%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : AGT033^1 : TPTP v9.2.1. Bugfixed v5.4.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n021.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 08:04:48 AM UTC 2026 % Result : Theorem 169.02s 169.36s % Output : Proof 169.02s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : AGT033^1 : TPTP v9.2.1. Bugfixed v5.4.0. % 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 : n021.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Wed Jun 3 01:34:35 EDT 2026 % 0.17/0.34 % CPUTime : % 0.29/0.51 %----Proving TH0 % 169.02/169.36 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 169.02/169.36 --- 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... % 169.02/169.36 --- 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... % 169.02/169.36 --- Run --ho-elim --full-saturate-quant at 18s... % 169.02/169.36 --- Run --ho-elim --no-e-matching --full-saturate-quant at 12s... % 169.02/169.36 % SZS status Theorem % 169.02/169.36 % SZS output start Proof % 169.02/169.36 ( % 169.02/169.36 (declare-sort $$unsorted 0) % 169.02/169.36 (declare-sort tptp.mu 0) % 169.02/169.36 (declare-const tptp.possibly_likes (-> tptp.mu tptp.mu $$unsorted Bool)) % 169.02/169.36 (declare-const tptp.very_much_likes (-> tptp.mu tptp.mu $$unsorted Bool)) % 169.02/169.36 (declare-const tptp.beer tptp.mu) % 169.02/169.36 (declare-const tptp.cola tptp.mu) % 169.02/169.36 (declare-const tptp.jan tptp.mu) % 169.02/169.36 (declare-const tptp.likes (-> tptp.mu tptp.mu $$unsorted Bool)) % 169.02/169.36 (declare-const tptp.a1 (-> $$unsorted $$unsorted Bool)) % 169.02/169.36 (declare-const tptp.pepsi tptp.mu) % 169.02/169.36 (declare-const tptp.piotr tptp.mu) % 169.02/169.36 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 169.02/169.36 (declare-const tptp.a2 (-> $$unsorted $$unsorted Bool)) % 169.02/169.36 (declare-const tptp.a3 (-> $$unsorted $$unsorted Bool)) % 169.02/169.36 (define tptp.meq_ind () (let ((_let_1 (@var "Y" tptp.mu))) (let ((_let_2 (@var "X" tptp.mu))) (lambda (@list _let_2 _let_1 (@var "W" $$unsorted)) (= _let_2 _let_1))))) % 169.02/169.36 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (= (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 169.02/169.36 (define tptp.mnot () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 169.02/169.36 (define tptp.mor () (let ((_let_1 (@var "W" $$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))))))) % 169.02/169.36 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mor (_ tptp.mnot _let_3)) (_ tptp.mnot _let_2))) _let_1)))))) % 169.02/169.36 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 169.02/169.36 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 169.02/169.36 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 169.02/169.36 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mequiv _let_3) _let_2)) _let_1)))))) % 169.02/169.36 (define tptp.mforall_ind () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 169.02/169.36 (define tptp.mforall_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 169.02/169.36 (define tptp.mexists_ind () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 169.02/169.36 (define tptp.mexists_prop () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 169.02/169.36 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 169.02/169.36 (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 $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ _let_4 _let_3) _let_1)) (_ _let_2 _let_1))))))))) % 169.02/169.36 (define tptp.mdia () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mbox _let_3) (_ tptp.mnot _let_2))) _let_1)))))) % 169.02/169.36 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 169.02/169.36 (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)))))))) % 169.02/169.36 (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)))))))) % 169.02/169.36 (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" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_2 _let_5 _let_1) (=> (and (_ _let_4 _let_5) (_ (_ _let_3 _let_5) _let_1)) (_ _let_4 _let_1)))))))))) % 169.02/169.36 (define tptp.meuclidean () (let ((_let_1 (@var "U" $$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)))))))))) % 169.02/169.36 (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 $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (= _let_2 _let_1)))))))))) % 169.02/169.36 (define tptp.mfunctional () (let ((_let_1 (@var "U" $$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))))))))))))) % 169.02/169.36 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (_ _let_5 _let_1) (exists (@list _let_2) (and (_ _let_5 _let_2) (_ (_ _let_3 _let_2) _let_1)))))))))))) % 169.02/169.36 (define tptp.mweakly_connected () (let ((_let_1 (@var "T" $$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))))))))))) % 169.02/169.36 (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))))))))))))) % 169.02/169.36 (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)))))) % 169.02/169.36 (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))))))) % 169.02/169.36 (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)))))) % 169.02/169.36 (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))))))) % 169.02/169.36 (define tptp.subrel () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R2" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "R1" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_3) (forall (@list _let_2 _let_1) (=> (_ (_ _let_4 _let_2) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))) % 169.02/169.36 (define tptp.cond4s () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "R2" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "V" $$unsorted))) (let ((_let_5 (@var "R1" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_5 _let_3) (forall (@list _let_2 _let_4 _let_1) (=> (and (_ (_ _let_5 _let_2) _let_4) (_ (_ _let_3 _let_4) _let_1)) (_ (_ _let_3 _let_2) _let_1)))))))))) % 169.02/169.36 (define @t1 () (_ tptp.likes tptp.jan)) % 169.02/169.36 (define @t2 () (_ @t1 tptp.cola)) % 169.02/169.36 (define @t3 () (_ tptp.mbox tptp.a1)) % 169.02/169.36 (define @t4 () (_ tptp.likes tptp.piotr)) % 169.02/169.36 (define @t5 () (_ @t4 tptp.pepsi)) % 169.02/169.36 (define @t6 () (@var "__flatten_var_0" $$unsorted)) % 169.02/169.36 (define @t7 () (@var "X" tptp.mu)) % 169.02/169.36 (define @t8 () (_ tptp.likes @t7)) % 169.02/169.36 (define @t9 () (_ @t8 tptp.cola)) % 169.02/169.36 (define @t10 () (_ @t8 tptp.pepsi)) % 169.02/169.36 (define @t11 () (_ tptp.mdia tptp.a1)) % 169.02/169.36 (define @t12 () (@list @t7 @t6)) % 169.02/169.36 (define @t13 () (_ tptp.mbox tptp.a2)) % 169.02/169.36 (define @t14 () (_ @t4 tptp.beer)) % 169.02/169.36 (define @t15 () (_ tptp.mbox tptp.a3)) % 169.02/169.36 (define @t16 () (_ tptp.mdia tptp.a3)) % 169.02/169.36 (define @t17 () (@var "Y" tptp.mu)) % 169.02/169.36 (define @t18 () (_ (_ tptp.very_much_likes @t7) @t17)) % 169.02/169.36 (define @t19 () (_ @t8 @t17)) % 169.02/169.36 (define @t20 () (@list @t17 @t6)) % 169.02/169.36 (define @t21 () (_ tptp.possibly_likes @t7)) % 169.02/169.36 (define @t22 () (_ @t21 @t17)) % 169.02/169.36 (define @t23 () (lambda @t20 (_ (_ (_ tptp.mimplies (_ @t16 @t19)) @t22) @t6))) % 169.02/169.36 (define @t24 () (lambda @t12 (_ (_ tptp.mforall_ind @t23) @t6))) % 169.02/169.36 (define @t25 () (_ tptp.subrel tptp.a1)) % 169.02/169.36 (define @t26 () (_ tptp.cond4s tptp.a1)) % 169.02/169.36 (define @t27 () (_ tptp.cond4s tptp.a2)) % 169.02/169.36 (define @t28 () (_ @t22 @t6)) % 169.02/169.36 (define @t29 () (lambda @t20 @t28)) % 169.02/169.36 (define @t30 () (lambda @t12 (_ (_ tptp.mexists_ind @t29) @t6))) % 169.02/169.36 (define @t31 () (not (_ tptp.mvalid (_ tptp.mexists_ind @t30)))) % 169.02/169.36 (define @t32 () (@var "W" $$unsorted)) % 169.02/169.36 (define @t33 () (lambda (@list @t7 @t17 @t32) (= @t7 @t17))) % 169.02/169.36 (define @t34 () (@var "Y" (-> $$unsorted Bool))) % 169.02/169.36 (define @t35 () (@var "X" (-> $$unsorted Bool))) % 169.02/169.36 (define @t36 () (lambda (@list @t35 @t34 @t32) (= (_ @t35 @t32) (_ @t34 @t32)))) % 169.02/169.36 (define @t37 () (@var "Phi" (-> $$unsorted Bool))) % 169.02/169.36 (define @t38 () (_ @t37 @t32)) % 169.02/169.36 (define @t39 () (not @t38)) % 169.02/169.36 (define @t40 () (@list @t37 @t32)) % 169.02/169.36 (define @t41 () (lambda @t40 @t39)) % 169.02/169.36 (define @t42 () (@var "Psi" (-> $$unsorted Bool))) % 169.02/169.36 (define @t43 () (_ @t42 @t32)) % 169.02/169.36 (define @t44 () (lambda (@list @t37 @t42 @t32) (or @t38 @t43))) % 169.02/169.36 (define @t45 () (_ tptp.mnot @t42)) % 169.02/169.36 (define @t46 () (_ tptp.mnot @t37)) % 169.02/169.36 (define @t47 () (_ tptp.mor @t46)) % 169.02/169.36 (define @t48 () (@list @t37 @t42 @t6)) % 169.02/169.36 (define @t49 () (lambda @t48 (_ (_ tptp.mnot (_ @t47 @t45)) @t6))) % 169.02/169.36 (define @t50 () (lambda @t48 (_ (_ @t47 @t42) @t6))) % 169.02/169.36 (define @t51 () (lambda @t48 (_ (_ (_ tptp.mor @t45) @t37) @t6))) % 169.02/169.36 (define @t52 () (lambda @t48 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t37) @t42)) (_ (_ tptp.mimplies @t42) @t37)) @t6))) % 169.02/169.36 (define @t53 () (lambda @t48 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t37) @t42)) @t6))) % 169.02/169.36 (define @t54 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 169.02/169.36 (define @t55 () (_ @t54 @t7)) % 169.02/169.36 (define @t56 () (_ @t55 @t32)) % 169.02/169.36 (define @t57 () (@list @t7)) % 169.02/169.36 (define @t58 () (forall @t57 @t56)) % 169.02/169.36 (define @t59 () (@list @t54 @t32)) % 169.02/169.36 (define @t60 () (lambda @t59 @t58)) % 169.02/169.36 (define @t61 () (@var "P" (-> $$unsorted Bool))) % 169.02/169.36 (define @t62 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 169.02/169.36 (define @t63 () (_ @t62 @t61)) % 169.02/169.36 (define @t64 () (lambda (@list @t62 @t32) (forall (@list @t61) (_ @t63 @t32)))) % 169.02/169.36 (define @t65 () (lambda @t12 (_ (_ tptp.mnot @t55) @t6))) % 169.02/169.36 (define @t66 () (@list @t54 @t6)) % 169.02/169.36 (define @t67 () (lambda @t66 (_ (_ tptp.mnot (_ tptp.mforall_ind @t65)) @t6))) % 169.02/169.36 (define @t68 () (lambda (@list @t62 @t6) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t61 @t6) (_ (_ tptp.mnot @t63) @t6)))) @t6))) % 169.02/169.36 (define @t69 () (@list @t32)) % 169.02/169.36 (define @t70 () (lambda @t69 true)) % 169.02/169.36 (define @t71 () (@var "V" $$unsorted)) % 169.02/169.36 (define @t72 () (_ @t37 @t71)) % 169.02/169.36 (define @t73 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 169.02/169.36 (define @t74 () (_ (_ @t73 @t32) @t71)) % 169.02/169.36 (define @t75 () (not @t74)) % 169.02/169.36 (define @t76 () (or @t75 @t72)) % 169.02/169.36 (define @t77 () (@list @t71)) % 169.02/169.36 (define @t78 () (forall @t77 @t76)) % 169.02/169.36 (define @t79 () (@list @t73 @t37 @t32)) % 169.02/169.36 (define @t80 () (lambda @t79 @t78)) % 169.02/169.36 (define @t81 () (@list @t73 @t37 @t6)) % 169.02/169.36 (define @t82 () (lambda @t81 (_ (_ tptp.mnot (_ (_ tptp.mbox @t73) @t46)) @t6))) % 169.02/169.36 (define @t83 () (@var "S" $$unsorted)) % 169.02/169.36 (define @t84 () (_ @t73 @t83)) % 169.02/169.36 (define @t85 () (@list @t83)) % 169.02/169.36 (define @t86 () (@list @t73)) % 169.02/169.36 (define @t87 () (lambda @t86 (forall @t85 (_ @t84 @t83)))) % 169.02/169.36 (define @t88 () (@var "T" $$unsorted)) % 169.02/169.36 (define @t89 () (_ @t73 @t88)) % 169.02/169.36 (define @t90 () (_ @t84 @t88)) % 169.02/169.36 (define @t91 () (lambda @t86 (forall (@list @t83 @t88) (=> @t90 (_ @t89 @t83))))) % 169.02/169.36 (define @t92 () (@list @t88)) % 169.02/169.36 (define @t93 () (lambda @t86 (forall @t85 (exists @t92 @t90)))) % 169.02/169.36 (define @t94 () (@var "U" $$unsorted)) % 169.02/169.36 (define @t95 () (_ @t84 @t94)) % 169.02/169.36 (define @t96 () (_ @t89 @t94)) % 169.02/169.36 (define @t97 () (@list @t83 @t88 @t94)) % 169.02/169.36 (define @t98 () (lambda @t86 (forall @t97 (=> (and @t90 @t96) @t95)))) % 169.02/169.36 (define @t99 () (and @t90 @t95)) % 169.02/169.36 (define @t100 () (lambda @t86 (forall @t97 (=> @t99 @t96)))) % 169.02/169.36 (define @t101 () (= @t88 @t94)) % 169.02/169.36 (define @t102 () (lambda @t86 (forall @t97 (=> @t99 @t101)))) % 169.02/169.36 (define @t103 () (@list @t94)) % 169.02/169.36 (define @t104 () (lambda @t86 (forall @t85 (exists @t92 (and @t90 (forall @t103 (=> @t95 @t101))))))) % 169.02/169.36 (define @t105 () (_ @t73 @t94)) % 169.02/169.36 (define @t106 () (_ @t105 @t88)) % 169.02/169.36 (define @t107 () (lambda @t86 (forall @t97 (=> @t90 (exists @t103 (and @t95 @t106)))))) % 169.02/169.36 (define @t108 () (lambda @t86 (forall @t97 (=> @t99 (or @t96 @t101 @t106))))) % 169.02/169.36 (define @t109 () (lambda @t86 (forall @t97 (=> @t99 (exists @t77 (and (_ @t89 @t71) (_ @t105 @t71))))))) % 169.02/169.36 (define @t110 () (forall @t69 @t38)) % 169.02/169.36 (define @t111 () (@list @t37)) % 169.02/169.36 (define @t112 () (lambda @t111 @t110)) % 169.02/169.36 (define @t113 () (lambda @t111 (forall @t69 @t39))) % 169.02/169.36 (define @t114 () (lambda @t111 (exists @t69 @t38))) % 169.02/169.36 (define @t115 () (lambda @t111 (exists @t69 @t39))) % 169.02/169.36 (define @t116 () (@var "Y" $$unsorted)) % 169.02/169.36 (define @t117 () (@var "X" $$unsorted)) % 169.02/169.36 (define @t118 () (@var "R2" (-> $$unsorted $$unsorted Bool))) % 169.02/169.36 (define @t119 () (@var "R1" (-> $$unsorted $$unsorted Bool))) % 169.02/169.36 (define @t120 () (@list @t119 @t118)) % 169.02/169.36 (define @t121 () (lambda @t120 (forall (@list @t117 @t116) (=> (_ (_ @t119 @t117) @t116) (_ (_ @t118 @t117) @t116))))) % 169.02/169.36 (define @t122 () (lambda @t120 (forall (@list @t94 @t71 @t32) (=> (and (_ (_ @t119 @t94) @t71) (_ (_ @t118 @t71) @t32)) (_ (_ @t118 @t94) @t32))))) % 169.02/169.36 (define @t123 () (@const 0 (@ho-elim-sort (-> tptp.mu tptp.mu $$unsorted Bool)))) % 169.02/169.36 (define @t124 () (@const 1 (-> (@ho-elim-sort (-> tptp.mu tptp.mu $$unsorted Bool)) tptp.mu (@ho-elim-sort (-> tptp.mu $$unsorted Bool))))) % 169.02/169.36 (define @t125 () (@const 2 (-> (@ho-elim-sort (-> tptp.mu $$unsorted Bool)) tptp.mu (@ho-elim-sort (-> $$unsorted Bool))))) % 169.02/169.36 (define @t126 () (_ @t125 (_ @t124 @t123 tptp.jan) tptp.cola)) % 169.02/169.36 (define @t127 () (@const 3 (-> (@ho-elim-sort (-> $$unsorted Bool)) $$unsorted Bool))) % 169.02/169.36 (define @t128 () (@const 4 (@ho-elim-sort (-> $$unsorted $$unsorted Bool)))) % 169.02/169.36 (define @t129 () (@const 5 (-> (@ho-elim-sort (-> $$unsorted $$unsorted Bool)) $$unsorted (@ho-elim-sort (-> $$unsorted Bool))))) % 169.02/169.36 (define @t130 () (_ @t129 @t128 @t32)) % 169.02/169.36 (define @t131 () (not (_ @t127 @t130 @t71))) % 169.02/169.36 (define @t132 () (@list @t32 @t71)) % 169.02/169.36 (define @t133 () (forall @t132 (or @t131 (_ @t127 @t126 @t71)))) % 169.02/169.36 (define @t134 () (tptp.likes tptp.jan tptp.cola @t71)) % 169.02/169.36 (define @t135 () (not (tptp.a3 @t32 @t71))) % 169.02/169.36 (define @t136 () (or @t135 @t134)) % 169.02/169.36 (define @t137 () (forall @t132 @t136)) % 169.02/169.36 (define @t138 () (forall @t77 @t136)) % 169.02/169.36 (define @t139 () (lambda @t69 @t138)) % 169.02/169.36 (define @t140 () (_ @t139 @t32)) % 169.02/169.36 (define @t141 () (forall @t69 @t140)) % 169.02/169.36 (define @t142 () (_ @t37 @t32)) % 169.02/169.36 (define @t143 () (lambda @t111 (forall @t69 @t142))) % 169.02/169.36 (define @t144 () (_ @t2 @t71)) % 169.02/169.36 (define @t145 () (or @t135 @t144)) % 169.02/169.36 (define @t146 () (_ @t2 @t71)) % 169.02/169.36 (define @t147 () (or @t135 @t146)) % 169.02/169.36 (define @t148 () (forall @t77 @t147)) % 169.02/169.36 (define @t149 () (lambda @t69 @t148)) % 169.02/169.36 (define @t150 () (_ @t37 @t71)) % 169.02/169.36 (define @t151 () (lambda @t40 (forall @t77 (or @t135 @t150)))) % 169.02/169.36 (define @t152 () (_ @t73 @t32 @t71)) % 169.02/169.36 (define @t153 () (not @t152)) % 169.02/169.36 (define @t154 () (forall @t77 (or @t153 @t150))) % 169.02/169.36 (define @t155 () (lambda @t79 @t154)) % 169.02/169.36 (define @t156 () (@var "BOUND_VARIABLE_9680" $$unsorted)) % 169.02/169.36 (define @t157 () (@var "BOUND_VARIABLE_9658" tptp.mu)) % 169.02/169.36 (define @t158 () (@const 6 (@ho-elim-sort (-> tptp.mu tptp.mu $$unsorted Bool)))) % 169.02/169.36 (define @t159 () (_ @t124 @t158 @t7)) % 169.02/169.36 (define @t160 () (@list @t32 @t7 @t157 @t156)) % 169.02/169.36 (define @t161 () (not (tptp.likes @t7 @t157 @t156))) % 169.02/169.36 (define @t162 () (not (tptp.a3 @t32 @t156))) % 169.02/169.36 (define @t163 () (tptp.possibly_likes @t7 @t157 @t32)) % 169.02/169.36 (define @t164 () (or @t163 @t162 @t161)) % 169.02/169.36 (define @t165 () (forall @t160 @t164)) % 169.02/169.36 (define @t166 () (forall (@list @t7 @t157 @t156) @t164)) % 169.02/169.36 (define @t167 () (lambda @t69 @t166)) % 169.02/169.36 (define @t168 () (_ @t167 @t32)) % 169.02/169.36 (define @t169 () (forall @t69 @t168)) % 169.02/169.36 (define @t170 () (@list @t157 @t156)) % 169.02/169.36 (define @t171 () (forall @t170 @t164)) % 169.02/169.36 (define @t172 () (forall @t170 (or (tptp.possibly_likes @t7 @t157 @t6) (not (tptp.a3 @t6 @t156)) @t161))) % 169.02/169.36 (define @t173 () (lambda @t12 @t172)) % 169.02/169.36 (define @t174 () (_ @t173 @t7 @t32)) % 169.02/169.36 (define @t175 () (forall @t57 @t174)) % 169.02/169.36 (define @t176 () (lambda @t69 @t175)) % 169.02/169.36 (define @t177 () (_ @t54 @t7 @t32)) % 169.02/169.36 (define @t178 () (forall @t57 @t177)) % 169.02/169.36 (define @t179 () (lambda @t59 @t178)) % 169.02/169.36 (define @t180 () (or @t162 @t161)) % 169.02/169.36 (define @t181 () (or @t180 @t163)) % 169.02/169.36 (define @t182 () (forall @t170 @t181)) % 169.02/169.36 (define @t183 () (@list @t156)) % 169.02/169.36 (define @t184 () (forall @t183 @t181)) % 169.02/169.36 (define @t185 () (@list @t157)) % 169.02/169.36 (define @t186 () (forall @t183 @t180)) % 169.02/169.36 (define @t187 () (or @t186 @t163)) % 169.02/169.36 (define @t188 () (forall @t77 (or @t135 (not (tptp.likes @t7 @t157 @t71))))) % 169.02/169.36 (define @t189 () (_ (_ @t21 @t157) @t32)) % 169.02/169.36 (define @t190 () (or @t188 @t189)) % 169.02/169.36 (define @t191 () (tptp.likes @t7 @t17 @t71)) % 169.02/169.36 (define @t192 () (not (tptp.a3 @t6 @t71))) % 169.02/169.36 (define @t193 () (forall @t77 (or @t192 (not @t191)))) % 169.02/169.36 (define @t194 () (or @t193 @t28)) % 169.02/169.36 (define @t195 () (lambda @t20 @t194)) % 169.02/169.36 (define @t196 () (_ @t195 @t157 @t32)) % 169.02/169.36 (define @t197 () (forall @t185 @t196)) % 169.02/169.36 (define @t198 () (lambda @t69 @t197)) % 169.02/169.36 (define @t199 () (@list @t7)) % 169.02/169.36 (define @t200 () (@list @t6)) % 169.02/169.36 (define @t201 () (lambda @t200 @t194)) % 169.02/169.36 (define @t202 () (_ @t42 @t6)) % 169.02/169.36 (define @t203 () (@list @t42 @t6)) % 169.02/169.36 (define @t204 () (not @t193)) % 169.02/169.36 (define @t205 () (lambda @t200 @t204)) % 169.02/169.36 (define @t206 () (_ @t205 @t6)) % 169.02/169.36 (define @t207 () (not @t206)) % 169.02/169.36 (define @t208 () (or @t207 @t202)) % 169.02/169.36 (define @t209 () (lambda @t203 @t208)) % 169.02/169.36 (define @t210 () (or (not (_ @t37 @t6)) @t202)) % 169.02/169.36 (define @t211 () (lambda @t48 @t210)) % 169.02/169.36 (define @t212 () (_ @t19 @t71)) % 169.02/169.36 (define @t213 () (not @t212)) % 169.02/169.36 (define @t214 () (or @t192 @t213)) % 169.02/169.36 (define @t215 () (_ @t19 @t71)) % 169.02/169.36 (define @t216 () (not @t215)) % 169.02/169.36 (define @t217 () (or @t192 @t216)) % 169.02/169.36 (define @t218 () (forall @t77 @t217)) % 169.02/169.36 (define @t219 () (not @t218)) % 169.02/169.36 (define @t220 () (lambda @t200 @t219)) % 169.02/169.36 (define @t221 () (not @t150)) % 169.02/169.36 (define @t222 () (lambda (@list @t37 @t6) (not (forall @t77 (or @t192 @t221))))) % 169.02/169.36 (define @t223 () (not (forall @t77 (or (not (_ @t73 @t6 @t71)) @t221)))) % 169.02/169.36 (define @t224 () (_ (lambda @t81 @t223) tptp.a3)) % 169.02/169.36 (define @t225 () (lambda @t20 (_ (_ (_ @t211 (_ @t224 @t19)) @t22) @t6))) % 169.02/169.36 (define @t226 () (forall @t77 (or @t153 @t221))) % 169.02/169.36 (define @t227 () (lambda @t69 @t226)) % 169.02/169.36 (define @t228 () (_ @t227 @t32)) % 169.02/169.36 (define @t229 () (not @t228)) % 169.02/169.36 (define @t230 () (lambda @t69 @t229)) % 169.02/169.36 (define @t231 () (not @t72)) % 169.02/169.36 (define @t232 () (or @t153 @t231)) % 169.02/169.36 (define @t233 () (lambda @t69 @t39)) % 169.02/169.36 (define @t234 () (_ @t233 @t71)) % 169.02/169.36 (define @t235 () (or @t153 @t234)) % 169.02/169.36 (define @t236 () (forall @t77 @t235)) % 169.02/169.36 (define @t237 () (lambda @t69 @t236)) % 169.02/169.36 (define @t238 () (lambda @t40 @t154)) % 169.02/169.36 (define @t239 () (or @t39 @t43)) % 169.02/169.36 (define @t240 () (lambda @t69 @t239)) % 169.02/169.36 (define @t241 () (@list @t42 @t32)) % 169.02/169.36 (define @t242 () (_ @t233 @t32)) % 169.02/169.36 (define @t243 () (or @t242 @t43)) % 169.02/169.36 (define @t244 () (lambda @t241 @t243)) % 169.02/169.36 (define @t245 () (_ @t125 (_ @t124 @t123 tptp.piotr) tptp.pepsi)) % 169.02/169.36 (define @t246 () (not (_ @t127 @t245 @t71))) % 169.02/169.36 (define @t247 () (@var "BOUND_VARIABLE_9878" tptp.mu)) % 169.02/169.36 (define @t248 () (_ @t125 @t159 @t247)) % 169.02/169.36 (define @t249 () (@list @t7 @t247)) % 169.02/169.36 (define @t250 () (forall @t69 (not (forall @t249 (not (_ @t127 @t248 @t32)))))) % 169.02/169.36 (define @t251 () (@quantifiers_skolemize @t250 0)) % 169.02/169.36 (define @t252 () (_ @t129 @t128 @t251)) % 169.02/169.36 (define @t253 () (@quantifiers_skolemize (forall @t77 (or (not (_ @t127 @t252 @t71)) @t246)) 0)) % 169.02/169.36 (define @t254 () (tptp.likes tptp.piotr tptp.pepsi @t71)) % 169.02/169.36 (define @t255 () (not @t254)) % 169.02/169.36 (define @t256 () (not (forall @t77 (or @t135 @t255)))) % 169.02/169.36 (define @t257 () (lambda @t200 (not (forall @t77 (or @t192 @t255))))) % 169.02/169.36 (define @t258 () (_ @t257 @t32)) % 169.02/169.36 (define @t259 () (forall @t69 @t258)) % 169.02/169.36 (define @t260 () (_ @t5 @t71)) % 169.02/169.36 (define @t261 () (not @t260)) % 169.02/169.36 (define @t262 () (or @t192 @t261)) % 169.02/169.36 (define @t263 () (_ @t5 @t71)) % 169.02/169.36 (define @t264 () (not @t263)) % 169.02/169.36 (define @t265 () (or @t192 @t264)) % 169.02/169.36 (define @t266 () (forall @t77 @t265)) % 169.02/169.36 (define @t267 () (not @t266)) % 169.02/169.36 (define @t268 () (lambda @t200 @t267)) % 169.02/169.36 (define @t269 () (_ @t127 @t252 @t253)) % 169.02/169.36 (define @t270 () (not @t269)) % 169.02/169.36 (define @t271 () (or @t270 (not (_ @t127 @t245 @t253)))) % 169.02/169.36 (define @t272 () (@list true)) % 169.02/169.36 (define @t273 () (not @t250)) % 169.02/169.36 (define @t274 () (not (forall @t249 (not (tptp.possibly_likes @t7 @t247 @t32))))) % 169.02/169.36 (define @t275 () (tptp.possibly_likes @t7 @t247 @t6)) % 169.02/169.36 (define @t276 () (not @t275)) % 169.02/169.36 (define @t277 () (forall @t249 @t276)) % 169.02/169.36 (define @t278 () (lambda @t200 (not @t277))) % 169.02/169.36 (define @t279 () (_ @t278 @t32)) % 169.02/169.36 (define @t280 () (forall @t69 @t279)) % 169.02/169.36 (define @t281 () (@list @t247)) % 169.02/169.36 (define @t282 () (forall @t281 @t276)) % 169.02/169.36 (define @t283 () (not @t282)) % 169.02/169.36 (define @t284 () (lambda @t12 @t283)) % 169.02/169.36 (define @t285 () (_ @t284 @t7 @t6)) % 169.02/169.36 (define @t286 () (not @t285)) % 169.02/169.36 (define @t287 () (forall @t57 @t286)) % 169.02/169.36 (define @t288 () (not @t287)) % 169.02/169.36 (define @t289 () (lambda @t200 @t288)) % 169.02/169.36 (define @t290 () (forall @t57 (not (_ @t54 @t7 @t6)))) % 169.02/169.36 (define @t291 () (not @t290)) % 169.02/169.36 (define @t292 () (lambda @t66 @t291)) % 169.02/169.36 (define @t293 () (_ (_ @t21 @t247) @t6)) % 169.02/169.36 (define @t294 () (not @t293)) % 169.02/169.36 (define @t295 () (_ @t29 @t247 @t6)) % 169.02/169.36 (define @t296 () (not @t295)) % 169.02/169.36 (define @t297 () (forall @t281 @t296)) % 169.02/169.36 (define @t298 () (not @t297)) % 169.02/169.36 (define @t299 () (lambda @t200 @t298)) % 169.02/169.36 (define @t300 () (lambda @t12 (_ (_ @t292 @t29) @t6))) % 169.02/169.36 (define @t301 () (forall @t57 (not @t177))) % 169.02/169.36 (define @t302 () (lambda @t69 @t301)) % 169.02/169.36 (define @t303 () (_ @t302 @t32)) % 169.02/169.36 (define @t304 () (not @t303)) % 169.02/169.36 (define @t305 () (lambda @t69 @t304)) % 169.02/169.36 (define @t306 () (not @t56)) % 169.02/169.36 (define @t307 () (not (_ @t55 @t6))) % 169.02/169.36 (define @t308 () (lambda @t12 @t307)) % 169.02/169.36 (define @t309 () (_ @t308 @t7 @t32)) % 169.02/169.36 (define @t310 () (forall @t57 @t309)) % 169.02/169.36 (define @t311 () (lambda @t69 @t310)) % 169.02/169.36 (define @t312 () (lambda @t69 @t306)) % 169.02/169.36 (define @t313 () (_ @t41 @t55)) % 169.02/169.36 (define @t314 () (forall @t249 (not (_ @t127 @t248 @t251)))) % 169.02/169.36 (define @t315 () (not (not @t314))) % 169.02/169.36 (define @t316 () (_ @t127 @t126 @t253)) % 169.02/169.36 (define @t317 () (not @t316)) % 169.02/169.36 (define @t318 () (_ @t127 (_ @t125 (_ @t124 @t158 tptp.jan) tptp.cola) @t251)) % 169.02/169.36 (define @t319 () (or @t318 @t270 @t317)) % 169.02/169.36 (define @t320 () (or @t270 @t316)) % 169.02/169.36 (define @t321 () (not @t320)) % 169.02/169.36 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 169.02/169.36 (assume @p2 (_ tptp.mvalid (_ @t3 @t2))) % 169.02/169.36 (assume @p3 (_ tptp.mvalid (_ @t3 @t5))) % 169.02/169.36 (assume @p4 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t12 (_ (_ @t3 (_ (_ tptp.mimplies (_ @t11 @t10)) @t9)) @t6))))) % 169.02/169.36 (assume @p5 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t12 (_ (_ @t3 (_ (_ tptp.mimplies (_ @t11 @t9)) @t10)) @t6))))) % 169.02/169.36 (assume @p6 (_ tptp.mvalid (_ @t13 (_ @t1 tptp.pepsi)))) % 169.02/169.36 (assume @p7 (_ tptp.mvalid (_ @t3 (_ @t4 tptp.cola)))) % 169.02/169.36 (assume @p8 (_ tptp.mvalid (_ @t3 @t14))) % 169.02/169.36 (assume @p9 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t12 (_ (_ @t13 (_ (_ tptp.mimplies @t10) @t9)) @t6))))) % 169.02/169.36 (assume @p10 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t12 (_ (_ @t13 (_ (_ tptp.mimplies @t9) @t10)) @t6))))) % 169.02/169.36 (assume @p11 (_ tptp.mvalid (_ @t15 @t2))) % 169.02/169.36 (assume @p12 (_ tptp.mvalid (_ @t16 @t5))) % 169.02/169.36 (assume @p13 (_ tptp.mvalid (_ @t11 @t14))) % 169.02/169.36 (assume @p14 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t12 (_ (_ tptp.mforall_ind (lambda @t20 (_ (_ @t15 (_ (_ tptp.mimplies (_ (_ tptp.mand @t19) (_ (_ tptp.mand (_ @t3 @t19)) (_ @t13 @t19)))) @t18)) @t6))) @t6))))) % 169.02/169.36 (assume @p15 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t12 (_ (_ tptp.mforall_ind (lambda @t20 (_ (_ (_ tptp.mimplies (_ @t15 @t18)) @t18) @t6))) @t6))))) % 169.02/169.36 (assume @p16 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t12 (_ (_ tptp.mforall_ind (lambda @t20 (_ (_ (_ tptp.mimplies (_ @t16 @t18)) @t19) @t6))) @t6))))) % 169.02/169.36 (assume @p17 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t12 (_ (_ tptp.mforall_ind (lambda @t20 (_ (_ (_ tptp.mimplies (_ @t11 @t19)) @t22) @t6))) @t6))))) % 169.02/169.36 (assume @p18 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t12 (_ (_ tptp.mforall_ind (lambda @t20 (_ (_ (_ tptp.mimplies (_ (_ tptp.mdia tptp.a2) @t19)) @t22) @t6))) @t6))))) % 169.02/169.36 (assume @p19 (_ tptp.mvalid (_ tptp.mforall_ind @t24))) % 169.02/169.36 (assume @p20 (_ tptp.msymmetric tptp.a1)) % 169.02/169.36 (assume @p21 (_ tptp.msymmetric tptp.a2)) % 169.02/169.36 (assume @p22 (_ tptp.msymmetric tptp.a3)) % 169.02/169.36 (assume @p23 (_ tptp.mserial tptp.a1)) % 169.02/169.36 (assume @p24 (_ tptp.mserial tptp.a2)) % 169.02/169.36 (assume @p25 (_ tptp.mserial tptp.a3)) % 169.02/169.36 (assume @p26 (_ @t25 tptp.a2)) % 169.02/169.36 (assume @p27 (_ @t25 tptp.a3)) % 169.02/169.36 (assume @p28 (_ (_ tptp.subrel tptp.a2) tptp.a3)) % 169.02/169.36 (assume @p29 (_ @t26 tptp.a1)) % 169.02/169.36 (assume @p30 (_ @t26 tptp.a2)) % 169.02/169.36 (assume @p31 (_ @t26 tptp.a3)) % 169.02/169.36 (assume @p32 (_ @t27 tptp.a1)) % 169.02/169.36 (assume @p33 (_ @t27 tptp.a2)) % 169.02/169.36 (assume @p34 (_ @t27 tptp.a3)) % 169.02/169.36 (assume @p35 (_ (_ tptp.cond4s tptp.a3) tptp.a3)) % 169.02/169.36 (assume @p36 (_ tptp.meuclidean tptp.a1)) % 169.02/169.36 (assume @p37 (_ tptp.meuclidean tptp.a2)) % 169.02/169.36 (assume @p38 (_ tptp.meuclidean tptp.a3)) % 169.02/169.36 (assume @p39 @t31) % 169.02/169.36 (assume @p40 true) % 169.02/169.36 (step @p41 (= tptp.meq_ind @t33) :rule refl :args (@t33)) % 169.02/169.36 (step @p42 (= tptp.meq_prop @t36) :rule refl :args (@t36)) % 169.02/169.36 (step @p43 (= tptp.mnot @t41) :rule refl :args (@t41)) % 169.02/169.36 (step @p44 (= tptp.mor @t44) :rule refl :args (@t44)) % 169.02/169.36 (step @p45 (= tptp.mand @t49) :rule refl :args (@t49)) % 169.02/169.36 (step @p46 (= tptp.mimplies @t50) :rule refl :args (@t50)) % 169.02/169.36 (step @p47 (= tptp.mimplied @t51) :rule refl :args (@t51)) % 169.02/169.36 (step @p48 (= tptp.mequiv @t52) :rule refl :args (@t52)) % 169.02/169.36 (step @p49 (= tptp.mxor @t53) :rule refl :args (@t53)) % 169.02/169.36 (step @p50 (= tptp.mforall_ind @t60) :rule refl :args (@t60)) % 169.02/169.36 (step @p51 (= tptp.mforall_prop @t64) :rule refl :args (@t64)) % 169.02/169.36 (step @p52 (= tptp.mexists_ind @t67) :rule refl :args (@t67)) % 169.02/169.36 (step @p53 (= tptp.mexists_prop @t68) :rule refl :args (@t68)) % 169.02/169.36 (step @p54 (= tptp.mtrue @t70) :rule refl :args (@t70)) % 169.02/169.36 (step @p55 (= tptp.mbox @t80) :rule refl :args (@t80)) % 169.02/169.36 (step @p56 (= tptp.mdia @t82) :rule refl :args (@t82)) % 169.02/169.36 (step @p57 (= tptp.mreflexive @t87) :rule refl :args (@t87)) % 169.02/169.36 (step @p58 (= tptp.msymmetric @t91) :rule refl :args (@t91)) % 169.02/169.36 (step @p59 (= tptp.mserial @t93) :rule refl :args (@t93)) % 169.02/169.36 (step @p60 (= tptp.mtransitive @t98) :rule refl :args (@t98)) % 169.02/169.36 (step @p61 (= tptp.meuclidean @t100) :rule refl :args (@t100)) % 169.02/169.36 (step @p62 (= tptp.mpartially_functional @t102) :rule refl :args (@t102)) % 169.02/169.36 (step @p63 (= tptp.mfunctional @t104) :rule refl :args (@t104)) % 169.02/169.36 (step @p64 (= tptp.mweakly_dense @t107) :rule refl :args (@t107)) % 169.02/169.36 (step @p65 (= tptp.mweakly_connected @t108) :rule refl :args (@t108)) % 169.02/169.36 (step @p66 (= tptp.mweakly_directed @t109) :rule refl :args (@t109)) % 169.02/169.36 (step @p67 (= tptp.mvalid @t112) :rule refl :args (@t112)) % 169.02/169.36 (step @p68 (= tptp.minvalid @t113) :rule refl :args (@t113)) % 169.02/169.36 (step @p69 (= tptp.msatisfiable @t114) :rule refl :args (@t114)) % 169.02/169.36 (step @p70 (= tptp.mcountersatisfiable @t115) :rule refl :args (@t115)) % 169.02/169.36 (step @p71 (= tptp.subrel @t121) :rule refl :args (@t121)) % 169.02/169.36 (step @p72 (= tptp.cond4s @t122) :rule refl :args (@t122)) % 169.02/169.36 ; WARNING: add trust step for TRUST % 169.02/169.36 ; trust TRUST PREPROCESS_HO_ELIM % 169.02/169.36 (step @p73 :rule trust :premises () :args ((= @t137 @t133))) % 169.02/169.36 (step @p74 :rule quant-merge-prenex :args ((= (forall @t69 @t138) @t137))) % 169.02/169.36 (step @p75 :rule beta-reduce :args ((= @t140 @t138))) % 169.02/169.36 (step @p76 :rule cong :premises (@p75) :args (@t141)) % 169.02/169.36 (step @p77 :rule trans :premises (@p76 @p74)) % 169.02/169.36 (step @p78 :rule beta-reduce :args ((= (_ @t143 @t139) @t141))) % 169.02/169.36 (step @p79 :rule trans :premises (@p78 @p77)) % 169.02/169.36 (step @p80 :rule refl :args (@t134)) % 169.02/169.36 (step @p81 :rule refl :args (@t144)) % 169.02/169.36 (step @p82 :rule cong :premises (@p81 @p80) :args ((= @t144 @t134))) % 169.02/169.36 (step @p83 :rule symm :premises (@p82)) % 169.02/169.36 (step @p84 :rule eq_resolve :premises (@p81 @p83)) % 169.02/169.36 (step @p85 :rule refl :args (@t135)) % 169.02/169.36 (step @p86 :rule nary_cong :premises (@p85 @p84) :args (@t145)) % 169.02/169.36 (step @p87 :rule cong :premises (@p86) :args ((forall @t77 @t145))) % 169.02/169.36 (step @p88 :rule refl :args (@t146)) % 169.02/169.36 (step @p89 :rule refl :args (@t135)) % 169.02/169.36 (step @p90 :rule nary_cong :premises (@p89 @p88) :args (@t147)) % 169.02/169.36 (step @p91 :rule cong :premises (@p90) :args (@t148)) % 169.02/169.36 (step @p92 :rule trans :premises (@p91 @p87)) % 169.02/169.36 (step @p93 :rule cong :premises (@p92) :args (@t149)) % 169.02/169.36 (step @p94 :rule beta-reduce :args ((= (_ @t151 @t2) @t149))) % 169.02/169.36 (step @p95 :rule trans :premises (@p94 @p93)) % 169.02/169.36 (step @p96 :rule refl :args (@t2)) % 169.02/169.36 (step @p97 :rule beta-reduce :args ((= (_ @t155 tptp.a3) @t151))) % 169.02/169.36 (step @p98 :rule ho_cong :premises (@p97 @p96)) % 169.02/169.36 (step @p99 :rule trans :premises (@p98 @p95)) % 169.02/169.36 (step @p100 :rule refl :args (@t143)) % 169.02/169.36 (step @p101 :rule ho_cong :premises (@p100 @p99)) % 169.02/169.36 (step @p102 :rule trans :premises (@p101 @p79)) % 169.02/169.36 (step @p103 :rule refl :args (tptp.a3)) % 169.02/169.36 (step @p104 :rule refl :args (@t150)) % 169.02/169.36 (step @p105 :rule refl :args (@t72)) % 169.02/169.36 (step @p106 :rule cong :premises (@p105 @p104) :args ((= @t72 @t150))) % 169.02/169.36 (step @p107 :rule symm :premises (@p106)) % 169.02/169.36 (step @p108 :rule eq_resolve :premises (@p105 @p107)) % 169.02/169.36 (step @p109 :rule refl :args (@t152)) % 169.02/169.36 (step @p110 :rule refl :args (@t74)) % 169.02/169.36 (step @p111 :rule cong :premises (@p110 @p109) :args ((= @t74 @t152))) % 169.02/169.36 (step @p112 :rule symm :premises (@p111)) % 169.02/169.36 (step @p113 :rule eq_resolve :premises (@p110 @p112)) % 169.02/169.36 (step @p114 :rule cong :premises (@p113) :args (@t75)) % 169.02/169.36 (step @p115 :rule nary_cong :premises (@p114 @p108) :args (@t76)) % 169.02/169.36 (step @p116 :rule cong :premises (@p115) :args (@t78)) % 169.02/169.36 (step @p117 :rule cong :premises (@p116) :args (@t80)) % 169.02/169.36 (step @p118 :rule trans :premises (@p55 @p117)) % 169.02/169.36 (step @p119 :rule ho_cong :premises (@p118 @p103)) % 169.02/169.36 (step @p120 :rule ho_cong :premises (@p119 @p96)) % 169.02/169.36 (step @p121 :rule refl :args (@t142)) % 169.02/169.36 (step @p122 :rule refl :args (@t38)) % 169.02/169.36 (step @p123 :rule cong :premises (@p122 @p121) :args ((= @t38 @t142))) % 169.02/169.36 (step @p124 :rule symm :premises (@p123)) % 169.02/169.36 (step @p125 :rule eq_resolve :premises (@p122 @p124)) % 169.02/169.36 (step @p126 :rule cong :premises (@p125) :args (@t110)) % 169.02/169.36 (step @p127 :rule cong :premises (@p126) :args (@t112)) % 169.02/169.36 (step @p128 :rule trans :premises (@p67 @p127)) % 169.02/169.36 (step @p129 :rule ho_cong :premises (@p128 @p120)) % 169.02/169.36 (step @p130 :rule trans :premises (@p129 @p102)) % 169.02/169.36 (step @p131 :rule trans :premises (@p130 @p73)) % 169.02/169.36 (step @p132 :rule eq_resolve :premises (@p11 @p131)) % 169.02/169.36 ; trust TRUST PREPROCESS_HO_ELIM % 169.02/169.36 (step @p133 :rule trust :premises () :args ((= @t165 (forall @t160 (or (_ @t127 (_ @t125 @t159 @t157) @t32) (not (_ @t127 @t130 @t156)) (not (_ @t127 (_ @t125 (_ @t124 @t123 @t7) @t157) @t156))))))) % 169.02/169.36 (step @p134 :rule quant-merge-prenex :args ((= (forall @t69 @t166) @t165))) % 169.02/169.36 (step @p135 :rule beta-reduce :args ((= @t168 @t166))) % 169.02/169.36 (step @p136 :rule cong :premises (@p135) :args (@t169)) % 169.02/169.36 (step @p137 :rule trans :premises (@p136 @p134)) % 169.02/169.36 (step @p138 :rule beta-reduce :args ((= (_ @t143 @t167) @t169))) % 169.02/169.36 (step @p139 :rule trans :premises (@p138 @p137)) % 169.02/169.36 (step @p140 :rule quant-merge-prenex :args ((= (forall @t57 @t171) @t166))) % 169.02/169.36 (step @p141 :rule beta-reduce :args ((= @t174 @t171))) % 169.02/169.36 (step @p142 :rule cong :premises (@p141) :args (@t175)) % 169.02/169.36 (step @p143 :rule trans :premises (@p142 @p140)) % 169.02/169.36 (step @p144 :rule cong :premises (@p143) :args (@t176)) % 169.02/169.36 (step @p145 :rule beta-reduce :args ((= (_ @t179 @t173) @t176))) % 169.02/169.36 (step @p146 :rule trans :premises (@p145 @p144)) % 169.02/169.36 (step @p147 :rule beta-reduce :args ((= (_ (lambda @t69 @t171) @t6) @t172))) % 169.02/169.36 (step @p148 :rule refl :args (@t6)) % 169.02/169.36 (step @p149 :rule aci_norm :args ((= @t181 @t164))) % 169.02/169.36 (step @p150 :rule cong :premises (@p149) :args (@t182)) % 169.02/169.36 (step @p151 :rule quant-merge-prenex :args ((= (forall @t185 @t184) @t182))) % 169.02/169.36 (step @p152 :rule refl :args (@t163)) % 169.02/169.36 (step @p153 :rule alpha_equiv :args (@t186 (@list @t156) (@list @t71))) % 169.02/169.36 (step @p154 :rule nary_cong :premises (@p153 @p152) :args (@t187)) % 169.02/169.36 (step @p155 :rule quant-miniscope-or :args ((= @t184 @t187))) % 169.02/169.36 (step @p156 :rule trans :premises (@p155 @p154)) % 169.02/169.36 (step @p157 :rule symm :premises (@p156)) % 169.02/169.36 (step @p158 :rule cong :premises (@p157) :args ((forall @t185 (or @t188 @t163)))) % 169.02/169.36 (step @p159 :rule trans :premises (@p158 @p151)) % 169.02/169.36 (step @p160 :rule trans :premises (@p159 @p150)) % 169.02/169.36 (step @p161 :rule refl :args (@t163)) % 169.02/169.36 (step @p162 :rule refl :args (@t189)) % 169.02/169.36 (step @p163 :rule cong :premises (@p162 @p161) :args ((= @t189 @t163))) % 169.02/169.36 (step @p164 :rule symm :premises (@p163)) % 169.02/169.36 (step @p165 :rule eq_resolve :premises (@p162 @p164)) % 169.02/169.36 (step @p166 :rule refl :args (@t188)) % 169.02/169.36 (step @p167 :rule nary_cong :premises (@p166 @p165) :args (@t190)) % 169.02/169.36 (step @p168 :rule cong :premises (@p167) :args ((forall @t185 @t190))) % 169.02/169.36 (step @p169 :rule trans :premises (@p168 @p160)) % 169.02/169.36 (step @p170 :rule beta-reduce :args ((= @t196 @t190))) % 169.02/169.36 (step @p171 :rule cong :premises (@p170) :args (@t197)) % 169.02/169.36 (step @p172 :rule trans :premises (@p171 @p169)) % 169.02/169.36 (step @p173 :rule cong :premises (@p172) :args (@t198)) % 169.02/169.36 (step @p174 :rule beta-reduce :args ((= (_ (lambda @t59 (forall @t185 (_ @t54 @t157 @t32))) @t195) @t198))) % 169.02/169.36 (step @p175 :rule trans :premises (@p174 @p173)) % 169.02/169.36 (step @p176 :rule refl :args (@t195)) % 169.02/169.36 (step @p177 :rule alpha_equiv :args (@t178 @t199 (@list @t157))) % 169.02/169.36 (step @p178 :rule cong :premises (@p177) :args (@t179)) % 169.02/169.36 (step @p179 :rule ho_cong :premises (@p178 @p176)) % 169.02/169.36 (step @p180 :rule trans :premises (@p179 @p175)) % 169.02/169.36 (step @p181 :rule beta-reduce :args ((= (_ @t201 @t6) @t194))) % 169.02/169.36 (step @p182 :rule beta-reduce :args ((= (_ (lambda @t203 (or @t193 @t202)) @t22) @t201))) % 169.02/169.36 (step @p183 :rule refl :args (@t22)) % 169.02/169.36 (step @p184 :rule refl :args (@t202)) % 169.02/169.36 (step @p185 :rule bool-double-not-elim :args (@t193)) % 169.02/169.36 (step @p186 :rule beta-reduce :args ((= @t206 @t204))) % 169.02/169.36 (step @p187 :rule cong :premises (@p186) :args (@t207)) % 169.02/169.36 (step @p188 :rule trans :premises (@p187 @p185)) % 169.02/169.36 (step @p189 :rule nary_cong :premises (@p188 @p184) :args (@t208)) % 169.02/169.36 (step @p190 :rule cong :premises (@p189) :args (@t209)) % 169.02/169.36 (step @p191 :rule beta-reduce :args ((= (_ @t211 @t205) @t209))) % 169.02/169.36 (step @p192 :rule trans :premises (@p191 @p190)) % 169.02/169.36 (step @p193 :rule refl :args (@t191)) % 169.02/169.36 (step @p194 :rule refl :args (@t212)) % 169.02/169.36 (step @p195 :rule cong :premises (@p194 @p193) :args ((= @t212 @t191))) % 169.02/169.36 (step @p196 :rule symm :premises (@p195)) % 169.02/169.36 (step @p197 :rule eq_resolve :premises (@p194 @p196)) % 169.02/169.36 (step @p198 :rule cong :premises (@p197) :args (@t213)) % 169.02/169.36 (step @p199 :rule refl :args (@t192)) % 169.02/169.36 (step @p200 :rule nary_cong :premises (@p199 @p198) :args (@t214)) % 169.02/169.36 (step @p201 :rule cong :premises (@p200) :args ((forall @t77 @t214))) % 169.02/169.36 (step @p202 :rule refl :args (@t215)) % 169.02/169.36 (step @p203 :rule cong :premises (@p202) :args (@t216)) % 169.02/169.36 (step @p204 :rule refl :args (@t192)) % 169.02/169.36 (step @p205 :rule nary_cong :premises (@p204 @p203) :args (@t217)) % 169.02/169.36 (step @p206 :rule cong :premises (@p205) :args (@t218)) % 169.02/169.36 (step @p207 :rule trans :premises (@p206 @p201)) % 169.02/169.36 (step @p208 :rule cong :premises (@p207) :args (@t219)) % 169.02/169.36 (step @p209 :rule cong :premises (@p208) :args (@t220)) % 169.02/169.36 (step @p210 :rule beta-reduce :args ((= (_ @t222 @t19) @t220))) % 169.02/169.36 (step @p211 :rule trans :premises (@p210 @p209)) % 169.02/169.36 (step @p212 :rule refl :args (@t19)) % 169.02/169.36 (step @p213 :rule beta-reduce :args ((= @t224 @t222))) % 169.02/169.36 (step @p214 :rule ho_cong :premises (@p213 @p212)) % 169.02/169.36 (step @p215 :rule trans :premises (@p214 @p211)) % 169.02/169.36 (step @p216 :rule refl :args (@t211)) % 169.02/169.36 (step @p217 :rule ho_cong :premises (@p216 @p215)) % 169.02/169.36 (step @p218 :rule trans :premises (@p217 @p192)) % 169.02/169.36 (step @p219 :rule ho_cong :premises (@p218 @p183)) % 169.02/169.36 (step @p220 :rule trans :premises (@p219 @p182)) % 169.02/169.36 (step @p221 :rule ho_cong :premises (@p220 @p148)) % 169.02/169.36 (step @p222 :rule trans :premises (@p221 @p181)) % 169.02/169.36 (step @p223 :rule cong :premises (@p222) :args (@t225)) % 169.02/169.36 (step @p224 :rule refl :args (@t179)) % 169.02/169.36 (step @p225 :rule ho_cong :premises (@p224 @p223)) % 169.02/169.36 (step @p226 :rule trans :premises (@p225 @p180)) % 169.02/169.36 (step @p227 :rule ho_cong :premises (@p226 @p148)) % 169.02/169.36 (step @p228 :rule trans :premises (@p227 @p147)) % 169.02/169.36 (step @p229 :rule cong :premises (@p228) :args ((lambda @t12 (_ (_ @t179 @t225) @t6)))) % 169.02/169.36 (step @p230 :rule ho_cong :premises (@p224 @p229)) % 169.02/169.36 (step @p231 :rule trans :premises (@p230 @p146)) % 169.02/169.36 (step @p232 :rule ho_cong :premises (@p100 @p231)) % 169.02/169.36 (step @p233 :rule trans :premises (@p232 @p139)) % 169.02/169.36 (step @p234 :rule beta-reduce :args ((= (_ (lambda @t69 (not @t226)) @t6) @t223))) % 169.02/169.36 (step @p235 :rule beta-reduce :args ((= @t228 @t226))) % 169.02/169.36 (step @p236 :rule cong :premises (@p235) :args (@t229)) % 169.02/169.36 (step @p237 :rule cong :premises (@p236) :args (@t230)) % 169.02/169.36 (step @p238 :rule beta-reduce :args ((= (_ @t41 @t227) @t230))) % 169.02/169.36 (step @p239 :rule trans :premises (@p238 @p237)) % 169.02/169.36 (step @p240 :rule cong :premises (@p108) :args (@t231)) % 169.02/169.36 (step @p241 :rule refl :args (@t153)) % 169.02/169.36 (step @p242 :rule nary_cong :premises (@p241 @p240) :args (@t232)) % 169.02/169.36 (step @p243 :rule cong :premises (@p242) :args ((forall @t77 @t232))) % 169.02/169.36 (step @p244 :rule beta-reduce :args ((= @t234 @t231))) % 169.02/169.36 (step @p245 :rule refl :args (@t153)) % 169.02/169.36 (step @p246 :rule nary_cong :premises (@p245 @p244) :args (@t235)) % 169.02/169.36 (step @p247 :rule cong :premises (@p246) :args (@t236)) % 169.02/169.36 (step @p248 :rule trans :premises (@p247 @p243)) % 169.02/169.36 (step @p249 :rule cong :premises (@p248) :args (@t237)) % 169.02/169.36 (step @p250 :rule beta-reduce :args ((= (_ @t238 @t233) @t237))) % 169.02/169.36 (step @p251 :rule trans :premises (@p250 @p249)) % 169.02/169.36 (step @p252 :rule beta-reduce :args ((= (_ @t41 @t37) @t233))) % 169.02/169.36 (step @p253 :rule beta-reduce :args ((= (_ @t155 @t73) @t238))) % 169.02/169.36 (step @p254 :rule ho_cong :premises (@p253 @p252)) % 169.02/169.36 (step @p255 :rule trans :premises (@p254 @p251)) % 169.02/169.36 (step @p256 :rule refl :args (@t41)) % 169.02/169.36 (step @p257 :rule ho_cong :premises (@p256 @p255)) % 169.02/169.36 (step @p258 :rule trans :premises (@p257 @p239)) % 169.02/169.36 (step @p259 :rule ho_cong :premises (@p258 @p148)) % 169.02/169.36 (step @p260 :rule trans :premises (@p259 @p234)) % 169.02/169.36 (step @p261 :rule refl :args (@t37)) % 169.02/169.36 (step @p262 :rule ho_cong :premises (@p43 @p261)) % 169.02/169.36 (step @p263 :rule refl :args (@t73)) % 169.02/169.36 (step @p264 :rule ho_cong :premises (@p118 @p263)) % 169.02/169.36 (step @p265 :rule ho_cong :premises (@p264 @p262)) % 169.02/169.36 (step @p266 :rule ho_cong :premises (@p43 @p265)) % 169.02/169.36 (step @p267 :rule ho_cong :premises (@p266 @p148)) % 169.02/169.36 (step @p268 :rule trans :premises (@p267 @p260)) % 169.02/169.36 (step @p269 :rule cong :premises (@p268) :args (@t82)) % 169.02/169.36 (step @p270 :rule trans :premises (@p56 @p269)) % 169.02/169.36 (step @p271 :rule ho_cong :premises (@p270 @p103)) % 169.02/169.36 (step @p272 :rule ho_cong :premises (@p271 @p212)) % 169.02/169.36 (step @p273 :rule beta-reduce :args ((= (_ @t240 @t6) @t210))) % 169.02/169.36 (step @p274 :rule beta-reduce :args ((= (_ (lambda @t241 @t239) @t42) @t240))) % 169.02/169.36 (step @p275 :rule refl :args (@t42)) % 169.02/169.36 (step @p276 :rule refl :args (@t43)) % 169.02/169.36 (step @p277 :rule beta-reduce :args ((= @t242 @t39))) % 169.02/169.36 (step @p278 :rule nary_cong :premises (@p277 @p276) :args (@t243)) % 169.02/169.36 (step @p279 :rule cong :premises (@p278) :args (@t244)) % 169.02/169.36 (step @p280 :rule beta-reduce :args ((= (_ @t44 @t233) @t244))) % 169.02/169.36 (step @p281 :rule trans :premises (@p280 @p279)) % 169.02/169.36 (step @p282 :rule refl :args (@t44)) % 169.02/169.36 (step @p283 :rule ho_cong :premises (@p282 @p252)) % 169.02/169.36 (step @p284 :rule trans :premises (@p283 @p281)) % 169.02/169.36 (step @p285 :rule ho_cong :premises (@p284 @p275)) % 169.02/169.36 (step @p286 :rule trans :premises (@p285 @p274)) % 169.02/169.36 (step @p287 :rule ho_cong :premises (@p286 @p148)) % 169.02/169.36 (step @p288 :rule trans :premises (@p287 @p273)) % 169.02/169.36 (step @p289 :rule ho_cong :premises (@p44 @p262)) % 169.02/169.36 (step @p290 :rule ho_cong :premises (@p289 @p275)) % 169.02/169.36 (step @p291 :rule ho_cong :premises (@p290 @p148)) % 169.02/169.36 (step @p292 :rule trans :premises (@p291 @p288)) % 169.02/169.36 (step @p293 :rule cong :premises (@p292) :args (@t50)) % 169.02/169.36 (step @p294 :rule trans :premises (@p46 @p293)) % 169.02/169.36 (step @p295 :rule ho_cong :premises (@p294 @p272)) % 169.02/169.36 (step @p296 :rule ho_cong :premises (@p295 @p183)) % 169.02/169.36 (step @p297 :rule ho_cong :premises (@p296 @p148)) % 169.02/169.36 (step @p298 :rule cong :premises (@p297) :args (@t23)) % 169.02/169.36 (step @p299 :rule refl :args (@t177)) % 169.02/169.36 (step @p300 :rule refl :args (@t56)) % 169.02/169.36 (step @p301 :rule cong :premises (@p300 @p299) :args ((= @t56 @t177))) % 169.02/169.36 (step @p302 :rule symm :premises (@p301)) % 169.02/169.36 (step @p303 :rule eq_resolve :premises (@p300 @p302)) % 169.02/169.36 (step @p304 :rule cong :premises (@p303) :args (@t58)) % 169.02/169.36 (step @p305 :rule cong :premises (@p304) :args (@t60)) % 169.02/169.36 (step @p306 :rule trans :premises (@p50 @p305)) % 169.02/169.36 (step @p307 :rule ho_cong :premises (@p306 @p298)) % 169.02/169.36 (step @p308 :rule ho_cong :premises (@p307 @p148)) % 169.02/169.36 (step @p309 :rule cong :premises (@p308) :args (@t24)) % 169.02/169.36 (step @p310 :rule ho_cong :premises (@p306 @p309)) % 169.02/169.36 (step @p311 :rule ho_cong :premises (@p128 @p310)) % 169.02/169.36 (step @p312 :rule trans :premises (@p311 @p233)) % 169.02/169.36 (step @p313 :rule trans :premises (@p312 @p133)) % 169.02/169.36 (step @p314 :rule eq_resolve :premises (@p19 @p313)) % 169.02/169.36 (step @p315 :rule instantiate :premises (@p314) :args ((@list @t251 tptp.jan tptp.cola @t253))) % 169.02/169.36 ; trust TRUST PREPROCESS_HO_ELIM % 169.02/169.36 (step @p316 :rule trust :premises () :args ((= (forall @t69 @t256) (forall @t69 (not (forall @t77 (or @t131 @t246))))))) % 169.02/169.36 (step @p317 :rule beta-reduce :args ((= @t258 @t256))) % 169.02/169.36 (step @p318 :rule cong :premises (@p317) :args (@t259)) % 169.02/169.36 (step @p319 :rule beta-reduce :args ((= (_ @t143 @t257) @t259))) % 169.02/169.36 (step @p320 :rule trans :premises (@p319 @p318)) % 169.02/169.36 (step @p321 :rule refl :args (@t254)) % 169.02/169.36 (step @p322 :rule refl :args (@t260)) % 169.02/169.36 (step @p323 :rule cong :premises (@p322 @p321) :args ((= @t260 @t254))) % 169.02/169.36 (step @p324 :rule symm :premises (@p323)) % 169.02/169.36 (step @p325 :rule eq_resolve :premises (@p322 @p324)) % 169.02/169.36 (step @p326 :rule cong :premises (@p325) :args (@t261)) % 169.02/169.36 (step @p327 :rule nary_cong :premises (@p199 @p326) :args (@t262)) % 169.02/169.36 (step @p328 :rule cong :premises (@p327) :args ((forall @t77 @t262))) % 169.02/169.36 (step @p329 :rule refl :args (@t263)) % 169.02/169.36 (step @p330 :rule cong :premises (@p329) :args (@t264)) % 169.02/169.36 (step @p331 :rule nary_cong :premises (@p204 @p330) :args (@t265)) % 169.02/169.36 (step @p332 :rule cong :premises (@p331) :args (@t266)) % 169.02/169.36 (step @p333 :rule trans :premises (@p332 @p328)) % 169.02/169.36 (step @p334 :rule cong :premises (@p333) :args (@t267)) % 169.02/169.36 (step @p335 :rule cong :premises (@p334) :args (@t268)) % 169.02/169.36 (step @p336 :rule beta-reduce :args ((= (_ @t222 @t5) @t268))) % 169.02/169.36 (step @p337 :rule trans :premises (@p336 @p335)) % 169.02/169.36 (step @p338 :rule refl :args (@t5)) % 169.02/169.36 (step @p339 :rule ho_cong :premises (@p213 @p338)) % 169.02/169.36 (step @p340 :rule trans :premises (@p339 @p337)) % 169.02/169.36 (step @p341 :rule ho_cong :premises (@p100 @p340)) % 169.02/169.36 (step @p342 :rule trans :premises (@p341 @p320)) % 169.02/169.36 (step @p343 :rule ho_cong :premises (@p271 @p338)) % 169.02/169.36 (step @p344 :rule ho_cong :premises (@p128 @p343)) % 169.02/169.36 (step @p345 :rule trans :premises (@p344 @p342)) % 169.02/169.36 (step @p346 :rule trans :premises (@p345 @p316)) % 169.02/169.36 (step @p347 :rule eq_resolve :premises (@p12 @p346)) % 169.02/169.36 (step @p348 :rule instantiate :premises (@p347) :args ((@list @t251))) % 169.02/169.36 (step @p349 :rule skolemize :premises (@p348)) % 169.02/169.36 (step @p350 :rule bool-double-not-elim :args (@t269)) % 169.02/169.36 (step @p351 :rule refl :args (@t271)) % 169.02/169.36 (step @p352 :rule nary_cong :premises (@p351 @p350) :args ((or @t271 (not @t270)))) % 169.02/169.36 (step @p353 :rule cnf_or_neg :args (@t271 0)) % 169.02/169.36 (step @p354 :rule eq_resolve :premises (@p353 @p352)) % 169.02/169.36 (step @p355 :rule reordering :premises (@p354) :args ((or @t269 @t271))) % 169.02/169.36 (step @p356 :rule chain_m_resolution :premises (@p355 @p349) :args (@t269 @t272 (@list @t271))) % 169.02/169.36 ; trust TRUST PREPROCESS_HO_ELIM % 169.02/169.36 (step @p357 :rule trust :premises () :args ((= (not (forall @t69 @t274)) @t273))) % 169.02/169.36 (step @p358 :rule beta-reduce :args ((= @t279 @t274))) % 169.02/169.36 (step @p359 :rule cong :premises (@p358) :args (@t280)) % 169.02/169.36 (step @p360 :rule beta-reduce :args ((= (_ @t143 @t278) @t280))) % 169.02/169.36 (step @p361 :rule trans :premises (@p360 @p359)) % 169.02/169.36 (step @p362 :rule quant-merge-prenex :args ((= (forall @t57 @t282) @t277))) % 169.02/169.36 (step @p363 :rule bool-double-not-elim :args (@t282)) % 169.02/169.36 (step @p364 :rule beta-reduce :args ((= @t285 @t283))) % 169.02/169.36 (step @p365 :rule cong :premises (@p364) :args (@t286)) % 169.02/169.36 (step @p366 :rule trans :premises (@p365 @p363)) % 169.02/169.36 (step @p367 :rule cong :premises (@p366) :args (@t287)) % 169.02/169.36 (step @p368 :rule trans :premises (@p367 @p362)) % 169.02/169.36 (step @p369 :rule cong :premises (@p368) :args (@t288)) % 169.02/169.36 (step @p370 :rule cong :premises (@p369) :args (@t289)) % 169.02/169.36 (step @p371 :rule beta-reduce :args ((= (_ @t292 @t284) @t289))) % 169.02/169.36 (step @p372 :rule trans :premises (@p371 @p370)) % 169.02/169.36 (step @p373 :rule beta-reduce :args ((= (_ (lambda @t200 @t283) @t6) @t283))) % 169.02/169.36 (step @p374 :rule refl :args (@t275)) % 169.02/169.36 (step @p375 :rule refl :args (@t293)) % 169.02/169.36 (step @p376 :rule cong :premises (@p375 @p374) :args ((= @t293 @t275))) % 169.02/169.36 (step @p377 :rule symm :premises (@p376)) % 169.02/169.36 (step @p378 :rule eq_resolve :premises (@p375 @p377)) % 169.02/169.36 (step @p379 :rule cong :premises (@p378) :args (@t294)) % 169.02/169.36 (step @p380 :rule cong :premises (@p379) :args ((forall @t281 @t294))) % 169.02/169.36 (step @p381 :rule beta-reduce :args ((= @t295 @t293))) % 169.02/169.36 (step @p382 :rule cong :premises (@p381) :args (@t296)) % 169.02/169.36 (step @p383 :rule cong :premises (@p382) :args (@t297)) % 169.02/169.36 (step @p384 :rule trans :premises (@p383 @p380)) % 169.02/169.36 (step @p385 :rule cong :premises (@p384) :args (@t298)) % 169.02/169.36 (step @p386 :rule cong :premises (@p385) :args (@t299)) % 169.02/169.36 (step @p387 :rule beta-reduce :args ((= (_ (lambda @t66 (not (forall @t281 (not (_ @t54 @t247 @t6))))) @t29) @t299))) % 169.02/169.36 (step @p388 :rule trans :premises (@p387 @p386)) % 169.02/169.36 (step @p389 :rule refl :args (@t29)) % 169.02/169.36 (step @p390 :rule alpha_equiv :args (@t290 @t199 (@list @t247))) % 169.02/169.36 (step @p391 :rule cong :premises (@p390) :args (@t291)) % 169.02/169.36 (step @p392 :rule cong :premises (@p391) :args (@t292)) % 169.02/169.36 (step @p393 :rule ho_cong :premises (@p392 @p389)) % 169.02/169.36 (step @p394 :rule trans :premises (@p393 @p388)) % 169.02/169.36 (step @p395 :rule ho_cong :premises (@p394 @p148)) % 169.02/169.36 (step @p396 :rule trans :premises (@p395 @p373)) % 169.02/169.36 (step @p397 :rule cong :premises (@p396) :args (@t300)) % 169.02/169.36 (step @p398 :rule refl :args (@t292)) % 169.02/169.36 (step @p399 :rule ho_cong :premises (@p398 @p397)) % 169.02/169.36 (step @p400 :rule trans :premises (@p399 @p372)) % 169.02/169.36 (step @p401 :rule ho_cong :premises (@p100 @p400)) % 169.02/169.36 (step @p402 :rule trans :premises (@p401 @p361)) % 169.02/169.36 (step @p403 :rule cong :premises (@p402) :args ((not (_ @t143 (_ @t292 @t300))))) % 169.02/169.36 (step @p404 :rule refl :args (@t29)) % 169.02/169.36 (step @p405 :rule beta-reduce :args ((= (_ (lambda @t69 (not @t301)) @t6) @t291))) % 169.02/169.36 (step @p406 :rule beta-reduce :args ((= @t303 @t301))) % 169.02/169.36 (step @p407 :rule cong :premises (@p406) :args (@t304)) % 169.02/169.36 (step @p408 :rule cong :premises (@p407) :args (@t305)) % 169.02/169.36 (step @p409 :rule beta-reduce :args ((= (_ @t41 @t302) @t305))) % 169.02/169.36 (step @p410 :rule trans :premises (@p409 @p408)) % 169.02/169.36 (step @p411 :rule cong :premises (@p303) :args (@t306)) % 169.02/169.36 (step @p412 :rule cong :premises (@p411) :args ((forall @t57 @t306))) % 169.02/169.36 (step @p413 :rule beta-reduce :args ((= @t309 @t306))) % 169.02/169.36 (step @p414 :rule cong :premises (@p413) :args (@t310)) % 169.02/169.36 (step @p415 :rule trans :premises (@p414 @p412)) % 169.02/169.36 (step @p416 :rule cong :premises (@p415) :args (@t311)) % 169.02/169.36 (step @p417 :rule beta-reduce :args ((= (_ @t179 @t308) @t311))) % 169.02/169.36 (step @p418 :rule trans :premises (@p417 @p416)) % 169.02/169.36 (step @p419 :rule beta-reduce :args ((= (_ @t312 @t6) @t307))) % 169.02/169.36 (step @p420 :rule beta-reduce :args ((= @t313 @t312))) % 169.02/169.36 (step @p421 :rule ho_cong :premises (@p420 @p148)) % 169.02/169.36 (step @p422 :rule trans :premises (@p421 @p419)) % 169.02/169.36 (step @p423 :rule cong :premises (@p422) :args ((lambda @t12 (_ @t313 @t6)))) % 169.02/169.36 (step @p424 :rule ho_cong :premises (@p224 @p423)) % 169.02/169.36 (step @p425 :rule trans :premises (@p424 @p418)) % 169.02/169.36 (step @p426 :rule ho_cong :premises (@p256 @p425)) % 169.02/169.36 (step @p427 :rule trans :premises (@p426 @p410)) % 169.02/169.36 (step @p428 :rule ho_cong :premises (@p427 @p148)) % 169.02/169.36 (step @p429 :rule trans :premises (@p428 @p405)) % 169.02/169.36 (step @p430 :rule refl :args (@t55)) % 169.02/169.36 (step @p431 :rule ho_cong :premises (@p43 @p430)) % 169.02/169.36 (step @p432 :rule ho_cong :premises (@p431 @p148)) % 169.02/169.36 (step @p433 :rule cong :premises (@p432) :args (@t65)) % 169.02/169.36 (step @p434 :rule ho_cong :premises (@p306 @p433)) % 169.02/169.36 (step @p435 :rule ho_cong :premises (@p43 @p434)) % 169.02/169.36 (step @p436 :rule ho_cong :premises (@p435 @p148)) % 169.02/169.36 (step @p437 :rule trans :premises (@p436 @p429)) % 169.02/169.36 (step @p438 :rule cong :premises (@p437) :args (@t67)) % 169.02/169.36 (step @p439 :rule trans :premises (@p52 @p438)) % 169.02/169.36 (step @p440 :rule ho_cong :premises (@p439 @p404)) % 169.02/169.36 (step @p441 :rule ho_cong :premises (@p440 @p148)) % 169.02/169.36 (step @p442 :rule cong :premises (@p441) :args (@t30)) % 169.02/169.36 (step @p443 :rule ho_cong :premises (@p439 @p442)) % 169.02/169.36 (step @p444 :rule ho_cong :premises (@p128 @p443)) % 169.02/169.36 (step @p445 :rule cong :premises (@p444) :args (@t31)) % 169.02/169.36 (step @p446 :rule trans :premises (@p445 @p403)) % 169.02/169.36 (step @p447 :rule trans :premises (@p446 @p357)) % 169.02/169.36 (step @p448 :rule eq_resolve :premises (@p39 @p447)) % 169.02/169.36 (step @p449 :rule refl :args (@t314)) % 169.02/169.36 (step @p450 :rule bool-double-not-elim :args (@t250)) % 169.02/169.36 (step @p451 :rule nary_cong :premises (@p450 @p449) :args ((or (not @t273) @t314))) % 169.02/169.36 (step @p452 :rule bool-double-not-elim :args (@t314)) % 169.02/169.36 (step @p453 :rule refl :args (@t273)) % 169.02/169.36 (step @p454 :rule cong :premises (@p453 @p452) :args ((=> @t273 @t315))) % 169.02/169.36 (assume-push @p476 @t273) % 169.02/169.36 (step @p456 :rule skolemize :premises (@p448)) % 169.02/169.36 (step-pop @p477 :rule scope :premises (@p456)) % 169.02/169.36 (step @p457 :rule process_scope :premises (@p477) :args (@t315)) % 169.02/169.36 (step @p459 :rule eq_resolve :premises (@p457 @p454)) % 169.02/169.36 (step @p460 :rule implies_elim :premises (@p459)) % 169.02/169.36 (step @p461 :rule eq_resolve :premises (@p460 @p451)) % 169.02/169.36 (step @p462 :rule chain_m_resolution :premises (@p461 @p448) :args (@t314 @t272 (@list @t250))) % 169.02/169.36 (step @p463 :rule instantiate :premises (@p462) :args ((@list tptp.jan tptp.cola))) % 169.02/169.36 (step @p464 :rule cnf_or_pos :args (@t319)) % 169.02/169.36 (step @p465 :rule reordering :premises (@p464) :args ((or @t318 @t270 @t317 (not @t319)))) % 169.02/169.36 (step @p466 :rule chain_m_resolution :premises (@p465 @p463 @p356 @p315) :args (@t317 (@list true false false) (@list @t318 @t269 @t319))) % 169.02/169.36 (step @p467 :rule cnf_or_pos :args (@t320)) % 169.02/169.36 (step @p468 :rule reordering :premises (@p467) :args ((or @t270 @t316 @t321))) % 169.02/169.36 (step @p469 :rule chain_m_resolution :premises (@p468 @p356 @p466) :args (@t321 (@list false true) (@list @t269 @t316))) % 169.02/169.36 (assume-push @p478 @t133) % 169.02/169.36 (step @p471 :rule instantiate :premises (@p132) :args ((@list @t251 @t253))) % 169.02/169.36 (step-pop @p479 :rule scope :premises (@p471)) % 169.02/169.36 (step @p472 :rule process_scope :premises (@p479) :args (@t320)) % 169.02/169.36 (step @p474 :rule implies_elim :premises (@p472)) % 169.02/169.36 (step @p475 false :rule chain_m_resolution :premises (@p474 @p469 @p132) :args (false (@list true false) (@list @t320 @t133))) % 169.02/169.36 ) % 169.02/169.36 % SZS output end Proof % 169.02/169.36 % cvc5 exiting %------------------------------------------------------------------------------