%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : ITP019^2 : TPTP v9.2.1. Bugfixed v7.5.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n009.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 08:24:42 AM UTC 2026 % Result : Theorem 0.34s 0.58s % Output : Proof 0.34s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.13 % Problem : ITP019^2 : TPTP v9.2.1. Bugfixed v7.5.0. % 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.35 % Computer : n009.cluster.edu % 0.16/0.35 % Model : x86_64 x86_64 % 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.35 % Memory : 8042.1875MB % 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.35 % CPULimit : 300 % 0.16/0.35 % WCLimit : 300 % 0.16/0.35 % DateTime : Tue Jun 2 03:59:29 EDT 2026 % 0.16/0.35 % CPUTime : % 0.27/0.49 %----Proving TH0 % 0.34/0.58 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.34/0.58 % SZS status Theorem % 0.34/0.58 % SZS output start Proof % 0.34/0.58 ( % 0.34/0.58 (declare-sort tptp.del 0) % 0.34/0.58 (declare-sort $$unsorted 0) % 0.34/0.58 (declare-sort tptp.tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal 0) % 0.34/0.58 (declare-sort tptp.tp__ty_2Erealax_2Ereal 0) % 0.34/0.58 (declare-sort tptp.tp__ty_2Enum_2Enum 0) % 0.34/0.58 (declare-const tptp.c_2Ecomplex_2Ecomplex__inv $$unsorted) % 0.34/0.58 (declare-const tptp.c_2Ecomplex_2Ecomplex__of__num $$unsorted) % 0.34/0.58 (declare-const tptp.c_2Ebool_2E_21 (-> tptp.del $$unsorted)) % 0.34/0.58 (declare-const tptp.inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (-> tptp.tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal $$unsorted)) % 0.34/0.58 (declare-const tptp.inj__ty_2Erealax_2Ereal (-> tptp.tp__ty_2Erealax_2Ereal $$unsorted)) % 0.34/0.58 (declare-const tptp.c_2Enum_2E0 $$unsorted) % 0.34/0.58 (declare-const tptp.ty_2Enum_2Enum tptp.del) % 0.34/0.58 (declare-const tptp.ty_2Epair_2Eprod (-> tptp.del tptp.del tptp.del)) % 0.34/0.58 (declare-const tptp.inj__o (-> Bool $$unsorted)) % 0.34/0.58 (declare-const tptp.surj__ty_2Erealax_2Ereal (-> $$unsorted tptp.tp__ty_2Erealax_2Ereal)) % 0.34/0.58 (declare-const tptp.inj__ty_2Enum_2Enum (-> tptp.tp__ty_2Enum_2Enum $$unsorted)) % 0.34/0.58 (declare-const tptp.p (-> $$unsorted Bool)) % 0.34/0.58 (declare-const tptp.c_2Ebool_2ET $$unsorted) % 0.34/0.58 (declare-const tptp.surj__ty_2Enum_2Enum (-> $$unsorted tptp.tp__ty_2Enum_2Enum)) % 0.34/0.58 (declare-const tptp.bool tptp.del) % 0.34/0.58 (declare-const tptp.mem (-> $$unsorted tptp.del Bool)) % 0.34/0.58 (declare-const tptp.ap (-> $$unsorted $$unsorted $$unsorted)) % 0.34/0.58 (declare-const tptp.arr (-> tptp.del tptp.del tptp.del)) % 0.34/0.58 (declare-const tptp.ty_2Erealax_2Ereal tptp.del) % 0.34/0.58 (declare-const tptp.c_2Ebool_2E_7E $$unsorted) % 0.34/0.58 (declare-const tptp.c_2Emin_2E_3D (-> tptp.del $$unsorted)) % 0.34/0.58 (declare-const tptp.surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (-> $$unsorted tptp.tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal)) % 0.34/0.58 (declare-const tptp.fo__c_2Enum_2E0 tptp.tp__ty_2Enum_2Enum) % 0.34/0.58 (declare-const tptp.c_2Emin_2E_3D_3D_3E $$unsorted) % 0.34/0.58 (declare-const tptp.c_2Ebool_2EF $$unsorted) % 0.34/0.58 (declare-const tptp.lam (-> tptp.del (-> $$unsorted $$unsorted) $$unsorted)) % 0.34/0.58 (declare-const tptp.c_2Ebool_2E_2F_5C $$unsorted) % 0.34/0.58 (define @t1 () (@var "X" Bool)) % 0.34/0.58 (define @t2 () (_ tptp.inj__o @t1)) % 0.34/0.58 (define @t3 () (@list @t1)) % 0.34/0.58 (define @t4 () (@var "X" $$unsorted)) % 0.34/0.58 (define @t5 () (_ tptp.mem @t4)) % 0.34/0.58 (define @t6 () (@list @t4)) % 0.34/0.58 (define @t7 () (@var "B" tptp.del)) % 0.34/0.58 (define @t8 () (@var "F" $$unsorted)) % 0.34/0.58 (define @t9 () (_ (_ tptp.ap @t8) @t4)) % 0.34/0.58 (define @t10 () (@var "A" tptp.del)) % 0.34/0.58 (define @t11 () (_ @t5 @t10)) % 0.34/0.58 (define @t12 () (_ tptp.arr @t10)) % 0.34/0.58 (define @t13 () (_ @t12 @t7)) % 0.34/0.58 (define @t14 () (_ (_ tptp.mem @t8) @t13)) % 0.34/0.58 (define @t15 () (@list @t10 @t7 @t8)) % 0.34/0.58 (define @t16 () (@var "F" (-> $$unsorted $$unsorted))) % 0.34/0.58 (define @t17 () (_ (_ tptp.lam @t10) @t16)) % 0.34/0.58 (define @t18 () (_ @t16 @t4)) % 0.34/0.58 (define @t19 () (@var "G" $$unsorted)) % 0.34/0.58 (define @t20 () (_ tptp.arr tptp.bool)) % 0.34/0.58 (define @t21 () (_ @t20 tptp.bool)) % 0.34/0.58 (define @t22 () (@var "Q" $$unsorted)) % 0.34/0.58 (define @t23 () (_ tptp.p @t22)) % 0.34/0.58 (define @t24 () (_ tptp.mem @t22)) % 0.34/0.58 (define @t25 () (_ @t24 tptp.bool)) % 0.34/0.58 (define @t26 () (@list @t22)) % 0.34/0.58 (define @t27 () (_ @t20 @t21)) % 0.34/0.58 (define @t28 () (@var "R" $$unsorted)) % 0.34/0.58 (define @t29 () (_ tptp.p @t28)) % 0.34/0.58 (define @t30 () (_ (_ tptp.mem @t28) tptp.bool)) % 0.34/0.58 (define @t31 () (@list @t28)) % 0.34/0.58 (define @t32 () (@var "X" tptp.tp__ty_2Enum_2Enum)) % 0.34/0.58 (define @t33 () (_ tptp.inj__ty_2Enum_2Enum @t32)) % 0.34/0.58 (define @t34 () (@list @t32)) % 0.34/0.58 (define @t35 () (_ tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0)) % 0.34/0.58 (define @t36 () (@var "X" tptp.tp__ty_2Erealax_2Ereal)) % 0.34/0.58 (define @t37 () (_ tptp.inj__ty_2Erealax_2Ereal @t36)) % 0.34/0.58 (define @t38 () (@list @t36)) % 0.34/0.58 (define @t39 () (@var "X" tptp.tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal)) % 0.34/0.58 (define @t40 () (_ tptp.inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @t39)) % 0.34/0.58 (define @t41 () (@list @t39)) % 0.34/0.58 (define @t42 () (_ (_ tptp.ty_2Epair_2Eprod tptp.ty_2Erealax_2Ereal) tptp.ty_2Erealax_2Ereal)) % 0.34/0.58 (define @t43 () (@var "A_27a" tptp.del)) % 0.34/0.58 (define @t44 () (_ tptp.arr @t43)) % 0.34/0.58 (define @t45 () (_ @t44 tptp.bool)) % 0.34/0.58 (define @t46 () (@list @t43)) % 0.34/0.58 (define @t47 () (@var "Y" $$unsorted)) % 0.34/0.58 (define @t48 () (@var "V0t" $$unsorted)) % 0.34/0.58 (define @t49 () (_ tptp.p @t48)) % 0.34/0.58 (define @t50 () (@var "V1x" $$unsorted)) % 0.34/0.58 (define @t51 () (_ (_ tptp.mem @t48) tptp.bool)) % 0.34/0.58 (define @t52 () (_ tptp.ap tptp.c_2Ecomplex_2Ecomplex__of__num)) % 0.34/0.58 (define @t53 () (_ @t52 @t35)) % 0.34/0.58 (define @t54 () (_ tptp.surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @t53)) % 0.34/0.58 (define @t55 () (@var "V0z" tptp.tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal)) % 0.34/0.58 (define @t56 () (= @t55 @t54)) % 0.34/0.58 (define @t57 () (_ tptp.inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @t55)) % 0.34/0.58 (define @t58 () (_ tptp.ap tptp.c_2Ecomplex_2Ecomplex__inv)) % 0.34/0.58 (define @t59 () (_ @t58 @t57)) % 0.34/0.58 (define @t60 () (_ tptp.surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @t59)) % 0.34/0.58 (define @t61 () (= @t60 @t54)) % 0.34/0.58 (define @t62 () (= @t61 @t56)) % 0.34/0.58 (define @t63 () (@list @t55)) % 0.34/0.58 (define @t64 () (forall @t63 @t62)) % 0.34/0.58 (define @t65 () (not @t61)) % 0.34/0.58 (define @t66 () (not @t56)) % 0.34/0.58 (define @t67 () (=> @t66 @t65)) % 0.34/0.58 (define @t68 () (forall @t63 @t67)) % 0.34/0.58 (define @t69 () (not @t68)) % 0.34/0.58 (define @t70 () (tptp.inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @t55)) % 0.34/0.58 (define @t71 () (tptp.ap tptp.c_2Ecomplex_2Ecomplex__inv @t70)) % 0.34/0.58 (define @t72 () (tptp.surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @t71)) % 0.34/0.58 (define @t73 () (tptp.inj__ty_2Enum_2Enum tptp.fo__c_2Enum_2E0)) % 0.34/0.58 (define @t74 () (tptp.ap tptp.c_2Ecomplex_2Ecomplex__of__num @t73)) % 0.34/0.58 (define @t75 () (tptp.surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @t74)) % 0.34/0.58 (define @t76 () (= @t54 @t60)) % 0.34/0.58 (define @t77 () (= @t56 @t76)) % 0.34/0.58 (define @t78 () (not @t76)) % 0.34/0.58 (define @t79 () (or @t56 @t78)) % 0.34/0.58 (define @t80 () (= @t75 @t72)) % 0.34/0.58 (define @t81 () (= @t55 @t75)) % 0.34/0.58 (define @t82 () (forall @t63 (or @t81 (not @t80)))) % 0.34/0.58 (define @t83 () (@quantifiers_skolemize @t82 0)) % 0.34/0.58 (define @t84 () (= @t75 (tptp.surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (tptp.ap tptp.c_2Ecomplex_2Ecomplex__inv (tptp.inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @t83))))) % 0.34/0.58 (define @t85 () (not @t84)) % 0.34/0.58 (define @t86 () (= @t75 @t83)) % 0.34/0.58 (define @t87 () (or @t86 @t85)) % 0.34/0.58 (define @t88 () (not @t87)) % 0.34/0.58 (define @t89 () (not @t82)) % 0.34/0.58 (define @t90 () (= @t83 @t75)) % 0.34/0.58 (define @t91 () (or @t90 @t85)) % 0.34/0.58 (define @t92 () (not @t91)) % 0.34/0.58 (define @t93 () (@list true)) % 0.34/0.58 (define @t94 () (@list @t87)) % 0.34/0.58 (define @t95 () (= @t84 @t86)) % 0.34/0.58 (define @t96 () (not @t95)) % 0.34/0.58 (define @t97 () (= @t90 @t84)) % 0.34/0.58 (define @t98 () (forall @t63 (= @t81 @t80))) % 0.34/0.58 (assume @p1 (forall @t3 (= (_ tptp.p @t2) @t1))) % 0.34/0.58 (assume @p2 (forall @t3 (_ (_ tptp.mem @t2) tptp.bool))) % 0.34/0.58 (assume @p3 (forall @t6 (=> (_ @t5 tptp.bool) (= @t4 (_ tptp.inj__o (_ tptp.p @t4)))))) % 0.34/0.58 (assume @p4 (forall @t15 (=> @t14 (forall @t6 (=> @t11 (_ (_ tptp.mem @t9) @t7)))))) % 0.34/0.58 (assume @p5 (forall (@list @t10 @t7 @t16) (=> (forall @t6 (=> @t11 (_ (_ tptp.mem @t18) @t7))) (_ (_ tptp.mem @t17) @t13)))) % 0.34/0.58 (assume @p6 (forall @t15 (=> @t14 (forall (@list @t19) (=> (_ (_ tptp.mem @t19) @t13) (=> (forall @t6 (=> @t11 (= @t9 (_ (_ tptp.ap @t19) @t4)))) (= @t8 @t19))))))) % 0.34/0.58 (assume @p7 (forall (@list @t10 @t16 @t4) (=> @t11 (= (_ (_ tptp.ap @t17) @t4) @t18)))) % 0.34/0.58 (assume @p8 (_ (_ tptp.mem tptp.c_2Ebool_2E_7E) @t21)) % 0.34/0.58 (assume @p9 (forall @t26 (=> @t25 (= (_ tptp.p (_ (_ tptp.ap tptp.c_2Ebool_2E_7E) @t22)) (not @t23))))) % 0.34/0.58 (assume @p10 (_ (_ tptp.mem tptp.c_2Ebool_2EF) tptp.bool)) % 0.34/0.58 (assume @p11 (not (_ tptp.p tptp.c_2Ebool_2EF))) % 0.34/0.58 (assume @p12 (_ (_ tptp.mem tptp.c_2Ebool_2ET) tptp.bool)) % 0.34/0.58 (assume @p13 (_ tptp.p tptp.c_2Ebool_2ET)) % 0.34/0.58 (assume @p14 (_ (_ tptp.mem tptp.c_2Emin_2E_3D_3D_3E) @t27)) % 0.34/0.58 (assume @p15 (forall @t26 (=> @t25 (forall @t31 (=> @t30 (= (_ tptp.p (_ (_ tptp.ap (_ (_ tptp.ap tptp.c_2Emin_2E_3D_3D_3E) @t22)) @t28)) (=> @t23 @t29))))))) % 0.34/0.58 (assume @p16 (_ (_ tptp.mem tptp.c_2Ebool_2E_2F_5C) @t27)) % 0.34/0.58 (assume @p17 (forall @t26 (=> @t25 (forall @t31 (=> @t30 (= (_ tptp.p (_ (_ tptp.ap (_ (_ tptp.ap tptp.c_2Ebool_2E_2F_5C) @t22)) @t28)) (and @t23 @t29))))))) % 0.34/0.58 (assume @p18 (forall @t34 (= (_ tptp.surj__ty_2Enum_2Enum @t33) @t32))) % 0.34/0.58 (assume @p19 (forall @t34 (_ (_ tptp.mem @t33) tptp.ty_2Enum_2Enum))) % 0.34/0.58 (assume @p20 (forall @t6 (=> (_ @t5 tptp.ty_2Enum_2Enum) (= @t4 (_ tptp.inj__ty_2Enum_2Enum (_ tptp.surj__ty_2Enum_2Enum @t4)))))) % 0.34/0.58 (assume @p21 (_ (_ tptp.mem tptp.c_2Enum_2E0) tptp.ty_2Enum_2Enum)) % 0.34/0.58 (assume @p22 (= @t35 tptp.c_2Enum_2E0)) % 0.34/0.58 (assume @p23 (forall @t38 (= (_ tptp.surj__ty_2Erealax_2Ereal @t37) @t36))) % 0.34/0.58 (assume @p24 (forall @t38 (_ (_ tptp.mem @t37) tptp.ty_2Erealax_2Ereal))) % 0.34/0.58 (assume @p25 (forall @t6 (=> (_ @t5 tptp.ty_2Erealax_2Ereal) (= @t4 (_ tptp.inj__ty_2Erealax_2Ereal (_ tptp.surj__ty_2Erealax_2Ereal @t4)))))) % 0.34/0.58 (assume @p26 (forall @t41 (= (_ tptp.surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @t40) @t39))) % 0.34/0.58 (assume @p27 (forall @t41 (_ (_ tptp.mem @t40) @t42))) % 0.34/0.58 (assume @p28 (forall @t6 (=> (_ @t5 @t42) (= @t4 (_ tptp.inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal (_ tptp.surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @t4)))))) % 0.34/0.58 (assume @p29 (_ (_ tptp.mem tptp.c_2Ecomplex_2Ecomplex__of__num) (_ (_ tptp.arr tptp.ty_2Enum_2Enum) @t42))) % 0.34/0.58 (assume @p30 (_ (_ tptp.mem tptp.c_2Ecomplex_2Ecomplex__inv) (_ (_ tptp.arr @t42) @t42))) % 0.34/0.58 (assume @p31 (forall @t46 (_ (_ tptp.mem (_ tptp.c_2Emin_2E_3D @t43)) (_ @t44 @t45)))) % 0.34/0.58 (assume @p32 (forall (@list @t10 @t4) (=> @t11 (forall (@list @t47) (=> (_ (_ tptp.mem @t47) @t10) (= (_ tptp.p (_ (_ tptp.ap (_ (_ tptp.ap (_ tptp.c_2Emin_2E_3D @t10)) @t4)) @t47)) (= @t4 @t47))))))) % 0.34/0.58 (assume @p33 (forall @t46 (_ (_ tptp.mem (_ tptp.c_2Ebool_2E_21 @t43)) (_ (_ tptp.arr @t45) tptp.bool)))) % 0.34/0.58 (assume @p34 (forall (@list @t10 @t22) (=> (_ @t24 (_ @t12 tptp.bool)) (= (_ tptp.p (_ (_ tptp.ap (_ tptp.c_2Ebool_2E_21 @t10)) @t22)) (forall @t6 (=> @t11 (_ tptp.p (_ (_ tptp.ap @t22) @t4)))))))) % 0.34/0.58 (assume @p35 true) % 0.34/0.58 (assume @p36 (forall (@list @t43 @t48) (=> @t51 (= (forall (@list @t50) (=> (_ (_ tptp.mem @t50) @t43) @t49)) @t49)))) % 0.34/0.58 (assume @p37 (forall (@list @t48) (=> @t51 (and (= (=> true @t49) @t49) (= (=> @t49 true) true) (= (=> false @t49) true) (= (=> @t49 @t49) true) (= (=> @t49 false) (not @t49)))))) % 0.34/0.58 (assume @p38 @t64) % 0.34/0.58 (assume @p39 @t69) % 0.34/0.58 (step @p40 :rule refl :args ((tptp.surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @t59))) % 0.34/0.58 (step @p41 :rule refl :args ((tptp.ap tptp.c_2Ecomplex_2Ecomplex__inv @t57))) % 0.34/0.58 (step @p42 :rule refl :args (@t70)) % 0.34/0.58 (step @p43 :rule refl :args (tptp.c_2Ecomplex_2Ecomplex__inv)) % 0.34/0.58 (step @p44 :rule cong :premises (@p43 @p42) :args (@t71)) % 0.34/0.58 (step @p45 :rule trans :premises (@p44 @p41)) % 0.34/0.58 (step @p46 :rule cong :premises (@p45) :args (@t72)) % 0.34/0.58 (step @p47 :rule trans :premises (@p46 @p40)) % 0.34/0.58 (step @p48 :rule refl :args (tptp.surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal)) % 0.34/0.58 (step @p49 :rule ho_cong :premises (@p48 @p45)) % 0.34/0.58 (step @p50 :rule cong :premises (@p49 @p47) :args ((= (_ tptp.surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @t71) @t72))) % 0.34/0.58 (step @p51 :rule symm :premises (@p50)) % 0.34/0.58 (step @p52 :rule refl :args (@t60)) % 0.34/0.58 (step @p53 :rule eq_resolve :premises (@p52 @p51)) % 0.34/0.58 (step @p54 :rule refl :args (@t58)) % 0.34/0.58 (step @p55 :rule ho_cong :premises (@p54 @p42)) % 0.34/0.58 (step @p56 :rule cong :premises (@p55 @p45) :args ((= (_ @t58 @t70) @t71))) % 0.34/0.58 (step @p57 :rule symm :premises (@p56)) % 0.34/0.58 (step @p58 :rule refl :args (@t59)) % 0.34/0.58 (step @p59 :rule eq_resolve :premises (@p58 @p57)) % 0.34/0.58 (step @p60 :rule refl :args (@t57)) % 0.34/0.58 (step @p61 :rule cong :premises (@p60 @p42) :args ((= @t57 @t70))) % 0.34/0.58 (step @p62 :rule symm :premises (@p61)) % 0.34/0.58 (step @p63 :rule eq_resolve :premises (@p60 @p62)) % 0.34/0.58 (step @p64 :rule ho_cong :premises (@p54 @p63)) % 0.34/0.58 (step @p65 :rule trans :premises (@p64 @p59)) % 0.34/0.58 (step @p66 :rule ho_cong :premises (@p48 @p65)) % 0.34/0.58 (step @p67 :rule trans :premises (@p66 @p53)) % 0.34/0.58 (step @p68 :rule refl :args ((tptp.surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @t53))) % 0.34/0.58 (step @p69 :rule refl :args ((tptp.ap tptp.c_2Ecomplex_2Ecomplex__of__num @t35))) % 0.34/0.58 (step @p70 :rule refl :args (@t73)) % 0.34/0.58 (step @p71 :rule refl :args (tptp.c_2Ecomplex_2Ecomplex__of__num)) % 0.34/0.58 (step @p72 :rule cong :premises (@p71 @p70) :args (@t74)) % 0.34/0.58 (step @p73 :rule trans :premises (@p72 @p69)) % 0.34/0.58 (step @p74 :rule cong :premises (@p73) :args (@t75)) % 0.34/0.58 (step @p75 :rule trans :premises (@p74 @p68)) % 0.34/0.58 (step @p76 :rule ho_cong :premises (@p48 @p73)) % 0.34/0.58 (step @p77 :rule cong :premises (@p76 @p75) :args ((= (_ tptp.surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @t74) @t75))) % 0.34/0.58 (step @p78 :rule symm :premises (@p77)) % 0.34/0.58 (step @p79 :rule refl :args (@t54)) % 0.34/0.58 (step @p80 :rule eq_resolve :premises (@p79 @p78)) % 0.34/0.58 (step @p81 :rule refl :args (@t52)) % 0.34/0.58 (step @p82 :rule ho_cong :premises (@p81 @p70)) % 0.34/0.58 (step @p83 :rule cong :premises (@p82 @p73) :args ((= (_ @t52 @t73) @t74))) % 0.34/0.58 (step @p84 :rule symm :premises (@p83)) % 0.34/0.58 (step @p85 :rule refl :args (@t53)) % 0.34/0.58 (step @p86 :rule eq_resolve :premises (@p85 @p84)) % 0.34/0.58 (step @p87 :rule refl :args (@t35)) % 0.34/0.58 (step @p88 :rule cong :premises (@p87 @p70) :args ((= @t35 @t73))) % 0.34/0.58 (step @p89 :rule symm :premises (@p88)) % 0.34/0.58 (step @p90 :rule eq_resolve :premises (@p87 @p89)) % 0.34/0.58 (step @p91 :rule ho_cong :premises (@p81 @p90)) % 0.34/0.58 (step @p92 :rule trans :premises (@p91 @p86)) % 0.34/0.58 (step @p93 :rule ho_cong :premises (@p48 @p92)) % 0.34/0.58 (step @p94 :rule trans :premises (@p93 @p80)) % 0.34/0.58 (step @p95 :rule cong :premises (@p94 @p67) :args (@t76)) % 0.34/0.58 (step @p96 :rule refl :args (@t55)) % 0.34/0.58 (step @p97 :rule cong :premises (@p96 @p94) :args (@t56)) % 0.34/0.58 (step @p98 :rule cong :premises (@p97 @p95) :args (@t77)) % 0.34/0.58 (step @p99 :rule cong :premises (@p98) :args ((forall @t63 @t77))) % 0.34/0.58 (step @p100 :rule eq-symm :args (@t76 @t56)) % 0.34/0.58 (step @p101 :rule refl :args (@t56)) % 0.34/0.58 (step @p102 :rule eq-symm :args (@t60 @t54)) % 0.34/0.58 (step @p103 :rule cong :premises (@p102 @p101) :args (@t62)) % 0.34/0.58 (step @p104 :rule trans :premises (@p103 @p100)) % 0.34/0.58 (step @p105 :rule cong :premises (@p104) :args (@t64)) % 0.34/0.58 (step @p106 :rule trans :premises (@p105 @p99)) % 0.34/0.58 (step @p107 :rule eq_resolve :premises (@p38 @p106)) % 0.34/0.58 (step @p108 :rule cong :premises (@p95) :args (@t78)) % 0.34/0.58 (step @p109 :rule nary_cong :premises (@p97 @p108) :args (@t79)) % 0.34/0.58 (step @p110 :rule cong :premises (@p109) :args ((forall @t63 @t79))) % 0.34/0.58 (step @p111 :rule refl :args (@t78)) % 0.34/0.58 (step @p112 :rule bool-double-not-elim :args (@t56)) % 0.34/0.58 (step @p113 :rule nary_cong :premises (@p112 @p111) :args ((or (not @t66) @t78))) % 0.34/0.58 (step @p114 :rule bool-impl-elim :args (@t66 @t78)) % 0.34/0.58 (step @p115 :rule trans :premises (@p114 @p113)) % 0.34/0.58 (step @p116 :rule cong :premises (@p115) :args ((forall @t63 (=> @t66 @t78)))) % 0.34/0.58 (step @p117 :rule trans :premises (@p116 @p110)) % 0.34/0.58 (step @p118 :rule cong :premises (@p102) :args (@t65)) % 0.34/0.58 (step @p119 :rule refl :args (@t66)) % 0.34/0.58 (step @p120 :rule cong :premises (@p119 @p118) :args (@t67)) % 0.34/0.58 (step @p121 :rule cong :premises (@p120) :args (@t68)) % 0.34/0.58 (step @p122 :rule trans :premises (@p121 @p117)) % 0.34/0.58 (step @p123 :rule cong :premises (@p122) :args (@t69)) % 0.34/0.58 (step @p124 :rule eq_resolve :premises (@p39 @p123)) % 0.34/0.58 (step @p125 :rule refl :args (@t88)) % 0.34/0.58 (step @p126 :rule bool-double-not-elim :args (@t82)) % 0.34/0.58 (step @p127 :rule nary_cong :premises (@p126 @p125) :args ((or (not @t89) @t88))) % 0.34/0.58 (step @p128 :rule refl :args (@t85)) % 0.34/0.58 (step @p129 :rule eq-symm :args (@t83 @t75)) % 0.34/0.58 (step @p130 :rule nary_cong :premises (@p129 @p128) :args (@t91)) % 0.34/0.58 (step @p131 :rule cong :premises (@p130) :args (@t92)) % 0.34/0.58 (step @p132 :rule refl :args (@t89)) % 0.34/0.58 (step @p133 :rule cong :premises (@p132 @p131) :args ((=> @t89 @t92))) % 0.34/0.58 (assume-push @p167 @t89) % 0.34/0.58 (step @p135 :rule skolemize :premises (@p124)) % 0.34/0.58 (step-pop @p168 :rule scope :premises (@p135)) % 0.34/0.58 (step @p136 :rule process_scope :premises (@p168) :args (@t92)) % 0.34/0.58 (step @p138 :rule eq_resolve :premises (@p136 @p133)) % 0.34/0.58 (step @p139 :rule implies_elim :premises (@p138)) % 0.34/0.58 (step @p140 :rule eq_resolve :premises (@p139 @p127)) % 0.34/0.58 (step @p141 :rule chain_m_resolution :premises (@p140 @p124) :args (@t88 @t93 (@list @t82))) % 0.34/0.58 (step @p142 :rule cnf_or_neg :args (@t87 0)) % 0.34/0.58 (step @p143 :rule chain_m_resolution :premises (@p142 @p141) :args ((not @t86) @t93 @t94)) % 0.34/0.58 (step @p144 :rule bool-double-not-elim :args (@t84)) % 0.34/0.58 (step @p145 :rule refl :args (@t87)) % 0.34/0.58 (step @p146 :rule nary_cong :premises (@p145 @p144) :args ((or @t87 (not @t85)))) % 0.34/0.58 (step @p147 :rule cnf_or_neg :args (@t87 1)) % 0.34/0.58 (step @p148 :rule eq_resolve :premises (@p147 @p146)) % 0.34/0.58 (step @p149 :rule reordering :premises (@p148) :args ((or @t84 @t87))) % 0.34/0.58 (step @p150 :rule chain_m_resolution :premises (@p149 @p141) :args (@t84 @t93 @t94)) % 0.34/0.58 (step @p151 :rule cnf_equiv_pos1 :args (@t95)) % 0.34/0.58 (step @p152 :rule reordering :premises (@p151) :args ((or @t85 @t86 @t96))) % 0.34/0.58 (step @p153 :rule chain_m_resolution :premises (@p152 @p150 @p143) :args (@t96 (@list false true) (@list @t84 @t86))) % 0.34/0.58 (step @p154 :rule eq-symm :args (@t86 @t84)) % 0.34/0.58 (step @p155 :rule refl :args (@t84)) % 0.34/0.58 (step @p156 :rule cong :premises (@p129 @p155) :args (@t97)) % 0.34/0.58 (step @p157 :rule trans :premises (@p156 @p154)) % 0.34/0.58 (step @p158 :rule refl :args (@t98)) % 0.34/0.58 (step @p159 :rule cong :premises (@p158 @p157) :args ((=> @t98 @t97))) % 0.34/0.58 (assume-push @p169 @t98) % 0.34/0.58 (step @p161 :rule instantiate :premises (@p107) :args ((@list @t83))) % 0.34/0.58 (step-pop @p170 :rule scope :premises (@p161)) % 0.34/0.58 (step @p162 :rule process_scope :premises (@p170) :args (@t97)) % 0.34/0.58 (step @p164 :rule eq_resolve :premises (@p162 @p159)) % 0.34/0.58 (step @p165 :rule implies_elim :premises (@p164)) % 0.34/0.58 (step @p166 false :rule chain_m_resolution :premises (@p165 @p153 @p107) :args (false (@list true false) (@list @t95 @t98))) % 0.34/0.58 ) % 0.34/0.58 % SZS output end Proof % 0.34/0.58 % cvc5 exiting %------------------------------------------------------------------------------