @t419))) % 168.83/169.83 (step @p568 :rule refl :args (@t422)) % 168.83/169.83 (step @p569 :rule nary_cong :premises (@p568 @p567) :args (@t425)) % 168.83/169.83 (step @p570 :rule quant-miniscope-or :args ((= (forall @t59 @t426) @t425))) % 168.83/169.83 (step @p571 :rule trans :premises (@p570 @p569)) % 168.83/169.83 (step @p572 :rule beta-reduce :args ((= @t428 @t426))) % 168.83/169.83 (step @p573 :rule cong :premises (@p572) :args (@t429)) % 168.83/169.83 (step @p574 :rule trans :premises (@p573 @p571)) % 168.83/169.83 (step @p575 :rule beta-reduce :args ((= (_ @t160 @t427) @t429))) % 168.83/169.83 (step @p576 :rule trans :premises (@p575 @p574)) % 168.83/169.83 (step @p577 :rule quant-miniscope-or :args ((= (forall @t67 @t430) @t426))) % 168.83/169.83 (step @p578 :rule aci_norm :args ((= @t431 @t430))) % 168.83/169.83 (step @p579 :rule cong :premises (@p578) :args ((forall @t67 @t431))) % 168.83/169.83 (step @p580 :rule trans :premises (@p579 @p577)) % 168.83/169.83 (step @p581 :rule beta-reduce :args ((= @t433 @t422))) % 168.83/169.83 (step @p582 :rule refl :args (@t150)) % 168.83/169.83 (step @p583 :rule nary_cong :premises (@p582 @p581) :args (@t434)) % 168.83/169.83 (step @p584 :rule cong :premises (@p583) :args (@t435)) % 168.83/169.83 (step @p585 :rule trans :premises (@p584 @p580)) % 168.83/169.83 (step @p586 :rule cong :premises (@p585) :args (@t436)) % 168.83/169.83 (step @p587 :rule beta-reduce :args ((= (_ @t201 @t432) @t436))) % 168.83/169.83 (step @p588 :rule trans :premises (@p587 @p586)) % 168.83/169.83 (step @p589 :rule beta-reduce :args ((= (_ @t437 tptp.france) @t422))) % 168.83/169.83 (step @p590 :rule beta-reduce :args ((= @t438 @t437))) % 168.83/169.83 (step @p591 :rule ho_cong :premises (@p590 @p352)) % 168.83/169.83 (step @p592 :rule trans :premises (@p591 @p589)) % 168.83/169.83 (step @p593 :rule cong :premises (@p592) :args ((lambda @t16 (_ @t438 tptp.france)))) % 168.83/169.83 (step @p594 :rule ho_cong :premises (@p97 @p593)) % 168.83/169.83 (step @p595 :rule trans :premises (@p594 @p588)) % 168.83/169.83 (step @p596 :rule ho_cong :premises (@p111 @p595)) % 168.83/169.83 (step @p597 :rule trans :premises (@p596 @p576)) % 168.83/169.83 (step @p598 :rule ho_cong :premises (@p453 @p522)) % 168.83/169.83 (step @p599 :rule ho_cong :premises (@p598 @p352)) % 168.83/169.83 (step @p600 :rule cong :premises (@p599) :args (@t18)) % 168.83/169.83 (step @p601 :rule ho_cong :premises (@p133 @p600)) % 168.83/169.83 (step @p602 :rule ho_cong :premises (@p179 @p601)) % 168.83/169.83 (step @p603 :rule trans :premises (@p602 @p597)) % 168.83/169.83 (step @p604 :rule trans :premises (@p603 @p566)) % 168.83/169.83 (step @p605 :rule eq_resolve :premises (@p8 @p604)) % 168.83/169.83 (step @p606 :rule reordering :premises (@p605) :args ((or @t418 @t416))) % 168.83/169.83 (step @p607 :rule chain_m_resolution :premises (@p606 @p565) :args (@t418 @t283 (@list @t416))) % 168.83/169.83 (assume-push @p622 @t418) % 168.83/169.83 (step @p609 :rule instantiate :premises (@p622) :args ((@list @t213 @t212))) % 168.83/169.83 (step-pop @p623 :rule scope :premises (@p609)) % 168.83/169.83 (step @p610 :rule process_scope :premises (@p623) :args ((not @t215))) % 168.83/169.83 (step @p612 :rule implies_elim :premises (@p610)) % 168.83/169.83 (step @p613 false :rule chain_m_resolution :premises (@p612 @p607 @p317) :args (false @t285 (@list @t418 @t215))) % 168.83/169.83 ) % 168.83/169.83 % SZS output end Proof % 168.83/169.83 % cvc5 exiting %------------------------------------------------------------------------------