%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : ALG283^5 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n025.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 08:05:44 AM UTC 2026 % Result : Theorem 171.58s 171.92s % Output : Proof 171.58s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ALG283^5 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n025.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Wed Jun 3 01:58:01 EDT 2026 % 0.16/0.34 % CPUTime : % 0.29/0.49 %----Proving TH0 % 171.58/171.92 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 171.58/171.92 --- 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... % 171.58/171.92 --- 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... % 171.58/171.92 --- Run --ho-elim --full-saturate-quant at 18s... % 171.58/171.92 --- Run --ho-elim --no-e-matching --full-saturate-quant at 12s... % 171.58/171.92 % SZS status Theorem % 171.58/171.92 % SZS output start Proof % 171.58/171.92 ( % 171.58/171.92 (declare-sort tptp.a 0) % 171.58/171.92 (declare-const tptp.cJ (-> tptp.a tptp.a)) % 171.58/171.92 (declare-const tptp.cE tptp.a) % 171.58/171.92 (declare-const tptp.cP (-> tptp.a tptp.a tptp.a)) % 171.58/171.92 (define @t1 () (@var "Y" tptp.a)) % 171.58/171.92 (define @t2 () (@var "Z" tptp.a)) % 171.58/171.92 (define @t3 () (@var "X" tptp.a)) % 171.58/171.92 (define @t4 () (_ (_ tptp.cP @t3) @t2)) % 171.58/171.92 (define @t5 () (@list @t2)) % 171.58/171.92 (define @t6 () (exists @t5 (= @t4 @t1))) % 171.58/171.92 (define @t7 () (@list @t3 @t1)) % 171.58/171.92 (define @t8 () (forall @t7 @t6)) % 171.58/171.92 (define @t9 () (@var "Xy" tptp.a)) % 171.58/171.92 (define @t10 () (_ tptp.cJ @t9)) % 171.58/171.92 (define @t11 () (_ (_ tptp.cP @t10) @t9)) % 171.58/171.92 (define @t12 () (@list @t9)) % 171.58/171.92 (define @t13 () (forall @t12 (= @t11 tptp.cE))) % 171.58/171.92 (define @t14 () (@var "Xx" tptp.a)) % 171.58/171.92 (define @t15 () (_ (_ tptp.cP tptp.cE) @t14)) % 171.58/171.92 (define @t16 () (@list @t14)) % 171.58/171.92 (define @t17 () (forall @t16 (= @t15 @t14))) % 171.58/171.92 (define @t18 () (@var "Xz" tptp.a)) % 171.58/171.92 (define @t19 () (_ (_ tptp.cP @t9) @t18)) % 171.58/171.92 (define @t20 () (_ tptp.cP @t14)) % 171.58/171.92 (define @t21 () (_ @t20 @t19)) % 171.58/171.92 (define @t22 () (_ @t20 @t9)) % 171.58/171.92 (define @t23 () (_ (_ tptp.cP @t22) @t18)) % 171.58/171.92 (define @t24 () (= @t23 @t21)) % 171.58/171.92 (define @t25 () (@list @t14 @t9 @t18)) % 171.58/171.92 (define @t26 () (forall @t25 @t24)) % 171.58/171.92 (define @t27 () (and @t26 @t17 @t13)) % 171.58/171.92 (define @t28 () (=> @t27 @t8)) % 171.58/171.92 (define @t29 () (not @t28)) % 171.58/171.92 (define @t30 () (@const 0 (@ho-elim-sort (-> tptp.a tptp.a tptp.a)))) % 171.58/171.92 (define @t31 () (@const 1 (-> (@ho-elim-sort (-> tptp.a tptp.a tptp.a)) tptp.a (@ho-elim-sort (-> tptp.a tptp.a))))) % 171.58/171.92 (define @t32 () (@const 2 (-> (@ho-elim-sort (-> tptp.a tptp.a)) tptp.a tptp.a))) % 171.58/171.92 (define @t33 () (forall @t7 (not (forall @t5 (not (= @t1 (_ @t32 (_ @t31 @t30 @t3) @t2))))))) % 171.58/171.92 (define @t34 () (@const 3 (@ho-elim-sort (-> tptp.a tptp.a)))) % 171.58/171.92 (define @t35 () (forall @t12 (= tptp.cE (_ @t32 (_ @t31 @t30 (_ @t32 @t34 @t9)) @t9)))) % 171.58/171.92 (define @t36 () (_ @t31 @t30 tptp.cE)) % 171.58/171.92 (define @t37 () (forall @t16 (= @t14 (_ @t32 @t36 @t14)))) % 171.58/171.92 (define @t38 () (_ @t31 @t30 @t14)) % 171.58/171.92 (define @t39 () (_ @t32 (_ @t31 @t30 (_ @t32 @t38 @t9)) @t18)) % 171.58/171.92 (define @t40 () (_ @t32 @t38 (_ @t32 (_ @t31 @t30 @t9) @t18))) % 171.58/171.92 (define @t41 () (forall @t25 (= @t39 @t40))) % 171.58/171.92 (define @t42 () (and @t41 @t37 @t35)) % 171.58/171.92 (define @t43 () (=> @t42 @t33)) % 171.58/171.92 (define @t44 () (not @t43)) % 171.58/171.92 (define @t45 () (tptp.cP @t3 @t2)) % 171.58/171.92 (define @t46 () (tptp.cJ @t9)) % 171.58/171.92 (define @t47 () (tptp.cP @t46 @t9)) % 171.58/171.92 (define @t48 () (tptp.cP tptp.cE @t14)) % 171.58/171.92 (define @t49 () (tptp.cP @t9 @t18)) % 171.58/171.92 (define @t50 () (tptp.cP @t14 @t49)) % 171.58/171.92 (define @t51 () (tptp.cP @t14 @t9)) % 171.58/171.92 (define @t52 () (tptp.cP @t51 @t18)) % 171.58/171.92 (define @t53 () (= @t1 @t4)) % 171.58/171.92 (define @t54 () (not @t53)) % 171.58/171.92 (define @t55 () (forall @t5 @t54)) % 171.58/171.92 (define @t56 () (not @t55)) % 171.58/171.92 (define @t57 () (= tptp.cE @t11)) % 171.58/171.92 (define @t58 () (= @t14 @t15)) % 171.58/171.92 (define @t59 () (@list tptp.cE)) % 171.58/171.92 (define @t60 () (@quantifiers_skolemize @t33 0)) % 171.58/171.92 (define @t61 () (@list @t60)) % 171.58/171.92 (define @t62 () (@var "y" (@ho-elim-sort (-> tptp.a tptp.a)))) % 171.58/171.92 (define @t63 () (@var "x" (@ho-elim-sort (-> tptp.a tptp.a)))) % 171.58/171.92 (define @t64 () (@var "z" tptp.a)) % 171.58/171.92 (define @t65 () (@list @t64)) % 171.58/171.92 (define @t66 () (_ @t32 @t34 tptp.cE)) % 171.58/171.92 (define @t67 () (_ @t31 @t30 @t66)) % 171.58/171.92 (define @t68 () (forall @t65 (= (_ @t32 @t36 @t64) (_ @t32 @t67 @t64)))) % 171.58/171.92 (define @t69 () (@quantifiers_skolemize @t68 0)) % 171.58/171.92 (define @t70 () (_ @t32 @t36 @t69)) % 171.58/171.92 (define @t71 () (= @t70 (_ @t32 @t67 @t69))) % 171.58/171.92 (define @t72 () (not @t71)) % 171.58/171.92 (define @t73 () (not @t68)) % 171.58/171.92 (define @t74 () (@list false)) % 171.58/171.92 (define @t75 () (= @t36 @t67)) % 171.58/171.92 (define @t76 () (or @t73 @t75)) % 171.58/171.92 (define @t77 () (@quantifiers_skolemize @t33 1)) % 171.58/171.92 (define @t78 () (_ @t32 @t34 @t60)) % 171.58/171.92 (define @t79 () (@list @t78)) % 171.58/171.92 (define @t80 () (@var "ii" tptp.a)) % 171.58/171.92 (define @t81 () (@var "u" (@ho-elim-sort (-> tptp.a tptp.a tptp.a)))) % 171.58/171.92 (define @t82 () (@var "e" (@ho-elim-sort (-> tptp.a tptp.a)))) % 171.58/171.92 (define @t83 () (@var "i" tptp.a)) % 171.58/171.92 (define @t84 () (@var "v" (@ho-elim-sort (-> tptp.a tptp.a tptp.a)))) % 171.58/171.92 (define @t85 () (_ @t31 @t84 @t80)) % 171.58/171.92 (define @t86 () (@list @t80)) % 171.58/171.92 (define @t87 () (@list @t84)) % 171.58/171.92 (define @t88 () (forall (@list @t81 @t82 @t83) (not (forall @t87 (not (forall @t86 (= @t85 (ite (= @t83 @t80) @t82 (_ @t31 @t81 @t80))))))))) % 171.58/171.92 (define @t89 () (_ @t31 @t30 @t80)) % 171.58/171.92 (define @t90 () (ite (= @t77 @t80) @t36 @t89)) % 171.58/171.92 (define @t91 () (= @t85 @t90)) % 171.58/171.92 (define @t92 () (forall @t86 @t91)) % 171.58/171.92 (define @t93 () (not @t92)) % 171.58/171.92 (define @t94 () (forall @t87 @t93)) % 171.58/171.92 (define @t95 () (not @t94)) % 171.58/171.92 (define @t96 () (ite (= @t80 @t77) @t36 @t89)) % 171.58/171.92 (define @t97 () (forall @t87 (not (forall @t86 (= @t85 @t96))))) % 171.58/171.92 (define @t98 () (not @t97)) % 171.58/171.92 (define @t99 () (@quantifiers_skolemize @t97 0)) % 171.58/171.92 (define @t100 () (_ @t31 @t99 @t80)) % 171.58/171.92 (define @t101 () (forall @t86 (= @t96 @t100))) % 171.58/171.92 (define @t102 () (forall @t86 (= @t100 @t96))) % 171.58/171.92 (define @t103 () (not (not @t102))) % 171.58/171.92 (define @t104 () (@list true)) % 171.58/171.92 (define @t105 () (_ @t31 @t99 tptp.cE)) % 171.58/171.92 (define @t106 () (= tptp.cE @t77)) % 171.58/171.92 (define @t107 () (= (ite @t106 @t36 @t36) @t105)) % 171.58/171.92 (define @t108 () (= @t36 @t105)) % 171.58/171.92 (define @t109 () (@list @t101)) % 171.58/171.92 (define @t110 () (_ @t31 @t30 @t60)) % 171.58/171.92 (define @t111 () (_ @t32 @t110 @t78)) % 171.58/171.92 (define @t112 () (_ @t31 @t30 @t111)) % 171.58/171.92 (define @t113 () (= @t77 @t111)) % 171.58/171.92 (define @t114 () (ite @t113 @t36 @t112)) % 171.58/171.92 (define @t115 () (@purify @t114)) % 171.58/171.92 (define @t116 () (_ @t31 @t99 @t111)) % 171.58/171.92 (define @t117 () (= @t116 @t114)) % 171.58/171.92 (define @t118 () (ite (= @t111 @t77) @t36 @t112)) % 171.58/171.92 (define @t119 () (= @t118 @t116)) % 171.58/171.92 (define @t120 () (= @t116 @t115)) % 171.58/171.92 (define @t121 () (forall @t5 (not (= @t77 (_ @t32 @t110 @t2))))) % 171.58/171.92 (define @t122 () (not @t33)) % 171.58/171.92 (define @t123 () (not (not @t121))) % 171.58/171.92 (define @t124 () (= @t114 @t112)) % 171.58/171.92 (define @t125 () (= @t114 @t36)) % 171.58/171.92 (define @t126 () (= @t112 @t115)) % 171.58/171.92 (define @t127 () (_ @t32 @t34 @t78)) % 171.58/171.92 (define @t128 () (_ @t31 @t30 @t78)) % 171.58/171.92 (define @t129 () (_ @t32 @t128 @t77)) % 171.58/171.92 (define @t130 () (_ @t32 @t110 @t129)) % 171.58/171.92 (define @t131 () (= @t77 @t130)) % 171.58/171.92 (define @t132 () (= @t130 (_ @t32 @t112 @t77))) % 171.58/171.92 (define @t133 () (not @t132)) % 171.58/171.92 (define @t134 () (_ @t31 @t30 @t127)) % 171.58/171.92 (define @t135 () (_ @t32 @t134 tptp.cE)) % 171.58/171.92 (define @t136 () (_ @t31 @t30 @t135)) % 171.58/171.92 (define @t137 () (_ @t32 @t136 @t78)) % 171.58/171.92 (define @t138 () (_ @t32 @t36 @t78)) % 171.58/171.92 (define @t139 () (= (_ @t32 @t134 @t138) @t137)) % 171.58/171.92 (define @t140 () (not @t139)) % 171.58/171.92 (define @t141 () (_ @t32 @t134 @t78)) % 171.58/171.92 (define @t142 () (_ @t31 @t30 @t141)) % 171.58/171.92 (define @t143 () (_ @t32 @t142 @t60)) % 171.58/171.92 (define @t144 () (_ @t32 @t128 @t60)) % 171.58/171.92 (define @t145 () (= (_ @t32 @t134 @t144) @t143)) % 171.58/171.92 (define @t146 () (not @t145)) % 171.58/171.92 (define @t147 () (not @t126)) % 171.58/171.92 (define @t148 () (not @t120)) % 171.58/171.92 (define @t149 () (not @t108)) % 171.58/171.92 (define @t150 () (= tptp.cE @t141)) % 171.58/171.92 (define @t151 () (not @t150)) % 171.58/171.92 (define @t152 () (= @t78 @t138)) % 171.58/171.92 (define @t153 () (not @t152)) % 171.58/171.92 (define @t154 () (_ @t32 @t36 @t77)) % 171.58/171.92 (define @t155 () (= @t77 @t154)) % 171.58/171.92 (define @t156 () (not @t155)) % 171.58/171.92 (define @t157 () (not @t75)) % 171.58/171.92 (define @t158 () (= tptp.cE @t144)) % 171.58/171.92 (define @t159 () (not @t158)) % 171.58/171.92 (define @t160 () (= @t60 (_ @t32 @t36 @t60))) % 171.58/171.92 (define @t161 () (not @t160)) % 171.58/171.92 (define @t162 () (_ @t32 @t36 tptp.cE)) % 171.58/171.92 (define @t163 () (= tptp.cE @t162)) % 171.58/171.92 (define @t164 () (not @t163)) % 171.58/171.92 (define @t165 () (not @t131)) % 171.58/171.92 (define @t166 () (and @t131 @t165)) % 171.58/171.92 (assume @p1 @t29) % 171.58/171.92 (assume @p2 true) % 171.58/171.92 (step @p3 :rule refl :args (@t33)) % 171.58/171.92 (step @p4 :rule refl :args (@t35)) % 171.58/171.92 (step @p5 :rule refl :args (@t37)) % 171.58/171.92 (step @p6 :rule eq-symm :args (@t39 @t40)) % 171.58/171.92 (step @p7 :rule cong :premises (@p6) :args (@t41)) % 171.58/171.92 (step @p8 :rule nary_cong :premises (@p7 @p5 @p4) :args (@t42)) % 171.58/171.92 (step @p9 :rule cong :premises (@p8 @p3) :args (@t43)) % 171.58/171.92 (step @p10 :rule cong :premises (@p9) :args (@t44)) % 171.58/171.92 ; WARNING: add trust step for TRUST % 171.58/171.92 ; trust TRUST PREPROCESS_HO_ELIM % 171.58/171.92 (step @p11 :rule trust :premises () :args ((= (not (=> (and (forall @t25 (= @t52 @t50)) (forall @t16 (= @t14 @t48)) (forall @t12 (= tptp.cE @t47))) (forall @t7 (not (forall @t5 (not (= @t1 @t45))))))) @t44))) % 171.58/171.92 (step @p12 :rule refl :args (@t45)) % 171.58/171.92 (step @p13 :rule refl :args (@t4)) % 171.58/171.92 (step @p14 :rule cong :premises (@p13 @p12) :args ((= @t4 @t45))) % 171.58/171.92 (step @p15 :rule symm :premises (@p14)) % 171.58/171.92 (step @p16 :rule eq_resolve :premises (@p13 @p15)) % 171.58/171.92 (step @p17 :rule refl :args (@t1)) % 171.58/171.92 (step @p18 :rule cong :premises (@p17 @p16) :args (@t53)) % 171.58/171.92 (step @p19 :rule cong :premises (@p18) :args (@t54)) % 171.58/171.92 (step @p20 :rule cong :premises (@p19) :args (@t55)) % 171.58/171.92 (step @p21 :rule cong :premises (@p20) :args (@t56)) % 171.58/171.92 (step @p22 :rule exists-elim :args ((= (exists @t5 @t53) @t56))) % 171.58/171.92 (step @p23 :rule trans :premises (@p22 @p21)) % 171.58/171.92 (step @p24 :rule eq-symm :args (@t4 @t1)) % 171.58/171.92 (step @p25 :rule cong :premises (@p24) :args (@t6)) % 171.58/171.92 (step @p26 :rule trans :premises (@p25 @p23)) % 171.58/171.92 (step @p27 :rule cong :premises (@p26) :args (@t8)) % 171.58/171.92 (step @p28 :rule refl :args ((tptp.cP @t10 @t9))) % 171.58/171.92 (step @p29 :rule refl :args (@t9)) % 171.58/171.92 (step @p30 :rule refl :args (@t46)) % 171.58/171.92 (step @p31 :rule cong :premises (@p30 @p29) :args (@t47)) % 171.58/171.92 (step @p32 :rule trans :premises (@p31 @p28)) % 171.58/171.92 (step @p33 :rule refl :args (tptp.cP)) % 171.58/171.92 (step @p34 :rule ho_cong :premises (@p33 @p30)) % 171.58/171.92 (step @p35 :rule ho_cong :premises (@p34 @p29)) % 171.58/171.92 (step @p36 :rule cong :premises (@p35 @p32) :args ((= (_ (_ tptp.cP @t46) @t9) @t47))) % 171.58/171.92 (step @p37 :rule symm :premises (@p36)) % 171.58/171.92 (step @p38 :rule refl :args (@t11)) % 171.58/171.92 (step @p39 :rule eq_resolve :premises (@p38 @p37)) % 171.58/171.92 (step @p40 :rule refl :args (@t10)) % 171.58/171.92 (step @p41 :rule cong :premises (@p40 @p30) :args ((= @t10 @t46))) % 171.58/171.92 (step @p42 :rule symm :premises (@p41)) % 171.58/171.92 (step @p43 :rule eq_resolve :premises (@p40 @p42)) % 171.58/171.92 (step @p44 :rule ho_cong :premises (@p33 @p43)) % 171.58/171.92 (step @p45 :rule ho_cong :premises (@p44 @p29)) % 171.58/171.92 (step @p46 :rule trans :premises (@p45 @p39)) % 171.58/171.92 (step @p47 :rule refl :args (tptp.cE)) % 171.58/171.92 (step @p48 :rule cong :premises (@p47 @p46) :args (@t57)) % 171.58/171.92 (step @p49 :rule cong :premises (@p48) :args ((forall @t12 @t57))) % 171.58/171.92 (step @p50 :rule eq-symm :args (@t11 tptp.cE)) % 171.58/171.92 (step @p51 :rule cong :premises (@p50) :args (@t13)) % 171.58/171.92 (step @p52 :rule trans :premises (@p51 @p49)) % 171.58/171.92 (step @p53 :rule refl :args (@t48)) % 171.58/171.92 (step @p54 :rule refl :args (@t15)) % 171.58/171.92 (step @p55 :rule cong :premises (@p54 @p53) :args ((= @t15 @t48))) % 171.58/171.92 (step @p56 :rule symm :premises (@p55)) % 171.58/171.92 (step @p57 :rule eq_resolve :premises (@p54 @p56)) % 171.58/171.92 (step @p58 :rule refl :args (@t14)) % 171.58/171.92 (step @p59 :rule cong :premises (@p58 @p57) :args (@t58)) % 171.58/171.92 (step @p60 :rule cong :premises (@p59) :args ((forall @t16 @t58))) % 171.58/171.92 (step @p61 :rule eq-symm :args (@t15 @t14)) % 171.58/171.92 (step @p62 :rule cong :premises (@p61) :args (@t17)) % 171.58/171.92 (step @p63 :rule trans :premises (@p62 @p60)) % 171.58/171.92 (step @p64 :rule refl :args ((tptp.cP @t14 @t19))) % 171.58/171.92 (step @p65 :rule refl :args (@t49)) % 171.58/171.92 (step @p66 :rule cong :premises (@p58 @p65) :args (@t50)) % 171.58/171.92 (step @p67 :rule trans :premises (@p66 @p64)) % 171.58/171.92 (step @p68 :rule refl :args (@t20)) % 171.58/171.92 (step @p69 :rule ho_cong :premises (@p68 @p65)) % 171.58/171.92 (step @p70 :rule cong :premises (@p69 @p67) :args ((= (_ @t20 @t49) @t50))) % 171.58/171.92 (step @p71 :rule symm :premises (@p70)) % 171.58/171.92 (step @p72 :rule refl :args (@t21)) % 171.58/171.92 (step @p73 :rule eq_resolve :premises (@p72 @p71)) % 171.58/171.92 (step @p74 :rule refl :args (@t19)) % 171.58/171.92 (step @p75 :rule cong :premises (@p74 @p65) :args ((= @t19 @t49))) % 171.58/171.92 (step @p76 :rule symm :premises (@p75)) % 171.58/171.92 (step @p77 :rule eq_resolve :premises (@p74 @p76)) % 171.58/171.92 (step @p78 :rule ho_cong :premises (@p68 @p77)) % 171.58/171.92 (step @p79 :rule trans :premises (@p78 @p73)) % 171.58/171.92 (step @p80 :rule refl :args ((tptp.cP @t22 @t18))) % 171.58/171.92 (step @p81 :rule refl :args (@t18)) % 171.58/171.92 (step @p82 :rule refl :args (@t51)) % 171.58/171.92 (step @p83 :rule cong :premises (@p82 @p81) :args (@t52)) % 171.58/171.92 (step @p84 :rule trans :premises (@p83 @p80)) % 171.58/171.92 (step @p85 :rule ho_cong :premises (@p33 @p82)) % 171.58/171.92 (step @p86 :rule ho_cong :premises (@p85 @p81)) % 171.58/171.92 (step @p87 :rule cong :premises (@p86 @p84) :args ((= (_ (_ tptp.cP @t51) @t18) @t52))) % 171.58/171.92 (step @p88 :rule symm :premises (@p87)) % 171.58/171.92 (step @p89 :rule refl :args (@t23)) % 171.58/171.92 (step @p90 :rule eq_resolve :premises (@p89 @p88)) % 171.58/171.92 (step @p91 :rule refl :args (@t22)) % 171.58/171.92 (step @p92 :rule cong :premises (@p91 @p82) :args ((= @t22 @t51))) % 171.58/171.92 (step @p93 :rule symm :premises (@p92)) % 171.58/171.92 (step @p94 :rule eq_resolve :premises (@p91 @p93)) % 171.58/171.92 (step @p95 :rule ho_cong :premises (@p33 @p94)) % 171.58/171.92 (step @p96 :rule ho_cong :premises (@p95 @p81)) % 171.58/171.92 (step @p97 :rule trans :premises (@p96 @p90)) % 171.58/171.92 (step @p98 :rule cong :premises (@p97 @p79) :args (@t24)) % 171.58/171.92 (step @p99 :rule cong :premises (@p98) :args (@t26)) % 171.58/171.92 (step @p100 :rule nary_cong :premises (@p99 @p63 @p52) :args (@t27)) % 171.58/171.92 (step @p101 :rule cong :premises (@p100 @p27) :args (@t28)) % 171.58/171.92 (step @p102 :rule cong :premises (@p101) :args (@t29)) % 171.58/171.92 (step @p103 :rule trans :premises (@p102 @p11 @p10)) % 171.58/171.92 (step @p104 :rule eq_resolve :premises (@p1 @p103)) % 171.58/171.92 (step @p105 :rule not_implies_elim1 :premises (@p104)) % 171.58/171.92 (step @p106 :rule and_elim :premises (@p105) :args (1)) % 171.58/171.92 (step @p107 :rule instantiate :premises (@p106) :args (@t59)) % 171.58/171.92 (step @p108 :rule instantiate :premises (@p106) :args (@t61)) % 171.58/171.92 (step @p109 :rule and_elim :premises (@p105) :args (2)) % 171.58/171.92 (step @p110 :rule instantiate :premises (@p109) :args (@t61)) % 171.58/171.92 ; trust TRUST PREPROCESS_HO_ELIM_LEMMA % 171.58/171.92 (step @p111 :rule trust :premises () :args ((forall (@list @t63 @t62) (or (not (forall @t65 (= (_ @t32 @t63 @t64) (_ @t32 @t62 @t64)))) (= @t63 @t62))))) % 171.58/171.92 (step @p112 :rule instantiate :premises (@p111) :args ((@list @t36 @t67))) % 171.58/171.92 (step @p113 :rule instantiate :premises (@p106) :args ((@list @t69))) % 171.58/171.92 (step @p114 :rule symm :premises (@p113)) % 171.58/171.92 (step @p115 :rule refl :args (@t67)) % 171.58/171.92 (step @p116 :rule cong :premises (@p115 @p114) :args ((_ @t32 @t67 @t70))) % 171.58/171.92 (step @p117 :rule and_elim :premises (@p105) :args (0)) % 171.58/171.92 (step @p118 :rule instantiate :premises (@p117) :args ((@list @t66 tptp.cE @t69))) % 171.58/171.92 (step @p119 :rule symm :premises (@p118)) % 171.58/171.92 (step @p120 :rule refl :args (@t69)) % 171.58/171.92 (step @p121 :rule instantiate :premises (@p109) :args (@t59)) % 171.58/171.92 (step @p122 :rule refl :args (@t30)) % 171.58/171.92 (step @p123 :rule cong :premises (@p122 @p121) :args (@t36)) % 171.58/171.92 (step @p124 :rule cong :premises (@p123 @p120) :args (@t70)) % 171.58/171.92 (step @p125 :rule trans :premises (@p124 @p119 @p116)) % 171.58/171.92 (step @p126 :rule refl :args (@t72)) % 171.58/171.92 (step @p127 :rule bool-double-not-elim :args (@t68)) % 171.58/171.92 (step @p128 :rule nary_cong :premises (@p127 @p126) :args ((or (not @t73) @t72))) % 171.58/171.92 (assume-push @p364 @t73) % 171.58/171.92 (step @p130 :rule skolemize :premises (@p364)) % 171.58/171.92 (step-pop @p365 :rule scope :premises (@p130)) % 171.58/171.92 (step @p131 :rule process_scope :premises (@p365) :args (@t72)) % 171.58/171.92 (step @p133 :rule implies_elim :premises (@p131)) % 171.58/171.92 (step @p134 :rule eq_resolve :premises (@p133 @p128)) % 171.58/171.92 (step @p135 :rule chain_m_resolution :premises (@p134 @p125) :args (@t68 @t74 (@list @t71))) % 171.58/171.92 (step @p136 :rule cnf_or_pos :args (@t76)) % 171.58/171.92 (step @p137 :rule reordering :premises (@p136) :args ((or @t73 @t75 (not @t76)))) % 171.58/171.92 (step @p138 :rule chain_m_resolution :premises (@p137 @p135 @p112) :args (@t75 (@list false false) (@list @t68 @t76))) % 171.58/171.92 (step @p139 :rule instantiate :premises (@p106) :args ((@list @t77))) % 171.58/171.92 (step @p140 :rule instantiate :premises (@p106) :args (@t79)) % 171.58/171.92 (step @p141 :rule instantiate :premises (@p109) :args (@t79)) % 171.58/171.92 ; trust TRUST PREPROCESS_HO_ELIM_LEMMA % 171.58/171.92 (step @p142 :rule trust :premises () :args (@t88)) % 171.58/171.92 (step @p143 :rule refl :args (@t89)) % 171.58/171.92 (step @p144 :rule refl :args (@t36)) % 171.58/171.92 (step @p145 :rule eq-symm :args (@t77 @t80)) % 171.58/171.92 (step @p146 :rule cong :premises (@p145 @p144 @p143) :args (@t90)) % 171.58/171.92 (step @p147 :rule refl :args (@t85)) % 171.58/171.92 (step @p148 :rule cong :premises (@p147 @p146) :args (@t91)) % 171.58/171.92 (step @p149 :rule cong :premises (@p148) :args (@t92)) % 171.58/171.92 (step @p150 :rule cong :premises (@p149) :args (@t93)) % 171.58/171.92 (step @p151 :rule cong :premises (@p150) :args (@t94)) % 171.58/171.92 (step @p152 :rule cong :premises (@p151) :args (@t95)) % 171.58/171.92 (step @p153 :rule refl :args (@t88)) % 171.58/171.92 (step @p154 :rule cong :premises (@p153 @p152) :args ((=> @t88 @t95))) % 171.58/171.92 (assume-push @p366 @t88) % 171.58/171.92 (step @p156 :rule instantiate :premises (@p142) :args ((@list @t30 @t36 @t77))) % 171.58/171.92 (step-pop @p367 :rule scope :premises (@p156)) % 171.58/171.92 (step @p157 :rule process_scope :premises (@p367) :args (@t95)) % 171.58/171.92 (step @p159 :rule eq_resolve :premises (@p157 @p154)) % 171.58/171.92 (step @p160 :rule implies_elim :premises (@p159)) % 171.58/171.92 (step @p161 :rule chain_m_resolution :premises (@p160 @p142) :args (@t98 @t74 (@list @t88))) % 171.58/171.92 (step @p162 :rule refl :args (@t101)) % 171.58/171.92 (step @p163 :rule bool-double-not-elim :args (@t97)) % 171.58/171.92 (step @p164 :rule nary_cong :premises (@p163 @p162) :args ((or (not @t98) @t101))) % 171.58/171.92 (step @p165 :rule eq-symm :args (@t100 @t96)) % 171.58/171.92 (step @p166 :rule cong :premises (@p165) :args (@t102)) % 171.58/171.92 (step @p167 :rule bool-double-not-elim :args (@t102)) % 171.58/171.92 (step @p168 :rule trans :premises (@p167 @p166)) % 171.58/171.92 (step @p169 :rule refl :args (@t98)) % 171.58/171.92 (step @p170 :rule cong :premises (@p169 @p168) :args ((=> @t98 @t103))) % 171.58/171.92 (assume-push @p368 @t98) % 171.58/171.92 (step @p172 :rule skolemize :premises (@p161)) % 171.58/171.92 (step-pop @p369 :rule scope :premises (@p172)) % 171.58/171.92 (step @p173 :rule process_scope :premises (@p369) :args (@t103)) % 171.58/171.92 (step @p175 :rule eq_resolve :premises (@p173 @p170)) % 171.58/171.92 (step @p176 :rule implies_elim :premises (@p175)) % 171.58/171.92 (step @p177 :rule eq_resolve :premises (@p176 @p164)) % 171.58/171.92 (step @p178 :rule chain_m_resolution :premises (@p177 @p161) :args (@t101 @t104 (@list @t97))) % 171.58/171.92 (step @p179 :rule refl :args (@t105)) % 171.58/171.92 (step @p180 :rule ite-eq-branch :args (@t106 @t36)) % 171.58/171.92 (step @p181 :rule cong :premises (@p180 @p179) :args (@t107)) % 171.58/171.92 (step @p182 :rule cong :premises (@p162 @p181) :args ((=> @t101 @t107))) % 171.58/171.92 (assume-push @p370 @t101) % 171.58/171.92 (step @p184 :rule instantiate :premises (@p178) :args (@t59)) % 171.58/171.92 (step-pop @p371 :rule scope :premises (@p184)) % 171.58/171.92 (step @p185 :rule process_scope :premises (@p371) :args (@t107)) % 171.58/171.92 (step @p187 :rule eq_resolve :premises (@p185 @p182)) % 171.58/171.92 (step @p188 :rule implies_elim :premises (@p187)) % 171.58/171.92 (step @p189 :rule chain_m_resolution :premises (@p188 @p178) :args (@t108 @t74 @t109)) % 171.58/171.92 (step @p190 :rule eq-refl :args (@t114)) % 171.58/171.92 (step @p191 :rule skolem_intro :args (@t115)) % 171.58/171.92 (step @p192 :rule refl :args (@t114)) % 171.58/171.92 (step @p193 :rule cong :premises (@p192 @p191) :args ((= @t114 @t115))) % 171.58/171.92 (step @p194 :rule trans :premises (@p193 @p190)) % 171.58/171.92 (step @p195 :rule true_elim :premises (@p194)) % 171.58/171.92 (step @p196 :rule refl :args (@t116)) % 171.58/171.92 (step @p197 :rule cong :premises (@p196 @p195) :args (@t117)) % 171.58/171.92 (step @p198 :rule cong :premises (@p162 @p197) :args ((=> @t101 @t117))) % 171.58/171.92 (step @p199 :rule eq-symm :args (@t114 @t116)) % 171.58/171.92 (step @p200 :rule refl :args (@t112)) % 171.58/171.92 (step @p201 :rule eq-symm :args (@t111 @t77)) % 171.58/171.92 (step @p202 :rule cong :premises (@p201 @p144 @p200) :args (@t118)) % 171.58/171.92 (step @p203 :rule cong :premises (@p202 @p196) :args (@t119)) % 171.58/171.92 (step @p204 :rule trans :premises (@p203 @p199)) % 171.58/171.92 (step @p205 :rule cong :premises (@p162 @p204) :args ((=> @t101 @t119))) % 171.58/171.92 (assume-push @p372 @t101) % 171.58/171.92 (step @p207 :rule instantiate :premises (@p178) :args ((@list @t111))) % 171.58/171.92 (step-pop @p373 :rule scope :premises (@p207)) % 171.58/171.92 (step @p208 :rule process_scope :premises (@p373) :args (@t119)) % 171.58/171.92 (step @p210 :rule eq_resolve :premises (@p208 @p205)) % 171.58/171.92 (step @p211 :rule eq_resolve :premises (@p210 @p198)) % 171.58/171.92 (step @p212 :rule implies_elim :premises (@p211)) % 171.58/171.92 (step @p213 :rule chain_m_resolution :premises (@p212 @p178) :args (@t120 @t74 @t109)) % 171.58/171.92 (step @p214 :rule not_implies_elim2 :premises (@p104)) % 171.58/171.92 (step @p215 :rule refl :args (@t121)) % 171.58/171.92 (step @p216 :rule bool-double-not-elim :args (@t33)) % 171.58/171.92 (step @p217 :rule nary_cong :premises (@p216 @p215) :args ((or (not @t122) @t121))) % 171.58/171.92 (step @p218 :rule bool-double-not-elim :args (@t121)) % 171.58/171.92 (step @p219 :rule refl :args (@t122)) % 171.58/171.92 (step @p220 :rule cong :premises (@p219 @p218) :args ((=> @t122 @t123))) % 171.58/171.92 (assume-push @p374 @t122) % 171.58/171.92 (step @p222 :rule skolemize :premises (@p214)) % 171.58/171.92 (step-pop @p375 :rule scope :premises (@p222)) % 171.58/171.92 (step @p223 :rule process_scope :premises (@p375) :args (@t123)) % 171.58/171.92 (step @p225 :rule eq_resolve :premises (@p223 @p220)) % 171.58/171.92 (step @p226 :rule implies_elim :premises (@p225)) % 171.58/171.92 (step @p227 :rule eq_resolve :premises (@p226 @p217)) % 171.58/171.92 (step @p228 :rule chain_m_resolution :premises (@p227 @p214) :args (@t121 @t104 (@list @t33))) % 171.58/171.92 (step @p229 :rule instantiate :premises (@p228) :args (@t79)) % 171.58/171.92 (step @p230 :rule eq-symm :args (@t115 @t112)) % 171.58/171.92 (step @p231 :rule eq-symm :args (@t115 @t36)) % 171.58/171.92 (step @p232 :rule refl :args (@t113)) % 171.58/171.92 (step @p233 :rule cong :premises (@p232 @p231 @p230) :args ((ite @t113 (= @t115 @t36) (= @t115 @t112)))) % 171.58/171.92 (step @p234 :rule cong :premises (@p195 @p200) :args (@t124)) % 171.58/171.92 (step @p235 :rule cong :premises (@p195 @p144) :args (@t125)) % 171.58/171.92 (step @p236 :rule cong :premises (@p232 @p235 @p234) :args ((ite @t113 @t125 @t124))) % 171.58/171.92 (step @p237 :rule ite_eq :args (@t114)) % 171.58/171.92 (step @p238 :rule eq_resolve :premises (@p237 @p236)) % 171.58/171.92 (step @p239 :rule eq_resolve :premises (@p238 @p233)) % 171.58/171.92 (step @p240 :rule ite_elim2 :premises (@p239)) % 171.58/171.92 (step @p241 :rule chain_m_resolution :premises (@p240 @p229) :args (@t126 @t104 (@list @t113))) % 171.58/171.92 (step @p242 :rule instantiate :premises (@p117) :args ((@list @t127 @t78 @t60))) % 171.58/171.92 (step @p243 :rule instantiate :premises (@p117) :args ((@list @t127 tptp.cE @t78))) % 171.58/171.92 (step @p244 :rule instantiate :premises (@p117) :args ((@list @t60 @t78 @t77))) % 171.58/171.92 (step @p245 :rule instantiate :premises (@p228) :args ((@list @t129))) % 171.58/171.92 (step @p246 :rule bool-double-not-elim :args (@t131)) % 171.58/171.92 (step @p247 :rule refl :args (@t133)) % 171.58/171.92 (step @p248 :rule refl :args (@t140)) % 171.58/171.92 (step @p249 :rule refl :args (@t146)) % 171.58/171.92 (step @p250 :rule refl :args (@t147)) % 171.58/171.92 (step @p251 :rule refl :args (@t148)) % 171.58/171.92 (step @p252 :rule refl :args (@t149)) % 171.58/171.92 (step @p253 :rule refl :args (@t151)) % 171.58/171.92 (step @p254 :rule refl :args (@t153)) % 171.58/171.92 (step @p255 :rule refl :args (@t156)) % 171.58/171.92 (step @p256 :rule refl :args (@t157)) % 171.58/171.92 (step @p257 :rule refl :args (@t159)) % 171.58/171.92 (step @p258 :rule refl :args (@t161)) % 171.58/171.92 (step @p259 :rule refl :args (@t164)) % 171.58/171.92 (step @p260 :rule nary_cong :premises (@p259 @p258 @p257 @p256 @p255 @p254 @p253 @p252 @p251 @p250 @p249 @p248 @p247 @p246) :args ((or @t164 @t161 @t159 @t157 @t156 @t153 @t151 @t149 @t148 @t147 @t146 @t140 @t133 (not @t165)))) % 171.58/171.92 (assume-push @p376 @t131) % 171.58/171.92 (assume-push @p377 @t165) % 171.58/171.92 (step @p263 :rule evaluate :args ((= true false))) % 171.58/171.92 (step @p264 :rule false_intro :premises (@p245)) % 171.58/171.92 (step @p265 :rule true_intro :premises (@p376)) % 171.58/171.92 (step @p266 :rule symm :premises (@p265)) % 171.58/171.92 (step @p267 :rule trans :premises (@p266 @p264)) % 171.58/171.92 (step @p268 false :rule eq_resolve :premises (@p267 @p263)) % 171.58/171.92 (step-pop @p378 :rule scope :premises (@p268)) % 171.58/171.92 (step-pop @p379 :rule scope :premises (@p378)) % 171.58/171.92 (step @p269 :rule process_scope :premises (@p379) :args (false)) % 171.58/171.92 (assume-push @p380 @t163) % 171.58/171.92 (assume-push @p381 @t160) % 171.58/171.92 (assume-push @p382 @t158) % 171.58/171.92 (assume-push @p383 @t75) % 171.58/171.92 (assume-push @p384 @t155) % 171.58/171.92 (assume-push @p385 @t152) % 171.58/171.92 (assume-push @p386 @t150) % 171.58/171.92 (assume-push @p387 @t108) % 171.58/171.92 (assume-push @p388 @t120) % 171.58/171.92 (assume-push @p389 @t126) % 171.58/171.92 (assume-push @p390 @t145) % 171.58/171.92 (assume-push @p391 @t139) % 171.58/171.92 (assume-push @p392 @t132) % 171.58/171.92 (assume-push @p393 @t165) % 171.58/171.92 (assume-push @p394 @t132) % 171.58/171.92 (assume-push @p395 @t126) % 171.58/171.92 (assume-push @p396 @t120) % 171.58/171.92 (assume-push @p397 @t160) % 171.58/171.92 (assume-push @p398 @t163) % 171.58/171.92 (assume-push @p399 @t150) % 171.58/171.92 (assume-push @p400 @t145) % 171.58/171.92 (assume-push @p401 @t158) % 171.58/171.92 (assume-push @p402 @t139) % 171.58/171.92 (assume-push @p403 @t152) % 171.58/171.92 (assume-push @p404 @t108) % 171.58/171.92 (assume-push @p405 @t75) % 171.58/171.92 (assume-push @p406 @t155) % 171.58/171.92 (step @p299 :rule symm :premises (@p244)) % 171.58/171.92 (step @p300 :rule refl :args (@t77)) % 171.58/171.92 (step @p301 :rule symm :premises (@p241)) % 171.58/171.92 (step @p302 :rule refl :args (@t78)) % 171.58/171.92 (step @p303 :rule symm :premises (@p108)) % 171.58/171.92 (step @p304 :rule refl :args (@t60)) % 171.58/171.92 (step @p305 :rule symm :premises (@p141)) % 171.58/171.92 (step @p306 :rule cong :premises (@p122 @p305) :args (@t142)) % 171.58/171.92 (step @p307 :rule cong :premises (@p306 @p304) :args (@t143)) % 171.58/171.92 (step @p308 :rule refl :args (@t134)) % 171.58/171.92 (step @p309 :rule cong :premises (@p308 @p110) :args (@t135)) % 171.58/171.92 (step @p310 :rule trans :premises (@p309 @p242 @p307 @p303)) % 171.58/171.92 (step @p311 :rule cong :premises (@p122 @p310) :args (@t136)) % 171.58/171.92 (step @p312 :rule cong :premises (@p311 @p302) :args (@t137)) % 171.58/171.92 (step @p313 :rule cong :premises (@p308 @p140) :args (@t141)) % 171.58/171.92 (step @p314 :rule trans :premises (@p141 @p313 @p243 @p312)) % 171.58/171.92 (step @p315 :rule refl :args (@t99)) % 171.58/171.92 (step @p316 :rule cong :premises (@p315 @p314) :args (@t105)) % 171.58/171.92 (step @p317 :rule symm :premises (@p107)) % 171.58/171.92 (step @p318 :rule cong :premises (@p122 @p317) :args ((_ @t31 @t30 @t162))) % 171.58/171.92 (step @p319 :rule trans :premises (@p318 @p189 @p316 @p213 @p301)) % 171.58/171.92 (step @p320 :rule symm :premises (@p318)) % 171.58/171.92 (step @p321 :rule symm :premises (@p383)) % 171.58/171.92 (step @p322 :rule trans :premises (@p321 @p320)) % 171.58/171.92 (step @p323 :rule trans :premises (@p322 @p319)) % 171.58/171.92 (step @p324 :rule cong :premises (@p323 @p300) :args ((_ @t32 @t67 @t77))) % 171.58/171.92 (step @p325 :rule cong :premises (@p383 @p300) :args (@t154)) % 171.58/171.92 (step @p326 :rule trans :premises (@p139 @p325 @p324 @p299)) % 171.58/171.92 (step-pop @p407 :rule scope :premises (@p326)) % 171.58/171.92 (step-pop @p408 :rule scope :premises (@p407)) % 171.58/171.92 (step-pop @p409 :rule scope :premises (@p408)) % 171.58/171.92 (step-pop @p410 :rule scope :premises (@p409)) % 171.58/171.92 (step-pop @p411 :rule scope :premises (@p410)) % 171.58/171.92 (step-pop @p412 :rule scope :premises (@p411)) % 171.58/171.92 (step-pop @p413 :rule scope :premises (@p412)) % 171.58/171.92 (step-pop @p414 :rule scope :premises (@p413)) % 171.58/171.92 (step-pop @p415 :rule scope :premises (@p414)) % 171.58/171.92 (step-pop @p416 :rule scope :premises (@p415)) % 171.58/171.92 (step-pop @p417 :rule scope :premises (@p416)) % 171.58/171.92 (step-pop @p418 :rule scope :premises (@p417)) % 171.58/171.92 (step-pop @p419 :rule scope :premises (@p418)) % 171.58/171.92 (step @p327 :rule process_scope :premises (@p419) :args (@t131)) % 171.58/171.92 (step @p341 :rule and_intro :premises (@p244 @p241 @p213 @p108 @p107 @p141 @p242 @p110 @p243 @p140 @p189 @p383 @p139)) % 171.58/171.92 (step @p342 :rule modus_ponens :premises (@p341 @p327)) % 171.58/171.92 (step @p343 :rule and_intro :premises (@p342 @p245)) % 171.58/171.92 (step-pop @p420 :rule scope :premises (@p343)) % 171.58/171.92 (step-pop @p421 :rule scope :premises (@p420)) % 171.58/171.92 (step-pop @p422 :rule scope :premises (@p421)) % 171.58/171.92 (step-pop @p423 :rule scope :premises (@p422)) % 171.58/171.92 (step-pop @p424 :rule scope :premises (@p423)) % 171.58/171.92 (step-pop @p425 :rule scope :premises (@p424)) % 171.58/171.92 (step-pop @p426 :rule scope :premises (@p425)) % 171.58/171.92 (step-pop @p427 :rule scope :premises (@p426)) % 171.58/171.92 (step-pop @p428 :rule scope :premises (@p427)) % 171.58/171.92 (step-pop @p429 :rule scope :premises (@p428)) % 171.58/171.92 (step-pop @p430 :rule scope :premises (@p429)) % 171.58/171.92 (step-pop @p431 :rule scope :premises (@p430)) % 171.58/171.92 (step-pop @p432 :rule scope :premises (@p431)) % 171.58/171.92 (step-pop @p433 :rule scope :premises (@p432)) % 171.58/171.92 (step @p344 :rule process_scope :premises (@p433) :args (@t166)) % 171.58/171.92 (step @p359 :rule implies_elim :premises (@p344)) % 171.58/171.92 (step @p360 :rule resolution :premises (@p359 @p269) :args (true @t166)) % 171.58/171.92 (step @p361 :rule not_and :premises (@p360)) % 171.58/171.92 (step @p362 :rule eq_resolve :premises (@p361 @p260)) % 171.58/171.92 (step @p363 false :rule chain_m_resolution :premises (@p362 @p245 @p244 @p243 @p242 @p241 @p213 @p189 @p141 @p140 @p139 @p138 @p110 @p108 @p107) :args (false (@list true false false false false false false false false false false false false false) (@list @t131 @t132 @t139 @t145 @t126 @t120 @t108 @t150 @t152 @t155 @t75 @t158 @t160 @t163))) % 171.58/171.92 ) % 171.58/171.92 % SZS output end Proof % 171.58/171.92 % cvc5 exiting %------------------------------------------------------------------------------