%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : AGT033^2 : TPTP v9.2.1. Released v5.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n008.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 168.80s 169.15s % Output : Proof 168.80s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : AGT033^2 : TPTP v9.2.1. Released v5.2.0. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.18/0.35 % Computer : n008.cluster.edu % 0.18/0.35 % Model : x86_64 x86_64 % 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.35 % Memory : 8042.1875MB % 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.36 % CPULimit : 300 % 0.18/0.36 % WCLimit : 300 % 0.18/0.36 % DateTime : Wed Jun 3 01:34:03 EDT 2026 % 0.18/0.36 % CPUTime : % 0.29/0.53 %----Proving TH0 % 168.80/169.15 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 168.80/169.15 --- 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... % 168.80/169.15 --- 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... % 168.80/169.15 --- Run --ho-elim --full-saturate-quant at 18s... % 168.80/169.15 --- Run --ho-elim --no-e-matching --full-saturate-quant at 12s... % 168.80/169.15 % SZS status Theorem % 168.80/169.15 % SZS output start Proof % 168.80/169.15 ( % 168.80/169.15 (declare-sort $$unsorted 0) % 168.80/169.15 (declare-sort tptp.mu 0) % 168.80/169.15 (declare-const tptp.possibly_likes (-> tptp.mu tptp.mu $$unsorted Bool)) % 168.80/169.15 (declare-const tptp.very_much_likes (-> tptp.mu tptp.mu $$unsorted Bool)) % 168.80/169.15 (declare-const tptp.beer tptp.mu) % 168.80/169.15 (declare-const tptp.cola tptp.mu) % 168.80/169.15 (declare-const tptp.jan tptp.mu) % 168.80/169.15 (declare-const tptp.likes (-> tptp.mu tptp.mu $$unsorted Bool)) % 168.80/169.15 (declare-const tptp.a1 (-> $$unsorted $$unsorted Bool)) % 168.80/169.15 (declare-const tptp.pepsi tptp.mu) % 168.80/169.15 (declare-const tptp.piotr tptp.mu) % 168.80/169.15 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 168.80/169.15 (declare-const tptp.a2 (-> $$unsorted $$unsorted Bool)) % 168.80/169.15 (declare-const tptp.a3 (-> $$unsorted $$unsorted Bool)) % 168.80/169.15 (define tptp.meq_ind () (let ((_let_1 (@var "Y" tptp.mu))) (let ((_let_2 (@var "X" tptp.mu))) (lambda (@list _let_2 _let_1 (@var "W" $$unsorted)) (= _let_2 _let_1))))) % 168.80/169.15 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (= (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 168.80/169.15 (define tptp.mnot () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 168.80/169.15 (define tptp.mor () (let ((_let_1 (@var "W" $$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))))))) % 168.80/169.15 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mor (_ tptp.mnot _let_3)) (_ tptp.mnot _let_2))) _let_1)))))) % 168.80/169.15 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 168.80/169.15 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 168.80/169.15 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 168.80/169.15 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mequiv _let_3) _let_2)) _let_1)))))) % 168.80/169.15 (define tptp.mforall_ind () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 168.80/169.15 (define tptp.mforall_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 168.80/169.15 (define tptp.mexists_ind () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 168.80/169.15 (define tptp.mexists_prop () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 168.80/169.15 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 168.80/169.15 (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 $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ _let_4 _let_3) _let_1)) (_ _let_2 _let_1))))))))) % 168.80/169.15 (define tptp.mdia () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mbox _let_3) (_ tptp.mnot _let_2))) _let_1)))))) % 168.80/169.15 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 168.80/169.15 (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)))))))) % 168.80/169.15 (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)))))))) % 168.80/169.15 (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" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_2 _let_5 _let_1) (=> (and (_ _let_4 _let_5) (_ (_ _let_3 _let_5) _let_1)) (_ _let_4 _let_1)))))))))) % 168.80/169.15 (define tptp.meuclidean () (let ((_let_1 (@var "U" $$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)))))))))) % 168.80/169.15 (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 $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (= _let_2 _let_1)))))))))) % 168.80/169.15 (define tptp.mfunctional () (let ((_let_1 (@var "U" $$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))))))))))))) % 168.80/169.15 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (_ _let_5 _let_1) (exists (@list _let_2) (and (_ _let_5 _let_2) (_ (_ _let_3 _let_2) _let_1)))))))))))) % 168.80/169.15 (define tptp.mweakly_connected () (let ((_let_1 (@var "T" $$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))))))))))) % 168.80/169.15 (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))))))))))))) % 168.80/169.15 (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)))))) % 168.80/169.15 (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))))))) % 168.80/169.15 (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)))))) % 168.80/169.15 (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))))))) % 168.80/169.15 (define @t1 () (_ tptp.likes tptp.jan)) % 168.80/169.15 (define @t2 () (_ @t1 tptp.cola)) % 168.80/169.15 (define @t3 () (_ tptp.mbox tptp.a1)) % 168.80/169.15 (define @t4 () (_ tptp.likes tptp.piotr)) % 168.80/169.15 (define @t5 () (_ @t4 tptp.pepsi)) % 168.80/169.15 (define @t6 () (@var "__flatten_var_0" $$unsorted)) % 168.80/169.15 (define @t7 () (@var "X" tptp.mu)) % 168.80/169.15 (define @t8 () (_ tptp.likes @t7)) % 168.80/169.15 (define @t9 () (_ @t8 tptp.cola)) % 168.80/169.15 (define @t10 () (_ @t8 tptp.pepsi)) % 168.80/169.15 (define @t11 () (_ tptp.mdia tptp.a1)) % 168.80/169.15 (define @t12 () (@list @t7 @t6)) % 168.80/169.15 (define @t13 () (_ tptp.mbox tptp.a2)) % 168.80/169.15 (define @t14 () (_ @t4 tptp.beer)) % 168.80/169.15 (define @t15 () (_ tptp.mbox tptp.a3)) % 168.80/169.15 (define @t16 () (_ tptp.mdia tptp.a3)) % 168.80/169.15 (define @t17 () (@var "Y" tptp.mu)) % 168.80/169.15 (define @t18 () (_ (_ tptp.very_much_likes @t7) @t17)) % 168.80/169.15 (define @t19 () (_ @t8 @t17)) % 168.80/169.15 (define @t20 () (@list @t17 @t6)) % 168.80/169.15 (define @t21 () (_ tptp.possibly_likes @t7)) % 168.80/169.15 (define @t22 () (_ @t21 @t17)) % 168.80/169.15 (define @t23 () (lambda @t20 (_ (_ (_ tptp.mimplies (_ @t16 @t19)) @t22) @t6))) % 168.80/169.15 (define @t24 () (lambda @t12 (_ (_ tptp.mforall_ind @t23) @t6))) % 168.80/169.15 (define @t25 () (_ @t22 @t6)) % 168.80/169.15 (define @t26 () (lambda @t20 @t25)) % 168.80/169.15 (define @t27 () (lambda @t12 (_ (_ tptp.mexists_ind @t26) @t6))) % 168.80/169.15 (define @t28 () (not (_ tptp.mvalid (_ tptp.mexists_ind @t27)))) % 168.80/169.15 (define @t29 () (@var "W" $$unsorted)) % 168.80/169.15 (define @t30 () (lambda (@list @t7 @t17 @t29) (= @t7 @t17))) % 168.80/169.15 (define @t31 () (@var "Y" (-> $$unsorted Bool))) % 168.80/169.15 (define @t32 () (@var "X" (-> $$unsorted Bool))) % 168.80/169.15 (define @t33 () (lambda (@list @t32 @t31 @t29) (= (_ @t32 @t29) (_ @t31 @t29)))) % 168.80/169.15 (define @t34 () (@var "Phi" (-> $$unsorted Bool))) % 168.80/169.15 (define @t35 () (_ @t34 @t29)) % 168.80/169.15 (define @t36 () (not @t35)) % 168.80/169.15 (define @t37 () (@list @t34 @t29)) % 168.80/169.15 (define @t38 () (lambda @t37 @t36)) % 168.80/169.15 (define @t39 () (@var "Psi" (-> $$unsorted Bool))) % 168.80/169.15 (define @t40 () (_ @t39 @t29)) % 168.80/169.15 (define @t41 () (lambda (@list @t34 @t39 @t29) (or @t35 @t40))) % 168.80/169.15 (define @t42 () (_ tptp.mnot @t39)) % 168.80/169.15 (define @t43 () (_ tptp.mnot @t34)) % 168.80/169.15 (define @t44 () (_ tptp.mor @t43)) % 168.80/169.15 (define @t45 () (@list @t34 @t39 @t6)) % 168.80/169.15 (define @t46 () (lambda @t45 (_ (_ tptp.mnot (_ @t44 @t42)) @t6))) % 168.80/169.15 (define @t47 () (lambda @t45 (_ (_ @t44 @t39) @t6))) % 168.80/169.15 (define @t48 () (lambda @t45 (_ (_ (_ tptp.mor @t42) @t34) @t6))) % 168.80/169.15 (define @t49 () (lambda @t45 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t34) @t39)) (_ (_ tptp.mimplies @t39) @t34)) @t6))) % 168.80/169.15 (define @t50 () (lambda @t45 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t34) @t39)) @t6))) % 168.80/169.15 (define @t51 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 168.80/169.15 (define @t52 () (_ @t51 @t7)) % 168.80/169.15 (define @t53 () (_ @t52 @t29)) % 168.80/169.15 (define @t54 () (@list @t7)) % 168.80/169.15 (define @t55 () (forall @t54 @t53)) % 168.80/169.15 (define @t56 () (@list @t51 @t29)) % 168.80/169.15 (define @t57 () (lambda @t56 @t55)) % 168.80/169.15 (define @t58 () (@var "P" (-> $$unsorted Bool))) % 168.80/169.15 (define @t59 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 168.80/169.15 (define @t60 () (_ @t59 @t58)) % 168.80/169.15 (define @t61 () (lambda (@list @t59 @t29) (forall (@list @t58) (_ @t60 @t29)))) % 168.80/169.15 (define @t62 () (lambda @t12 (_ (_ tptp.mnot @t52) @t6))) % 168.80/169.15 (define @t63 () (@list @t51 @t6)) % 168.80/169.15 (define @t64 () (lambda @t63 (_ (_ tptp.mnot (_ tptp.mforall_ind @t62)) @t6))) % 168.80/169.15 (define @t65 () (lambda (@list @t59 @t6) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t58 @t6) (_ (_ tptp.mnot @t60) @t6)))) @t6))) % 168.80/169.15 (define @t66 () (@list @t29)) % 168.80/169.15 (define @t67 () (lambda @t66 true)) % 168.80/169.15 (define @t68 () (@var "V" $$unsorted)) % 168.80/169.15 (define @t69 () (_ @t34 @t68)) % 168.80/169.15 (define @t70 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 168.80/169.15 (define @t71 () (_ (_ @t70 @t29) @t68)) % 168.80/169.15 (define @t72 () (not @t71)) % 168.80/169.15 (define @t73 () (or @t72 @t69)) % 168.80/169.15 (define @t74 () (@list @t68)) % 168.80/169.15 (define @t75 () (forall @t74 @t73)) % 168.80/169.15 (define @t76 () (@list @t70 @t34 @t29)) % 168.80/169.15 (define @t77 () (lambda @t76 @t75)) % 168.80/169.15 (define @t78 () (@list @t70 @t34 @t6)) % 168.80/169.15 (define @t79 () (lambda @t78 (_ (_ tptp.mnot (_ (_ tptp.mbox @t70) @t43)) @t6))) % 168.80/169.15 (define @t80 () (@var "S" $$unsorted)) % 168.80/169.15 (define @t81 () (_ @t70 @t80)) % 168.80/169.15 (define @t82 () (@list @t80)) % 168.80/169.15 (define @t83 () (@list @t70)) % 168.80/169.15 (define @t84 () (lambda @t83 (forall @t82 (_ @t81 @t80)))) % 168.80/169.15 (define @t85 () (@var "T" $$unsorted)) % 168.80/169.15 (define @t86 () (_ @t70 @t85)) % 168.80/169.15 (define @t87 () (_ @t81 @t85)) % 168.80/169.15 (define @t88 () (lambda @t83 (forall (@list @t80 @t85) (=> @t87 (_ @t86 @t80))))) % 168.80/169.15 (define @t89 () (@list @t85)) % 168.80/169.15 (define @t90 () (lambda @t83 (forall @t82 (exists @t89 @t87)))) % 168.80/169.15 (define @t91 () (@var "U" $$unsorted)) % 168.80/169.15 (define @t92 () (_ @t81 @t91)) % 168.80/169.15 (define @t93 () (_ @t86 @t91)) % 168.80/169.15 (define @t94 () (@list @t80 @t85 @t91)) % 168.80/169.15 (define @t95 () (lambda @t83 (forall @t94 (=> (and @t87 @t93) @t92)))) % 168.80/169.15 (define @t96 () (and @t87 @t92)) % 168.80/169.15 (define @t97 () (lambda @t83 (forall @t94 (=> @t96 @t93)))) % 168.80/169.15 (define @t98 () (= @t85 @t91)) % 168.80/169.15 (define @t99 () (lambda @t83 (forall @t94 (=> @t96 @t98)))) % 168.80/169.15 (define @t100 () (@list @t91)) % 168.80/169.15 (define @t101 () (lambda @t83 (forall @t82 (exists @t89 (and @t87 (forall @t100 (=> @t92 @t98))))))) % 168.80/169.15 (define @t102 () (_ @t70 @t91)) % 168.80/169.15 (define @t103 () (_ @t102 @t85)) % 168.80/169.15 (define @t104 () (lambda @t83 (forall @t94 (=> @t87 (exists @t100 (and @t92 @t103)))))) % 168.80/169.15 (define @t105 () (lambda @t83 (forall @t94 (=> @t96 (or @t93 @t98 @t103))))) % 168.80/169.15 (define @t106 () (lambda @t83 (forall @t94 (=> @t96 (exists @t74 (and (_ @t86 @t68) (_ @t102 @t68))))))) % 168.80/169.15 (define @t107 () (forall @t66 @t35)) % 168.80/169.15 (define @t108 () (@list @t34)) % 168.80/169.15 (define @t109 () (lambda @t108 @t107)) % 168.80/169.15 (define @t110 () (lambda @t108 (forall @t66 @t36))) % 168.80/169.15 (define @t111 () (lambda @t108 (exists @t66 @t35))) % 168.80/169.15 (define @t112 () (lambda @t108 (exists @t66 @t36))) % 168.80/169.15 (define @t113 () (@const 0 (@ho-elim-sort (-> tptp.mu tptp.mu $$unsorted Bool)))) % 168.80/169.15 (define @t114 () (@const 1 (-> (@ho-elim-sort (-> tptp.mu tptp.mu $$unsorted Bool)) tptp.mu (@ho-elim-sort (-> tptp.mu $$unsorted Bool))))) % 168.80/169.15 (define @t115 () (@const 2 (-> (@ho-elim-sort (-> tptp.mu $$unsorted Bool)) tptp.mu (@ho-elim-sort (-> $$unsorted Bool))))) % 168.80/169.15 (define @t116 () (_ @t115 (_ @t114 @t113 tptp.jan) tptp.cola)) % 168.80/169.15 (define @t117 () (@const 3 (-> (@ho-elim-sort (-> $$unsorted Bool)) $$unsorted Bool))) % 168.80/169.15 (define @t118 () (@const 4 (@ho-elim-sort (-> $$unsorted $$unsorted Bool)))) % 168.80/169.15 (define @t119 () (@const 5 (-> (@ho-elim-sort (-> $$unsorted $$unsorted Bool)) $$unsorted (@ho-elim-sort (-> $$unsorted Bool))))) % 168.80/169.15 (define @t120 () (_ @t119 @t118 @t29)) % 168.80/169.15 (define @t121 () (not (_ @t117 @t120 @t68))) % 168.80/169.15 (define @t122 () (@list @t29 @t68)) % 168.80/169.15 (define @t123 () (forall @t122 (or @t121 (_ @t117 @t116 @t68)))) % 168.80/169.15 (define @t124 () (tptp.likes tptp.jan tptp.cola @t68)) % 168.80/169.15 (define @t125 () (not (tptp.a3 @t29 @t68))) % 168.80/169.15 (define @t126 () (or @t125 @t124)) % 168.80/169.15 (define @t127 () (forall @t122 @t126)) % 168.80/169.15 (define @t128 () (forall @t74 @t126)) % 168.80/169.15 (define @t129 () (lambda @t66 @t128)) % 168.80/169.15 (define @t130 () (_ @t129 @t29)) % 168.80/169.15 (define @t131 () (forall @t66 @t130)) % 168.80/169.15 (define @t132 () (_ @t34 @t29)) % 168.80/169.15 (define @t133 () (lambda @t108 (forall @t66 @t132))) % 168.80/169.15 (define @t134 () (_ @t2 @t68)) % 168.80/169.15 (define @t135 () (or @t125 @t134)) % 168.80/169.15 (define @t136 () (_ @t2 @t68)) % 168.80/169.15 (define @t137 () (or @t125 @t136)) % 168.80/169.15 (define @t138 () (forall @t74 @t137)) % 168.80/169.15 (define @t139 () (lambda @t66 @t138)) % 168.80/169.15 (define @t140 () (_ @t34 @t68)) % 168.80/169.15 (define @t141 () (lambda @t37 (forall @t74 (or @t125 @t140)))) % 168.80/169.15 (define @t142 () (_ @t70 @t29 @t68)) % 168.80/169.15 (define @t143 () (not @t142)) % 168.80/169.15 (define @t144 () (forall @t74 (or @t143 @t140))) % 168.80/169.15 (define @t145 () (lambda @t76 @t144)) % 168.80/169.15 (define @t146 () (@var "BOUND_VARIABLE_9590" $$unsorted)) % 168.80/169.15 (define @t147 () (@var "BOUND_VARIABLE_9568" tptp.mu)) % 168.80/169.15 (define @t148 () (@const 6 (@ho-elim-sort (-> tptp.mu tptp.mu $$unsorted Bool)))) % 168.80/169.15 (define @t149 () (_ @t114 @t148 @t7)) % 168.80/169.15 (define @t150 () (@list @t29 @t7 @t147 @t146)) % 168.80/169.15 (define @t151 () (not (tptp.likes @t7 @t147 @t146))) % 168.80/169.15 (define @t152 () (not (tptp.a3 @t29 @t146))) % 168.80/169.15 (define @t153 () (tptp.possibly_likes @t7 @t147 @t29)) % 168.80/169.15 (define @t154 () (or @t153 @t152 @t151)) % 168.80/169.15 (define @t155 () (forall @t150 @t154)) % 168.80/169.15 (define @t156 () (forall (@list @t7 @t147 @t146) @t154)) % 168.80/169.15 (define @t157 () (lambda @t66 @t156)) % 168.80/169.15 (define @t158 () (_ @t157 @t29)) % 168.80/169.15 (define @t159 () (forall @t66 @t158)) % 168.80/169.15 (define @t160 () (@list @t147 @t146)) % 168.80/169.15 (define @t161 () (forall @t160 @t154)) % 168.80/169.15 (define @t162 () (forall @t160 (or (tptp.possibly_likes @t7 @t147 @t6) (not (tptp.a3 @t6 @t146)) @t151))) % 168.80/169.15 (define @t163 () (lambda @t12 @t162)) % 168.80/169.15 (define @t164 () (_ @t163 @t7 @t29)) % 168.80/169.15 (define @t165 () (forall @t54 @t164)) % 168.80/169.15 (define @t166 () (lambda @t66 @t165)) % 168.80/169.15 (define @t167 () (_ @t51 @t7 @t29)) % 168.80/169.15 (define @t168 () (forall @t54 @t167)) % 168.80/169.15 (define @t169 () (lambda @t56 @t168)) % 168.80/169.15 (define @t170 () (or @t152 @t151)) % 168.80/169.15 (define @t171 () (or @t170 @t153)) % 168.80/169.15 (define @t172 () (forall @t160 @t171)) % 168.80/169.15 (define @t173 () (@list @t146)) % 168.80/169.15 (define @t174 () (forall @t173 @t171)) % 168.80/169.15 (define @t175 () (@list @t147)) % 168.80/169.15 (define @t176 () (forall @t173 @t170)) % 168.80/169.15 (define @t177 () (or @t176 @t153)) % 168.80/169.15 (define @t178 () (forall @t74 (or @t125 (not (tptp.likes @t7 @t147 @t68))))) % 168.80/169.15 (define @t179 () (_ (_ @t21 @t147) @t29)) % 168.80/169.15 (define @t180 () (or @t178 @t179)) % 168.80/169.15 (define @t181 () (tptp.likes @t7 @t17 @t68)) % 168.80/169.15 (define @t182 () (not (tptp.a3 @t6 @t68))) % 168.80/169.15 (define @t183 () (forall @t74 (or @t182 (not @t181)))) % 168.80/169.15 (define @t184 () (or @t183 @t25)) % 168.80/169.15 (define @t185 () (lambda @t20 @t184)) % 168.80/169.15 (define @t186 () (_ @t185 @t147 @t29)) % 168.80/169.15 (define @t187 () (forall @t175 @t186)) % 168.80/169.15 (define @t188 () (lambda @t66 @t187)) % 168.80/169.15 (define @t189 () (@list @t7)) % 168.80/169.15 (define @t190 () (@list @t6)) % 168.80/169.15 (define @t191 () (lambda @t190 @t184)) % 168.80/169.15 (define @t192 () (_ @t39 @t6)) % 168.80/169.15 (define @t193 () (@list @t39 @t6)) % 168.80/169.15 (define @t194 () (not @t183)) % 168.80/169.15 (define @t195 () (lambda @t190 @t194)) % 168.80/169.15 (define @t196 () (_ @t195 @t6)) % 168.80/169.15 (define @t197 () (not @t196)) % 168.80/169.15 (define @t198 () (or @t197 @t192)) % 168.80/169.15 (define @t199 () (lambda @t193 @t198)) % 168.80/169.15 (define @t200 () (or (not (_ @t34 @t6)) @t192)) % 168.80/169.15 (define @t201 () (lambda @t45 @t200)) % 168.80/169.15 (define @t202 () (_ @t19 @t68)) % 168.80/169.15 (define @t203 () (not @t202)) % 168.80/169.15 (define @t204 () (or @t182 @t203)) % 168.80/169.15 (define @t205 () (_ @t19 @t68)) % 168.80/169.15 (define @t206 () (not @t205)) % 168.80/169.15 (define @t207 () (or @t182 @t206)) % 168.80/169.15 (define @t208 () (forall @t74 @t207)) % 168.80/169.15 (define @t209 () (not @t208)) % 168.80/169.15 (define @t210 () (lambda @t190 @t209)) % 168.80/169.15 (define @t211 () (not @t140)) % 168.80/169.15 (define @t212 () (lambda (@list @t34 @t6) (not (forall @t74 (or @t182 @t211))))) % 168.80/169.15 (define @t213 () (not (forall @t74 (or (not (_ @t70 @t6 @t68)) @t211)))) % 168.80/169.15 (define @t214 () (_ (lambda @t78 @t213) tptp.a3)) % 168.80/169.15 (define @t215 () (lambda @t20 (_ (_ (_ @t201 (_ @t214 @t19)) @t22) @t6))) % 168.80/169.15 (define @t216 () (forall @t74 (or @t143 @t211))) % 168.80/169.15 (define @t217 () (lambda @t66 @t216)) % 168.80/169.15 (define @t218 () (_ @t217 @t29)) % 168.80/169.15 (define @t219 () (not @t218)) % 168.80/169.15 (define @t220 () (lambda @t66 @t219)) % 168.80/169.15 (define @t221 () (not @t69)) % 168.80/169.15 (define @t222 () (or @t143 @t221)) % 168.80/169.15 (define @t223 () (lambda @t66 @t36)) % 168.80/169.15 (define @t224 () (_ @t223 @t68)) % 168.80/169.15 (define @t225 () (or @t143 @t224)) % 168.80/169.15 (define @t226 () (forall @t74 @t225)) % 168.80/169.15 (define @t227 () (lambda @t66 @t226)) % 168.80/169.15 (define @t228 () (lambda @t37 @t144)) % 168.80/169.15 (define @t229 () (or @t36 @t40)) % 168.80/169.15 (define @t230 () (lambda @t66 @t229)) % 168.80/169.15 (define @t231 () (@list @t39 @t29)) % 168.80/169.15 (define @t232 () (_ @t223 @t29)) % 168.80/169.15 (define @t233 () (or @t232 @t40)) % 168.80/169.15 (define @t234 () (lambda @t231 @t233)) % 168.80/169.15 (define @t235 () (_ @t115 (_ @t114 @t113 tptp.piotr) tptp.pepsi)) % 168.80/169.15 (define @t236 () (not (_ @t117 @t235 @t68))) % 168.80/169.15 (define @t237 () (@var "BOUND_VARIABLE_9634" tptp.mu)) % 168.80/169.15 (define @t238 () (_ @t115 @t149 @t237)) % 168.80/169.15 (define @t239 () (@list @t7 @t237)) % 168.80/169.15 (define @t240 () (forall @t66 (not (forall @t239 (not (_ @t117 @t238 @t29)))))) % 168.80/169.15 (define @t241 () (@quantifiers_skolemize @t240 0)) % 168.80/169.15 (define @t242 () (_ @t119 @t118 @t241)) % 168.80/169.15 (define @t243 () (@quantifiers_skolemize (forall @t74 (or (not (_ @t117 @t242 @t68)) @t236)) 0)) % 168.80/169.15 (define @t244 () (tptp.likes tptp.piotr tptp.pepsi @t68)) % 168.80/169.15 (define @t245 () (not @t244)) % 168.80/169.15 (define @t246 () (not (forall @t74 (or @t125 @t245)))) % 168.80/169.15 (define @t247 () (lambda @t190 (not (forall @t74 (or @t182 @t245))))) % 168.80/169.15 (define @t248 () (_ @t247 @t29)) % 168.80/169.15 (define @t249 () (forall @t66 @t248)) % 168.80/169.15 (define @t250 () (_ @t5 @t68)) % 168.80/169.15 (define @t251 () (not @t250)) % 168.80/169.15 (define @t252 () (or @t182 @t251)) % 168.80/169.15 (define @t253 () (_ @t5 @t68)) % 168.80/169.15 (define @t254 () (not @t253)) % 168.80/169.15 (define @t255 () (or @t182 @t254)) % 168.80/169.15 (define @t256 () (forall @t74 @t255)) % 168.80/169.15 (define @t257 () (not @t256)) % 168.80/169.15 (define @t258 () (lambda @t190 @t257)) % 168.80/169.15 (define @t259 () (_ @t117 @t242 @t243)) % 168.80/169.15 (define @t260 () (not @t259)) % 168.80/169.15 (define @t261 () (or @t260 (not (_ @t117 @t235 @t243)))) % 168.80/169.15 (define @t262 () (@list true)) % 168.80/169.15 (define @t263 () (not @t240)) % 168.80/169.15 (define @t264 () (not (forall @t239 (not (tptp.possibly_likes @t7 @t237 @t29))))) % 168.80/169.15 (define @t265 () (tptp.possibly_likes @t7 @t237 @t6)) % 168.80/169.15 (define @t266 () (not @t265)) % 168.80/169.15 (define @t267 () (forall @t239 @t266)) % 168.80/169.15 (define @t268 () (lambda @t190 (not @t267))) % 168.80/169.15 (define @t269 () (_ @t268 @t29)) % 168.80/169.15 (define @t270 () (forall @t66 @t269)) % 168.80/169.15 (define @t271 () (@list @t237)) % 168.80/169.15 (define @t272 () (forall @t271 @t266)) % 168.80/169.15 (define @t273 () (not @t272)) % 168.80/169.15 (define @t274 () (lambda @t12 @t273)) % 168.80/169.15 (define @t275 () (_ @t274 @t7 @t6)) % 168.80/169.15 (define @t276 () (not @t275)) % 168.80/169.15 (define @t277 () (forall @t54 @t276)) % 168.80/169.15 (define @t278 () (not @t277)) % 168.80/169.15 (define @t279 () (lambda @t190 @t278)) % 168.80/169.15 (define @t280 () (forall @t54 (not (_ @t51 @t7 @t6)))) % 168.80/169.15 (define @t281 () (not @t280)) % 168.80/169.15 (define @t282 () (lambda @t63 @t281)) % 168.80/169.15 (define @t283 () (_ (_ @t21 @t237) @t6)) % 168.80/169.15 (define @t284 () (not @t283)) % 168.80/169.15 (define @t285 () (_ @t26 @t237 @t6)) % 168.80/169.15 (define @t286 () (not @t285)) % 168.80/169.15 (define @t287 () (forall @t271 @t286)) % 168.80/169.15 (define @t288 () (not @t287)) % 168.80/169.15 (define @t289 () (lambda @t190 @t288)) % 168.80/169.15 (define @t290 () (lambda @t12 (_ (_ @t282 @t26) @t6))) % 168.80/169.15 (define @t291 () (forall @t54 (not @t167))) % 168.80/169.15 (define @t292 () (lambda @t66 @t291)) % 168.80/169.15 (define @t293 () (_ @t292 @t29)) % 168.80/169.15 (define @t294 () (not @t293)) % 168.80/169.15 (define @t295 () (lambda @t66 @t294)) % 168.80/169.15 (define @t296 () (not @t53)) % 168.80/169.15 (define @t297 () (not (_ @t52 @t6))) % 168.80/169.15 (define @t298 () (lambda @t12 @t297)) % 168.80/169.15 (define @t299 () (_ @t298 @t7 @t29)) % 168.80/169.15 (define @t300 () (forall @t54 @t299)) % 168.80/169.15 (define @t301 () (lambda @t66 @t300)) % 168.80/169.15 (define @t302 () (lambda @t66 @t296)) % 168.80/169.15 (define @t303 () (_ @t38 @t52)) % 168.80/169.15 (define @t304 () (forall @t239 (not (_ @t117 @t238 @t241)))) % 168.80/169.15 (define @t305 () (not (not @t304))) % 168.80/169.15 (define @t306 () (_ @t117 @t116 @t243)) % 168.80/169.15 (define @t307 () (not @t306)) % 168.80/169.15 (define @t308 () (_ @t117 (_ @t115 (_ @t114 @t148 tptp.jan) tptp.cola) @t241)) % 168.80/169.15 (define @t309 () (or @t308 @t260 @t307)) % 168.80/169.15 (define @t310 () (or @t260 @t306)) % 168.80/169.15 (define @t311 () (not @t310)) % 168.80/169.15 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 168.80/169.15 (assume @p2 (_ tptp.mvalid (_ @t3 @t2))) % 168.80/169.15 (assume @p3 (_ tptp.mvalid (_ @t3 @t5))) % 168.80/169.15 (assume @p4 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t12 (_ (_ @t3 (_ (_ tptp.mimplies (_ @t11 @t10)) @t9)) @t6))))) % 168.80/169.15 (assume @p5 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t12 (_ (_ @t3 (_ (_ tptp.mimplies (_ @t11 @t9)) @t10)) @t6))))) % 168.80/169.15 (assume @p6 (_ tptp.mvalid (_ @t13 (_ @t1 tptp.pepsi)))) % 168.80/169.15 (assume @p7 (_ tptp.mvalid (_ @t3 (_ @t4 tptp.cola)))) % 168.80/169.15 (assume @p8 (_ tptp.mvalid (_ @t3 @t14))) % 168.80/169.15 (assume @p9 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t12 (_ (_ @t13 (_ (_ tptp.mimplies @t10) @t9)) @t6))))) % 168.80/169.15 (assume @p10 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t12 (_ (_ @t13 (_ (_ tptp.mimplies @t9) @t10)) @t6))))) % 168.80/169.15 (assume @p11 (_ tptp.mvalid (_ @t15 @t2))) % 168.80/169.15 (assume @p12 (_ tptp.mvalid (_ @t16 @t5))) % 168.80/169.15 (assume @p13 (_ tptp.mvalid (_ @t11 @t14))) % 168.80/169.15 (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))))) % 168.80/169.15 (assume @p15 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t12 (_ (_ tptp.mforall_ind (lambda @t20 (_ (_ (_ tptp.mimplies (_ @t15 @t18)) @t18) @t6))) @t6))))) % 168.80/169.15 (assume @p16 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t12 (_ (_ tptp.mforall_ind (lambda @t20 (_ (_ (_ tptp.mimplies (_ @t16 @t18)) @t19) @t6))) @t6))))) % 168.80/169.15 (assume @p17 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t12 (_ (_ tptp.mforall_ind (lambda @t20 (_ (_ (_ tptp.mimplies (_ @t11 @t19)) @t22) @t6))) @t6))))) % 168.80/169.15 (assume @p18 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t12 (_ (_ tptp.mforall_ind (lambda @t20 (_ (_ (_ tptp.mimplies (_ (_ tptp.mdia tptp.a2) @t19)) @t22) @t6))) @t6))))) % 168.80/169.15 (assume @p19 (_ tptp.mvalid (_ tptp.mforall_ind @t24))) % 168.80/169.15 (assume @p20 @t28) % 168.80/169.15 (assume @p21 true) % 168.80/169.15 (step @p22 (= tptp.meq_ind @t30) :rule refl :args (@t30)) % 168.80/169.15 (step @p23 (= tptp.meq_prop @t33) :rule refl :args (@t33)) % 168.80/169.15 (step @p24 (= tptp.mnot @t38) :rule refl :args (@t38)) % 168.80/169.15 (step @p25 (= tptp.mor @t41) :rule refl :args (@t41)) % 168.80/169.15 (step @p26 (= tptp.mand @t46) :rule refl :args (@t46)) % 168.80/169.15 (step @p27 (= tptp.mimplies @t47) :rule refl :args (@t47)) % 168.80/169.15 (step @p28 (= tptp.mimplied @t48) :rule refl :args (@t48)) % 168.80/169.15 (step @p29 (= tptp.mequiv @t49) :rule refl :args (@t49)) % 168.80/169.15 (step @p30 (= tptp.mxor @t50) :rule refl :args (@t50)) % 168.80/169.15 (step @p31 (= tptp.mforall_ind @t57) :rule refl :args (@t57)) % 168.80/169.15 (step @p32 (= tptp.mforall_prop @t61) :rule refl :args (@t61)) % 168.80/169.15 (step @p33 (= tptp.mexists_ind @t64) :rule refl :args (@t64)) % 168.80/169.15 (step @p34 (= tptp.mexists_prop @t65) :rule refl :args (@t65)) % 168.80/169.15 (step @p35 (= tptp.mtrue @t67) :rule refl :args (@t67)) % 168.80/169.15 (step @p36 (= tptp.mbox @t77) :rule refl :args (@t77)) % 168.80/169.15 (step @p37 (= tptp.mdia @t79) :rule refl :args (@t79)) % 168.80/169.15 (step @p38 (= tptp.mreflexive @t84) :rule refl :args (@t84)) % 168.80/169.15 (step @p39 (= tptp.msymmetric @t88) :rule refl :args (@t88)) % 168.80/169.15 (step @p40 (= tptp.mserial @t90) :rule refl :args (@t90)) % 168.80/169.15 (step @p41 (= tptp.mtransitive @t95) :rule refl :args (@t95)) % 168.80/169.15 (step @p42 (= tptp.meuclidean @t97) :rule refl :args (@t97)) % 168.80/169.15 (step @p43 (= tptp.mpartially_functional @t99) :rule refl :args (@t99)) % 168.80/169.15 (step @p44 (= tptp.mfunctional @t101) :rule refl :args (@t101)) % 168.80/169.15 (step @p45 (= tptp.mweakly_dense @t104) :rule refl :args (@t104)) % 168.80/169.15 (step @p46 (= tptp.mweakly_connected @t105) :rule refl :args (@t105)) % 168.80/169.15 (step @p47 (= tptp.mweakly_directed @t106) :rule refl :args (@t106)) % 168.80/169.15 (step @p48 (= tptp.mvalid @t109) :rule refl :args (@t109)) % 168.80/169.15 (step @p49 (= tptp.minvalid @t110) :rule refl :args (@t110)) % 168.80/169.15 (step @p50 (= tptp.msatisfiable @t111) :rule refl :args (@t111)) % 168.80/169.15 (step @p51 (= tptp.mcountersatisfiable @t112) :rule refl :args (@t112)) % 168.80/169.15 ; WARNING: add trust step for TRUST % 168.80/169.15 ; trust TRUST PREPROCESS_HO_ELIM % 168.80/169.15 (step @p52 :rule trust :premises () :args ((= @t127 @t123))) % 168.80/169.15 (step @p53 :rule quant-merge-prenex :args ((= (forall @t66 @t128) @t127))) % 168.80/169.15 (step @p54 :rule beta-reduce :args ((= @t130 @t128))) % 168.80/169.15 (step @p55 :rule cong :premises (@p54) :args (@t131)) % 168.80/169.15 (step @p56 :rule trans :premises (@p55 @p53)) % 168.80/169.15 (step @p57 :rule beta-reduce :args ((= (_ @t133 @t129) @t131))) % 168.80/169.15 (step @p58 :rule trans :premises (@p57 @p56)) % 168.80/169.15 (step @p59 :rule refl :args (@t124)) % 168.80/169.15 (step @p60 :rule refl :args (@t134)) % 168.80/169.15 (step @p61 :rule cong :premises (@p60 @p59) :args ((= @t134 @t124))) % 168.80/169.15 (step @p62 :rule symm :premises (@p61)) % 168.80/169.15 (step @p63 :rule eq_resolve :premises (@p60 @p62)) % 168.80/169.15 (step @p64 :rule refl :args (@t125)) % 168.80/169.15 (step @p65 :rule nary_cong :premises (@p64 @p63) :args (@t135)) % 168.80/169.15 (step @p66 :rule cong :premises (@p65) :args ((forall @t74 @t135))) % 168.80/169.15 (step @p67 :rule refl :args (@t136)) % 168.80/169.15 (step @p68 :rule refl :args (@t125)) % 168.80/169.15 (step @p69 :rule nary_cong :premises (@p68 @p67) :args (@t137)) % 168.80/169.15 (step @p70 :rule cong :premises (@p69) :args (@t138)) % 168.80/169.15 (step @p71 :rule trans :premises (@p70 @p66)) % 168.80/169.15 (step @p72 :rule cong :premises (@p71) :args (@t139)) % 168.80/169.15 (step @p73 :rule beta-reduce :args ((= (_ @t141 @t2) @t139))) % 168.80/169.15 (step @p74 :rule trans :premises (@p73 @p72)) % 168.80/169.15 (step @p75 :rule refl :args (@t2)) % 168.80/169.15 (step @p76 :rule beta-reduce :args ((= (_ @t145 tptp.a3) @t141))) % 168.80/169.15 (step @p77 :rule ho_cong :premises (@p76 @p75)) % 168.80/169.15 (step @p78 :rule trans :premises (@p77 @p74)) % 168.80/169.15 (step @p79 :rule refl :args (@t133)) % 168.80/169.15 (step @p80 :rule ho_cong :premises (@p79 @p78)) % 168.80/169.15 (step @p81 :rule trans :premises (@p80 @p58)) % 168.80/169.15 (step @p82 :rule refl :args (tptp.a3)) % 168.80/169.15 (step @p83 :rule refl :args (@t140)) % 168.80/169.15 (step @p84 :rule refl :args (@t69)) % 168.80/169.15 (step @p85 :rule cong :premises (@p84 @p83) :args ((= @t69 @t140))) % 168.80/169.15 (step @p86 :rule symm :premises (@p85)) % 168.80/169.15 (step @p87 :rule eq_resolve :premises (@p84 @p86)) % 168.80/169.15 (step @p88 :rule refl :args (@t142)) % 168.80/169.15 (step @p89 :rule refl :args (@t71)) % 168.80/169.15 (step @p90 :rule cong :premises (@p89 @p88) :args ((= @t71 @t142))) % 168.80/169.15 (step @p91 :rule symm :premises (@p90)) % 168.80/169.15 (step @p92 :rule eq_resolve :premises (@p89 @p91)) % 168.80/169.15 (step @p93 :rule cong :premises (@p92) :args (@t72)) % 168.80/169.15 (step @p94 :rule nary_cong :premises (@p93 @p87) :args (@t73)) % 168.80/169.15 (step @p95 :rule cong :premises (@p94) :args (@t75)) % 168.80/169.15 (step @p96 :rule cong :premises (@p95) :args (@t77)) % 168.80/169.15 (step @p97 :rule trans :premises (@p36 @p96)) % 168.80/169.15 (step @p98 :rule ho_cong :premises (@p97 @p82)) % 168.80/169.15 (step @p99 :rule ho_cong :premises (@p98 @p75)) % 168.80/169.15 (step @p100 :rule refl :args (@t132)) % 168.80/169.15 (step @p101 :rule refl :args (@t35)) % 168.80/169.15 (step @p102 :rule cong :premises (@p101 @p100) :args ((= @t35 @t132))) % 168.80/169.15 (step @p103 :rule symm :premises (@p102)) % 168.80/169.15 (step @p104 :rule eq_resolve :premises (@p101 @p103)) % 168.80/169.15 (step @p105 :rule cong :premises (@p104) :args (@t107)) % 168.80/169.15 (step @p106 :rule cong :premises (@p105) :args (@t109)) % 168.80/169.15 (step @p107 :rule trans :premises (@p48 @p106)) % 168.80/169.15 (step @p108 :rule ho_cong :premises (@p107 @p99)) % 168.80/169.15 (step @p109 :rule trans :premises (@p108 @p81)) % 168.80/169.15 (step @p110 :rule trans :premises (@p109 @p52)) % 168.80/169.15 (step @p111 :rule eq_resolve :premises (@p11 @p110)) % 168.80/169.15 ; trust TRUST PREPROCESS_HO_ELIM % 168.80/169.15 (step @p112 :rule trust :premises () :args ((= @t155 (forall @t150 (or (_ @t117 (_ @t115 @t149 @t147) @t29) (not (_ @t117 @t120 @t146)) (not (_ @t117 (_ @t115 (_ @t114 @t113 @t7) @t147) @t146))))))) % 168.80/169.15 (step @p113 :rule quant-merge-prenex :args ((= (forall @t66 @t156) @t155))) % 168.80/169.15 (step @p114 :rule beta-reduce :args ((= @t158 @t156))) % 168.80/169.15 (step @p115 :rule cong :premises (@p114) :args (@t159)) % 168.80/169.15 (step @p116 :rule trans :premises (@p115 @p113)) % 168.80/169.15 (step @p117 :rule beta-reduce :args ((= (_ @t133 @t157) @t159))) % 168.80/169.15 (step @p118 :rule trans :premises (@p117 @p116)) % 168.80/169.15 (step @p119 :rule quant-merge-prenex :args ((= (forall @t54 @t161) @t156))) % 168.80/169.15 (step @p120 :rule beta-reduce :args ((= @t164 @t161))) % 168.80/169.15 (step @p121 :rule cong :premises (@p120) :args (@t165)) % 168.80/169.15 (step @p122 :rule trans :premises (@p121 @p119)) % 168.80/169.15 (step @p123 :rule cong :premises (@p122) :args (@t166)) % 168.80/169.15 (step @p124 :rule beta-reduce :args ((= (_ @t169 @t163) @t166))) % 168.80/169.15 (step @p125 :rule trans :premises (@p124 @p123)) % 168.80/169.15 (step @p126 :rule beta-reduce :args ((= (_ (lambda @t66 @t161) @t6) @t162))) % 168.80/169.15 (step @p127 :rule refl :args (@t6)) % 168.80/169.15 (step @p128 :rule aci_norm :args ((= @t171 @t154))) % 168.80/169.15 (step @p129 :rule cong :premises (@p128) :args (@t172)) % 168.80/169.15 (step @p130 :rule quant-merge-prenex :args ((= (forall @t175 @t174) @t172))) % 168.80/169.15 (step @p131 :rule refl :args (@t153)) % 168.80/169.15 (step @p132 :rule alpha_equiv :args (@t176 (@list @t146) (@list @t68))) % 168.80/169.15 (step @p133 :rule nary_cong :premises (@p132 @p131) :args (@t177)) % 168.80/169.15 (step @p134 :rule quant-miniscope-or :args ((= @t174 @t177))) % 168.80/169.15 (step @p135 :rule trans :premises (@p134 @p133)) % 168.80/169.15 (step @p136 :rule symm :premises (@p135)) % 168.80/169.15 (step @p137 :rule cong :premises (@p136) :args ((forall @t175 (or @t178 @t153)))) % 168.80/169.15 (step @p138 :rule trans :premises (@p137 @p130)) % 168.80/169.15 (step @p139 :rule trans :premises (@p138 @p129)) % 168.80/169.15 (step @p140 :rule refl :args (@t153)) % 168.80/169.15 (step @p141 :rule refl :args (@t179)) % 168.80/169.15 (step @p142 :rule cong :premises (@p141 @p140) :args ((= @t179 @t153))) % 168.80/169.15 (step @p143 :rule symm :premises (@p142)) % 168.80/169.15 (step @p144 :rule eq_resolve :premises (@p141 @p143)) % 168.80/169.15 (step @p145 :rule refl :args (@t178)) % 168.80/169.15 (step @p146 :rule nary_cong :premises (@p145 @p144) :args (@t180)) % 168.80/169.15 (step @p147 :rule cong :premises (@p146) :args ((forall @t175 @t180))) % 168.80/169.15 (step @p148 :rule trans :premises (@p147 @p139)) % 168.80/169.15 (step @p149 :rule beta-reduce :args ((= @t186 @t180))) % 168.80/169.15 (step @p150 :rule cong :premises (@p149) :args (@t187)) % 168.80/169.15 (step @p151 :rule trans :premises (@p150 @p148)) % 168.80/169.15 (step @p152 :rule cong :premises (@p151) :args (@t188)) % 168.80/169.15 (step @p153 :rule beta-reduce :args ((= (_ (lambda @t56 (forall @t175 (_ @t51 @t147 @t29))) @t185) @t188))) % 168.80/169.15 (step @p154 :rule trans :premises (@p153 @p152)) % 168.80/169.15 (step @p155 :rule refl :args (@t185)) % 168.80/169.15 (step @p156 :rule alpha_equiv :args (@t168 @t189 (@list @t147))) % 168.80/169.15 (step @p157 :rule cong :premises (@p156) :args (@t169)) % 168.80/169.15 (step @p158 :rule ho_cong :premises (@p157 @p155)) % 168.80/169.15 (step @p159 :rule trans :premises (@p158 @p154)) % 168.80/169.15 (step @p160 :rule beta-reduce :args ((= (_ @t191 @t6) @t184))) % 168.80/169.15 (step @p161 :rule beta-reduce :args ((= (_ (lambda @t193 (or @t183 @t192)) @t22) @t191))) % 168.80/169.15 (step @p162 :rule refl :args (@t22)) % 168.80/169.15 (step @p163 :rule refl :args (@t192)) % 168.80/169.15 (step @p164 :rule bool-double-not-elim :args (@t183)) % 168.80/169.15 (step @p165 :rule beta-reduce :args ((= @t196 @t194))) % 168.80/169.15 (step @p166 :rule cong :premises (@p165) :args (@t197)) % 168.80/169.15 (step @p167 :rule trans :premises (@p166 @p164)) % 168.80/169.15 (step @p168 :rule nary_cong :premises (@p167 @p163) :args (@t198)) % 168.80/169.15 (step @p169 :rule cong :premises (@p168) :args (@t199)) % 168.80/169.15 (step @p170 :rule beta-reduce :args ((= (_ @t201 @t195) @t199))) % 168.80/169.15 (step @p171 :rule trans :premises (@p170 @p169)) % 168.80/169.15 (step @p172 :rule refl :args (@t181)) % 168.80/169.15 (step @p173 :rule refl :args (@t202)) % 168.80/169.15 (step @p174 :rule cong :premises (@p173 @p172) :args ((= @t202 @t181))) % 168.80/169.15 (step @p175 :rule symm :premises (@p174)) % 168.80/169.15 (step @p176 :rule eq_resolve :premises (@p173 @p175)) % 168.80/169.15 (step @p177 :rule cong :premises (@p176) :args (@t203)) % 168.80/169.15 (step @p178 :rule refl :args (@t182)) % 168.80/169.15 (step @p179 :rule nary_cong :premises (@p178 @p177) :args (@t204)) % 168.80/169.15 (step @p180 :rule cong :premises (@p179) :args ((forall @t74 @t204))) % 168.80/169.15 (step @p181 :rule refl :args (@t205)) % 168.80/169.15 (step @p182 :rule cong :premises (@p181) :args (@t206)) % 168.80/169.15 (step @p183 :rule refl :args (@t182)) % 168.80/169.15 (step @p184 :rule nary_cong :premises (@p183 @p182) :args (@t207)) % 168.80/169.15 (step @p185 :rule cong :premises (@p184) :args (@t208)) % 168.80/169.15 (step @p186 :rule trans :premises (@p185 @p180)) % 168.80/169.15 (step @p187 :rule cong :premises (@p186) :args (@t209)) % 168.80/169.15 (step @p188 :rule cong :premises (@p187) :args (@t210)) % 168.80/169.15 (step @p189 :rule beta-reduce :args ((= (_ @t212 @t19) @t210))) % 168.80/169.15 (step @p190 :rule trans :premises (@p189 @p188)) % 168.80/169.15 (step @p191 :rule refl :args (@t19)) % 168.80/169.15 (step @p192 :rule beta-reduce :args ((= @t214 @t212))) % 168.80/169.15 (step @p193 :rule ho_cong :premises (@p192 @p191)) % 168.80/169.15 (step @p194 :rule trans :premises (@p193 @p190)) % 168.80/169.15 (step @p195 :rule refl :args (@t201)) % 168.80/169.15 (step @p196 :rule ho_cong :premises (@p195 @p194)) % 168.80/169.15 (step @p197 :rule trans :premises (@p196 @p171)) % 168.80/169.15 (step @p198 :rule ho_cong :premises (@p197 @p162)) % 168.80/169.15 (step @p199 :rule trans :premises (@p198 @p161)) % 168.80/169.15 (step @p200 :rule ho_cong :premises (@p199 @p127)) % 168.80/169.15 (step @p201 :rule trans :premises (@p200 @p160)) % 168.80/169.15 (step @p202 :rule cong :premises (@p201) :args (@t215)) % 168.80/169.15 (step @p203 :rule refl :args (@t169)) % 168.80/169.15 (step @p204 :rule ho_cong :premises (@p203 @p202)) % 168.80/169.15 (step @p205 :rule trans :premises (@p204 @p159)) % 168.80/169.15 (step @p206 :rule ho_cong :premises (@p205 @p127)) % 168.80/169.15 (step @p207 :rule trans :premises (@p206 @p126)) % 168.80/169.15 (step @p208 :rule cong :premises (@p207) :args ((lambda @t12 (_ (_ @t169 @t215) @t6)))) % 168.80/169.15 (step @p209 :rule ho_cong :premises (@p203 @p208)) % 168.80/169.15 (step @p210 :rule trans :premises (@p209 @p125)) % 168.80/169.15 (step @p211 :rule ho_cong :premises (@p79 @p210)) % 168.80/169.15 (step @p212 :rule trans :premises (@p211 @p118)) % 168.80/169.15 (step @p213 :rule beta-reduce :args ((= (_ (lambda @t66 (not @t216)) @t6) @t213))) % 168.80/169.15 (step @p214 :rule beta-reduce :args ((= @t218 @t216))) % 168.80/169.15 (step @p215 :rule cong :premises (@p214) :args (@t219)) % 168.80/169.15 (step @p216 :rule cong :premises (@p215) :args (@t220)) % 168.80/169.15 (step @p217 :rule beta-reduce :args ((= (_ @t38 @t217) @t220))) % 168.80/169.15 (step @p218 :rule trans :premises (@p217 @p216)) % 168.80/169.15 (step @p219 :rule cong :premises (@p87) :args (@t221)) % 168.80/169.15 (step @p220 :rule refl :args (@t143)) % 168.80/169.15 (step @p221 :rule nary_cong :premises (@p220 @p219) :args (@t222)) % 168.80/169.15 (step @p222 :rule cong :premises (@p221) :args ((forall @t74 @t222))) % 168.80/169.15 (step @p223 :rule beta-reduce :args ((= @t224 @t221))) % 168.80/169.15 (step @p224 :rule refl :args (@t143)) % 168.80/169.15 (step @p225 :rule nary_cong :premises (@p224 @p223) :args (@t225)) % 168.80/169.15 (step @p226 :rule cong :premises (@p225) :args (@t226)) % 168.80/169.15 (step @p227 :rule trans :premises (@p226 @p222)) % 168.80/169.15 (step @p228 :rule cong :premises (@p227) :args (@t227)) % 168.80/169.15 (step @p229 :rule beta-reduce :args ((= (_ @t228 @t223) @t227))) % 168.80/169.15 (step @p230 :rule trans :premises (@p229 @p228)) % 168.80/169.15 (step @p231 :rule beta-reduce :args ((= (_ @t38 @t34) @t223))) % 168.80/169.15 (step @p232 :rule beta-reduce :args ((= (_ @t145 @t70) @t228))) % 168.80/169.15 (step @p233 :rule ho_cong :premises (@p232 @p231)) % 168.80/169.15 (step @p234 :rule trans :premises (@p233 @p230)) % 168.80/169.15 (step @p235 :rule refl :args (@t38)) % 168.80/169.15 (step @p236 :rule ho_cong :premises (@p235 @p234)) % 168.80/169.15 (step @p237 :rule trans :premises (@p236 @p218)) % 168.80/169.15 (step @p238 :rule ho_cong :premises (@p237 @p127)) % 168.80/169.15 (step @p239 :rule trans :premises (@p238 @p213)) % 168.80/169.15 (step @p240 :rule refl :args (@t34)) % 168.80/169.15 (step @p241 :rule ho_cong :premises (@p24 @p240)) % 168.80/169.15 (step @p242 :rule refl :args (@t70)) % 168.80/169.15 (step @p243 :rule ho_cong :premises (@p97 @p242)) % 168.80/169.15 (step @p244 :rule ho_cong :premises (@p243 @p241)) % 168.80/169.15 (step @p245 :rule ho_cong :premises (@p24 @p244)) % 168.80/169.15 (step @p246 :rule ho_cong :premises (@p245 @p127)) % 168.80/169.15 (step @p247 :rule trans :premises (@p246 @p239)) % 168.80/169.15 (step @p248 :rule cong :premises (@p247) :args (@t79)) % 168.80/169.15 (step @p249 :rule trans :premises (@p37 @p248)) % 168.80/169.15 (step @p250 :rule ho_cong :premises (@p249 @p82)) % 168.80/169.15 (step @p251 :rule ho_cong :premises (@p250 @p191)) % 168.80/169.15 (step @p252 :rule beta-reduce :args ((= (_ @t230 @t6) @t200))) % 168.80/169.15 (step @p253 :rule beta-reduce :args ((= (_ (lambda @t231 @t229) @t39) @t230))) % 168.80/169.15 (step @p254 :rule refl :args (@t39)) % 168.80/169.15 (step @p255 :rule refl :args (@t40)) % 168.80/169.15 (step @p256 :rule beta-reduce :args ((= @t232 @t36))) % 168.80/169.15 (step @p257 :rule nary_cong :premises (@p256 @p255) :args (@t233)) % 168.80/169.15 (step @p258 :rule cong :premises (@p257) :args (@t234)) % 168.80/169.15 (step @p259 :rule beta-reduce :args ((= (_ @t41 @t223) @t234))) % 168.80/169.15 (step @p260 :rule trans :premises (@p259 @p258)) % 168.80/169.15 (step @p261 :rule refl :args (@t41)) % 168.80/169.15 (step @p262 :rule ho_cong :premises (@p261 @p231)) % 168.80/169.15 (step @p263 :rule trans :premises (@p262 @p260)) % 168.80/169.15 (step @p264 :rule ho_cong :premises (@p263 @p254)) % 168.80/169.15 (step @p265 :rule trans :premises (@p264 @p253)) % 168.80/169.15 (step @p266 :rule ho_cong :premises (@p265 @p127)) % 168.80/169.15 (step @p267 :rule trans :premises (@p266 @p252)) % 168.80/169.15 (step @p268 :rule ho_cong :premises (@p25 @p241)) % 168.80/169.15 (step @p269 :rule ho_cong :premises (@p268 @p254)) % 168.80/169.15 (step @p270 :rule ho_cong :premises (@p269 @p127)) % 168.80/169.15 (step @p271 :rule trans :premises (@p270 @p267)) % 168.80/169.15 (step @p272 :rule cong :premises (@p271) :args (@t47)) % 168.80/169.15 (step @p273 :rule trans :premises (@p27 @p272)) % 168.80/169.15 (step @p274 :rule ho_cong :premises (@p273 @p251)) % 168.80/169.15 (step @p275 :rule ho_cong :premises (@p274 @p162)) % 168.80/169.15 (step @p276 :rule ho_cong :premises (@p275 @p127)) % 168.80/169.15 (step @p277 :rule cong :premises (@p276) :args (@t23)) % 168.80/169.15 (step @p278 :rule refl :args (@t167)) % 168.80/169.15 (step @p279 :rule refl :args (@t53)) % 168.80/169.15 (step @p280 :rule cong :premises (@p279 @p278) :args ((= @t53 @t167))) % 168.80/169.15 (step @p281 :rule symm :premises (@p280)) % 168.80/169.15 (step @p282 :rule eq_resolve :premises (@p279 @p281)) % 168.80/169.15 (step @p283 :rule cong :premises (@p282) :args (@t55)) % 168.80/169.15 (step @p284 :rule cong :premises (@p283) :args (@t57)) % 168.80/169.15 (step @p285 :rule trans :premises (@p31 @p284)) % 168.80/169.15 (step @p286 :rule ho_cong :premises (@p285 @p277)) % 168.80/169.15 (step @p287 :rule ho_cong :premises (@p286 @p127)) % 168.80/169.15 (step @p288 :rule cong :premises (@p287) :args (@t24)) % 168.80/169.15 (step @p289 :rule ho_cong :premises (@p285 @p288)) % 168.80/169.15 (step @p290 :rule ho_cong :premises (@p107 @p289)) % 168.80/169.15 (step @p291 :rule trans :premises (@p290 @p212)) % 168.80/169.15 (step @p292 :rule trans :premises (@p291 @p112)) % 168.80/169.15 (step @p293 :rule eq_resolve :premises (@p19 @p292)) % 168.80/169.15 (step @p294 :rule instantiate :premises (@p293) :args ((@list @t241 tptp.jan tptp.cola @t243))) % 168.80/169.15 ; trust TRUST PREPROCESS_HO_ELIM % 168.80/169.15 (step @p295 :rule trust :premises () :args ((= (forall @t66 @t246) (forall @t66 (not (forall @t74 (or @t121 @t236))))))) % 168.80/169.15 (step @p296 :rule beta-reduce :args ((= @t248 @t246))) % 168.80/169.15 (step @p297 :rule cong :premises (@p296) :args (@t249)) % 168.80/169.15 (step @p298 :rule beta-reduce :args ((= (_ @t133 @t247) @t249))) % 168.80/169.15 (step @p299 :rule trans :premises (@p298 @p297)) % 168.80/169.15 (step @p300 :rule refl :args (@t244)) % 168.80/169.15 (step @p301 :rule refl :args (@t250)) % 168.80/169.15 (step @p302 :rule cong :premises (@p301 @p300) :args ((= @t250 @t244))) % 168.80/169.15 (step @p303 :rule symm :premises (@p302)) % 168.80/169.15 (step @p304 :rule eq_resolve :premises (@p301 @p303)) % 168.80/169.15 (step @p305 :rule cong :premises (@p304) :args (@t251)) % 168.80/169.15 (step @p306 :rule nary_cong :premises (@p178 @p305) :args (@t252)) % 168.80/169.15 (step @p307 :rule cong :premises (@p306) :args ((forall @t74 @t252))) % 168.80/169.15 (step @p308 :rule refl :args (@t253)) % 168.80/169.15 (step @p309 :rule cong :premises (@p308) :args (@t254)) % 168.80/169.15 (step @p310 :rule nary_cong :premises (@p183 @p309) :args (@t255)) % 168.80/169.15 (step @p311 :rule cong :premises (@p310) :args (@t256)) % 168.80/169.15 (step @p312 :rule trans :premises (@p311 @p307)) % 168.80/169.15 (step @p313 :rule cong :premises (@p312) :args (@t257)) % 168.80/169.15 (step @p314 :rule cong :premises (@p313) :args (@t258)) % 168.80/169.15 (step @p315 :rule beta-reduce :args ((= (_ @t212 @t5) @t258))) % 168.80/169.15 (step @p316 :rule trans :premises (@p315 @p314)) % 168.80/169.15 (step @p317 :rule refl :args (@t5)) % 168.80/169.15 (step @p318 :rule ho_cong :premises (@p192 @p317)) % 168.80/169.15 (step @p319 :rule trans :premises (@p318 @p316)) % 168.80/169.15 (step @p320 :rule ho_cong :premises (@p79 @p319)) % 168.80/169.15 (step @p321 :rule trans :premises (@p320 @p299)) % 168.80/169.15 (step @p322 :rule ho_cong :premises (@p250 @p317)) % 168.80/169.15 (step @p323 :rule ho_cong :premises (@p107 @p322)) % 168.80/169.15 (step @p324 :rule trans :premises (@p323 @p321)) % 168.80/169.15 (step @p325 :rule trans :premises (@p324 @p295)) % 168.80/169.15 (step @p326 :rule eq_resolve :premises (@p12 @p325)) % 168.80/169.15 (step @p327 :rule instantiate :premises (@p326) :args ((@list @t241))) % 168.80/169.15 (step @p328 :rule skolemize :premises (@p327)) % 168.80/169.15 (step @p329 :rule bool-double-not-elim :args (@t259)) % 168.80/169.15 (step @p330 :rule refl :args (@t261)) % 168.80/169.15 (step @p331 :rule nary_cong :premises (@p330 @p329) :args ((or @t261 (not @t260)))) % 168.80/169.15 (step @p332 :rule cnf_or_neg :args (@t261 0)) % 168.80/169.15 (step @p333 :rule eq_resolve :premises (@p332 @p331)) % 168.80/169.15 (step @p334 :rule reordering :premises (@p333) :args ((or @t259 @t261))) % 168.80/169.15 (step @p335 :rule chain_m_resolution :premises (@p334 @p328) :args (@t259 @t262 (@list @t261))) % 168.80/169.15 ; trust TRUST PREPROCESS_HO_ELIM % 168.80/169.15 (step @p336 :rule trust :premises () :args ((= (not (forall @t66 @t264)) @t263))) % 168.80/169.15 (step @p337 :rule beta-reduce :args ((= @t269 @t264))) % 168.80/169.15 (step @p338 :rule cong :premises (@p337) :args (@t270)) % 168.80/169.15 (step @p339 :rule beta-reduce :args ((= (_ @t133 @t268) @t270))) % 168.80/169.15 (step @p340 :rule trans :premises (@p339 @p338)) % 168.80/169.15 (step @p341 :rule quant-merge-prenex :args ((= (forall @t54 @t272) @t267))) % 168.80/169.15 (step @p342 :rule bool-double-not-elim :args (@t272)) % 168.80/169.15 (step @p343 :rule beta-reduce :args ((= @t275 @t273))) % 168.80/169.15 (step @p344 :rule cong :premises (@p343) :args (@t276)) % 168.80/169.15 (step @p345 :rule trans :premises (@p344 @p342)) % 168.80/169.15 (step @p346 :rule cong :premises (@p345) :args (@t277)) % 168.80/169.15 (step @p347 :rule trans :premises (@p346 @p341)) % 168.80/169.15 (step @p348 :rule cong :premises (@p347) :args (@t278)) % 168.80/169.15 (step @p349 :rule cong :premises (@p348) :args (@t279)) % 168.80/169.15 (step @p350 :rule beta-reduce :args ((= (_ @t282 @t274) @t279))) % 168.80/169.15 (step @p351 :rule trans :premises (@p350 @p349)) % 168.80/169.15 (step @p352 :rule beta-reduce :args ((= (_ (lambda @t190 @t273) @t6) @t273))) % 168.80/169.15 (step @p353 :rule refl :args (@t265)) % 168.80/169.15 (step @p354 :rule refl :args (@t283)) % 168.80/169.15 (step @p355 :rule cong :premises (@p354 @p353) :args ((= @t283 @t265))) % 168.80/169.15 (step @p356 :rule symm :premises (@p355)) % 168.80/169.15 (step @p357 :rule eq_resolve :premises (@p354 @p356)) % 168.80/169.15 (step @p358 :rule cong :premises (@p357) :args (@t284)) % 168.80/169.15 (step @p359 :rule cong :premises (@p358) :args ((forall @t271 @t284))) % 168.80/169.15 (step @p360 :rule beta-reduce :args ((= @t285 @t283))) % 168.80/169.15 (step @p361 :rule cong :premises (@p360) :args (@t286)) % 168.80/169.15 (step @p362 :rule cong :premises (@p361) :args (@t287)) % 168.80/169.15 (step @p363 :rule trans :premises (@p362 @p359)) % 168.80/169.15 (step @p364 :rule cong :premises (@p363) :args (@t288)) % 168.80/169.15 (step @p365 :rule cong :premises (@p364) :args (@t289)) % 168.80/169.15 (step @p366 :rule beta-reduce :args ((= (_ (lambda @t63 (not (forall @t271 (not (_ @t51 @t237 @t6))))) @t26) @t289))) % 168.80/169.15 (step @p367 :rule trans :premises (@p366 @p365)) % 168.80/169.15 (step @p368 :rule refl :args (@t26)) % 168.80/169.15 (step @p369 :rule alpha_equiv :args (@t280 @t189 (@list @t237))) % 168.80/169.15 (step @p370 :rule cong :premises (@p369) :args (@t281)) % 168.80/169.15 (step @p371 :rule cong :premises (@p370) :args (@t282)) % 168.80/169.15 (step @p372 :rule ho_cong :premises (@p371 @p368)) % 168.80/169.15 (step @p373 :rule trans :premises (@p372 @p367)) % 168.80/169.15 (step @p374 :rule ho_cong :premises (@p373 @p127)) % 168.80/169.15 (step @p375 :rule trans :premises (@p374 @p352)) % 168.80/169.15 (step @p376 :rule cong :premises (@p375) :args (@t290)) % 168.80/169.15 (step @p377 :rule refl :args (@t282)) % 168.80/169.15 (step @p378 :rule ho_cong :premises (@p377 @p376)) % 168.80/169.15 (step @p379 :rule trans :premises (@p378 @p351)) % 168.80/169.15 (step @p380 :rule ho_cong :premises (@p79 @p379)) % 168.80/169.15 (step @p381 :rule trans :premises (@p380 @p340)) % 168.80/169.15 (step @p382 :rule cong :premises (@p381) :args ((not (_ @t133 (_ @t282 @t290))))) % 168.80/169.15 (step @p383 :rule refl :args (@t26)) % 168.80/169.15 (step @p384 :rule beta-reduce :args ((= (_ (lambda @t66 (not @t291)) @t6) @t281))) % 168.80/169.15 (step @p385 :rule beta-reduce :args ((= @t293 @t291))) % 168.80/169.15 (step @p386 :rule cong :premises (@p385) :args (@t294)) % 168.80/169.15 (step @p387 :rule cong :premises (@p386) :args (@t295)) % 168.80/169.15 (step @p388 :rule beta-reduce :args ((= (_ @t38 @t292) @t295))) % 168.80/169.15 (step @p389 :rule trans :premises (@p388 @p387)) % 168.80/169.15 (step @p390 :rule cong :premises (@p282) :args (@t296)) % 168.80/169.15 (step @p391 :rule cong :premises (@p390) :args ((forall @t54 @t296))) % 168.80/169.15 (step @p392 :rule beta-reduce :args ((= @t299 @t296))) % 168.80/169.15 (step @p393 :rule cong :premises (@p392) :args (@t300)) % 168.80/169.15 (step @p394 :rule trans :premises (@p393 @p391)) % 168.80/169.15 (step @p395 :rule cong :premises (@p394) :args (@t301)) % 168.80/169.15 (step @p396 :rule beta-reduce :args ((= (_ @t169 @t298) @t301))) % 168.80/169.15 (step @p397 :rule trans :premises (@p396 @p395)) % 168.80/169.15 (step @p398 :rule beta-reduce :args ((= (_ @t302 @t6) @t297))) % 168.80/169.15 (step @p399 :rule beta-reduce :args ((= @t303 @t302))) % 168.80/169.15 (step @p400 :rule ho_cong :premises (@p399 @p127)) % 168.80/169.15 (step @p401 :rule trans :premises (@p400 @p398)) % 168.80/169.15 (step @p402 :rule cong :premises (@p401) :args ((lambda @t12 (_ @t303 @t6)))) % 168.80/169.15 (step @p403 :rule ho_cong :premises (@p203 @p402)) % 168.80/169.15 (step @p404 :rule trans :premises (@p403 @p397)) % 168.80/169.15 (step @p405 :rule ho_cong :premises (@p235 @p404)) % 168.80/169.15 (step @p406 :rule trans :premises (@p405 @p389)) % 168.80/169.15 (step @p407 :rule ho_cong :premises (@p406 @p127)) % 168.80/169.15 (step @p408 :rule trans :premises (@p407 @p384)) % 168.80/169.15 (step @p409 :rule refl :args (@t52)) % 168.80/169.15 (step @p410 :rule ho_cong :premises (@p24 @p409)) % 168.80/169.15 (step @p411 :rule ho_cong :premises (@p410 @p127)) % 168.80/169.15 (step @p412 :rule cong :premises (@p411) :args (@t62)) % 168.80/169.15 (step @p413 :rule ho_cong :premises (@p285 @p412)) % 168.80/169.15 (step @p414 :rule ho_cong :premises (@p24 @p413)) % 168.80/169.15 (step @p415 :rule ho_cong :premises (@p414 @p127)) % 168.80/169.15 (step @p416 :rule trans :premises (@p415 @p408)) % 168.80/169.15 (step @p417 :rule cong :premises (@p416) :args (@t64)) % 168.80/169.15 (step @p418 :rule trans :premises (@p33 @p417)) % 168.80/169.15 (step @p419 :rule ho_cong :premises (@p418 @p383)) % 168.80/169.15 (step @p420 :rule ho_cong :premises (@p419 @p127)) % 168.80/169.15 (step @p421 :rule cong :premises (@p420) :args (@t27)) % 168.80/169.15 (step @p422 :rule ho_cong :premises (@p418 @p421)) % 168.80/169.15 (step @p423 :rule ho_cong :premises (@p107 @p422)) % 168.80/169.15 (step @p424 :rule cong :premises (@p423) :args (@t28)) % 168.80/169.15 (step @p425 :rule trans :premises (@p424 @p382)) % 168.80/169.15 (step @p426 :rule trans :premises (@p425 @p336)) % 168.80/169.15 (step @p427 :rule eq_resolve :premises (@p20 @p426)) % 168.80/169.15 (step @p428 :rule refl :args (@t304)) % 168.80/169.15 (step @p429 :rule bool-double-not-elim :args (@t240)) % 168.80/169.15 (step @p430 :rule nary_cong :premises (@p429 @p428) :args ((or (not @t263) @t304))) % 168.80/169.15 (step @p431 :rule bool-double-not-elim :args (@t304)) % 168.80/169.15 (step @p432 :rule refl :args (@t263)) % 168.80/169.15 (step @p433 :rule cong :premises (@p432 @p431) :args ((=> @t263 @t305))) % 168.80/169.15 (assume-push @p455 @t263) % 168.80/169.15 (step @p435 :rule skolemize :premises (@p427)) % 168.80/169.15 (step-pop @p456 :rule scope :premises (@p435)) % 168.80/169.15 (step @p436 :rule process_scope :premises (@p456) :args (@t305)) % 168.80/169.15 (step @p438 :rule eq_resolve :premises (@p436 @p433)) % 168.80/169.15 (step @p439 :rule implies_elim :premises (@p438)) % 168.80/169.15 (step @p440 :rule eq_resolve :premises (@p439 @p430)) % 168.80/169.15 (step @p441 :rule chain_m_resolution :premises (@p440 @p427) :args (@t304 @t262 (@list @t240))) % 168.80/169.15 (step @p442 :rule instantiate :premises (@p441) :args ((@list tptp.jan tptp.cola))) % 168.80/169.15 (step @p443 :rule cnf_or_pos :args (@t309)) % 168.80/169.15 (step @p444 :rule reordering :premises (@p443) :args ((or @t308 @t260 @t307 (not @t309)))) % 168.80/169.15 (step @p445 :rule chain_m_resolution :premises (@p444 @p442 @p335 @p294) :args (@t307 (@list true false false) (@list @t308 @t259 @t309))) % 168.80/169.15 (step @p446 :rule cnf_or_pos :args (@t310)) % 168.80/169.15 (step @p447 :rule reordering :premises (@p446) :args ((or @t260 @t306 @t311))) % 168.80/169.15 (step @p448 :rule chain_m_resolution :premises (@p447 @p335 @p445) :args (@t311 (@list false true) (@list @t259 @t306))) % 168.80/169.15 (assume-push @p457 @t123) % 168.80/169.15 (step @p450 :rule instantiate :premises (@p111) :args ((@list @t241 @t243))) % 168.80/169.15 (step-pop @p458 :rule scope :premises (@p450)) % 168.80/169.15 (step @p451 :rule process_scope :premises (@p458) :args (@t310)) % 168.80/169.15 (step @p453 :rule implies_elim :premises (@p451)) % 168.80/169.15 (step @p454 false :rule chain_m_resolution :premises (@p453 @p448 @p111) :args (false (@list true false) (@list @t310 @t123))) % 168.80/169.15 ) % 168.80/169.15 % SZS output end Proof % 168.80/169.15 % cvc5 exiting %------------------------------------------------------------------------------