%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU593^2 : TPTP v9.2.1. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n002.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:52:20 AM UTC 2026 % Result : Theorem 237.58s 237.88s % Output : Proof 237.58s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU593^2 : TPTP v9.2.1. Released v3.7.0. % 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n002.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 17:42:48 EDT 2026 % 0.17/0.34 % CPUTime : % 0.33/0.50 %----Proving TH0 % 237.58/237.88 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 237.58/237.88 --- 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... % 237.58/237.88 --- 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... % 237.58/237.88 --- Run --ho-elim --full-saturate-quant at 18s... % 237.58/237.88 --- Run --ho-elim --no-e-matching --full-saturate-quant at 12s... % 237.58/237.88 --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 12s... % 237.58/237.88 --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 9s... % 237.58/237.88 --- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 6s... % 237.58/237.88 --- Run --no-ho-matching --full-saturate-quant --enum-inst-interleave --ho-elim-store-ax at 21s... % 237.58/237.88 --- Run --no-ho-matching --full-saturate-quant --macros-quant-mode=all at 18s... % 237.58/237.88 % SZS status Theorem % 237.58/237.88 % SZS output start Proof % 237.58/237.88 ( % 237.58/237.88 (declare-sort $$unsorted 0) % 237.58/237.88 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 237.58/237.88 (declare-const tptp.dsetconstr (-> $$unsorted (-> $$unsorted Bool) $$unsorted)) % 237.58/237.88 (declare-const tptp.binintersectI Bool) % 237.58/237.88 (declare-const tptp.binintersectLsub Bool) % 237.58/237.88 (declare-const tptp.setextsub Bool) % 237.58/237.88 (declare-const tptp.subsetE Bool) % 237.58/237.88 (declare-const tptp.subsetI1 Bool) % 237.58/237.88 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 237.58/237.88 (define tptp.binintersect () (let ((_let_1 (@var "B" $$unsorted))) (let ((_let_2 (@var "Xx" $$unsorted))) (let ((_let_3 (@var "A" $$unsorted))) (lambda (@list _let_3 _let_1) (_ (_ tptp.dsetconstr _let_3) (lambda (@list _let_2) (_ (_ tptp.in _let_2) _let_1)))))))) % 237.58/237.88 (define @t1 () (@var "B" $$unsorted)) % 237.58/237.88 (define @t2 () (@var "A" $$unsorted)) % 237.58/237.88 (define @t3 () (_ (_ tptp.subset @t2) @t1)) % 237.58/237.88 (define @t4 () (@var "Xx" $$unsorted)) % 237.58/237.88 (define @t5 () (_ tptp.in @t4)) % 237.58/237.88 (define @t6 () (_ @t5 @t1)) % 237.58/237.88 (define @t7 () (_ @t5 @t2)) % 237.58/237.88 (define @t8 () (=> @t7 @t6)) % 237.58/237.88 (define @t9 () (@list @t4)) % 237.58/237.88 (define @t10 () (forall @t9 @t8)) % 237.58/237.88 (define @t11 () (=> @t10 @t3)) % 237.58/237.88 (define @t12 () (@list @t2 @t1)) % 237.58/237.88 (define @t13 () (forall @t12 @t11)) % 237.58/237.88 (define @t14 () (= tptp.subsetI1 @t13)) % 237.58/237.88 (define @t15 () (@list @t2 @t1 @t4)) % 237.58/237.88 (define @t16 () (forall @t15 (=> @t3 @t8))) % 237.58/237.88 (define @t17 () (= tptp.subsetE @t16)) % 237.58/237.88 (define @t18 () (= @t2 @t1)) % 237.58/237.88 (define @t19 () (_ (_ tptp.subset @t1) @t2)) % 237.58/237.88 (define @t20 () (=> @t19 @t18)) % 237.58/237.88 (define @t21 () (forall @t12 (=> @t3 @t20))) % 237.58/237.88 (define @t22 () (= tptp.setextsub @t21)) % 237.58/237.88 (define @t23 () (_ (_ tptp.binintersect @t2) @t1)) % 237.58/237.88 (define @t24 () (=> @t6 (_ @t5 @t23))) % 237.58/237.88 (define @t25 () (=> @t7 @t24)) % 237.58/237.88 (define @t26 () (forall @t15 @t25)) % 237.58/237.88 (define @t27 () (= tptp.binintersectI @t26)) % 237.58/237.88 (define @t28 () (forall @t12 (_ (_ tptp.subset @t23) @t2))) % 237.58/237.88 (define @t29 () (= tptp.binintersectLsub @t28)) % 237.58/237.88 (define @t30 () (= @t23 @t2)) % 237.58/237.88 (define @t31 () (=> @t3 @t30)) % 237.58/237.88 (define @t32 () (forall @t12 @t31)) % 237.58/237.88 (define @t33 () (=> tptp.binintersectLsub @t32)) % 237.58/237.88 (define @t34 () (=> tptp.binintersectI @t33)) % 237.58/237.88 (define @t35 () (=> tptp.setextsub @t34)) % 237.58/237.88 (define @t36 () (=> tptp.subsetE @t35)) % 237.58/237.88 (define @t37 () (=> tptp.subsetI1 @t36)) % 237.58/237.88 (define @t38 () (not @t37)) % 237.58/237.88 (define @t39 () (lambda @t9 @t6)) % 237.58/237.88 (define @t40 () (_ tptp.dsetconstr @t2)) % 237.58/237.88 (define @t41 () (_ @t40 @t39)) % 237.58/237.88 (define @t42 () (lambda @t12 @t41)) % 237.58/237.88 (define @t43 () (tptp.in @t4 @t1)) % 237.58/237.88 (define @t44 () (lambda @t9 @t43)) % 237.58/237.88 (define @t45 () (tptp.dsetconstr @t2 @t44)) % 237.58/237.88 (define @t46 () (tptp.subset @t2 @t1)) % 237.58/237.88 (define @t47 () (not @t46)) % 237.58/237.88 (define @t48 () (forall @t12 (or @t47 (= @t2 @t45)))) % 237.58/237.88 (define @t49 () (tptp.subset @t45 @t2)) % 237.58/237.88 (define @t50 () (_ (_ tptp.subset @t41) @t2)) % 237.58/237.88 (define @t51 () (lambda (@list @t1) @t41)) % 237.58/237.88 (define @t52 () (_ @t42 @t2)) % 237.58/237.88 (define @t53 () (_ @t52 @t1)) % 237.58/237.88 (define @t54 () (forall @t12 (_ (_ tptp.subset @t53) @t2))) % 237.58/237.88 (define @t55 () (=> tptp.binintersectLsub @t48)) % 237.58/237.88 (define @t56 () (@var "BOUND_VARIABLE_7526" $$unsorted)) % 237.58/237.88 (define @t57 () (_ (_ tptp.in @t56) @t1)) % 237.58/237.88 (define @t58 () (@list @t56)) % 237.58/237.88 (define @t59 () (lambda @t58 @t57)) % 237.58/237.88 (define @t60 () (_ @t40 @t59)) % 237.58/237.88 (define @t61 () (tptp.in @t56 @t1)) % 237.58/237.88 (define @t62 () (lambda @t58 @t61)) % 237.58/237.88 (define @t63 () (tptp.dsetconstr @t2 @t62)) % 237.58/237.88 (define @t64 () (tptp.in @t4 @t63)) % 237.58/237.88 (define @t65 () (_ @t5 @t60)) % 237.58/237.88 (define @t66 () (not @t6)) % 237.58/237.88 (define @t67 () (tptp.in @t4 @t2)) % 237.58/237.88 (define @t68 () (not @t7)) % 237.58/237.88 (define @t69 () (or @t68 @t66 @t65)) % 237.58/237.88 (define @t70 () (=> @t6 @t65)) % 237.58/237.88 (define @t71 () (=> @t6 (_ @t5 @t41))) % 237.58/237.88 (define @t72 () (=> @t7 @t71)) % 237.58/237.88 (define @t73 () (=> @t6 (_ @t5 @t53))) % 237.58/237.88 (define @t74 () (=> @t7 @t73)) % 237.58/237.88 (define @t75 () (forall @t15 @t74)) % 237.58/237.88 (define @t76 () (=> tptp.binintersectI @t55)) % 237.58/237.88 (define @t77 () (tptp.subset @t1 @t2)) % 237.58/237.88 (define @t78 () (not @t19)) % 237.58/237.88 (define @t79 () (not @t3)) % 237.58/237.88 (define @t80 () (or @t79 @t78 @t18)) % 237.58/237.88 (define @t81 () (=> tptp.setextsub @t76)) % 237.58/237.88 (define @t82 () (or @t79 @t68 @t6)) % 237.58/237.88 (define @t83 () (or @t68 @t6)) % 237.58/237.88 (define @t84 () (=> tptp.subsetE @t81)) % 237.58/237.88 (define @t85 () (not @t67)) % 237.58/237.88 (define @t86 () (forall @t9 (or @t85 @t43))) % 237.58/237.88 (define @t87 () (not @t86)) % 237.58/237.88 (define @t88 () (or @t87 @t3)) % 237.58/237.88 (define @t89 () (=> tptp.subsetI1 @t84)) % 237.58/237.88 (define @t90 () (= @t2 @t41)) % 237.58/237.88 (define @t91 () (or @t79 @t90)) % 237.58/237.88 (define @t92 () (= @t53 @t2)) % 237.58/237.88 (define @t93 () (=> @t3 @t92)) % 237.58/237.88 (define @t94 () (forall @t12 @t93)) % 237.58/237.88 (define @t95 () (=> tptp.binintersectLsub @t94)) % 237.58/237.88 (define @t96 () (=> tptp.binintersectI @t95)) % 237.58/237.88 (define @t97 () (=> tptp.setextsub @t96)) % 237.58/237.88 (define @t98 () (=> tptp.subsetE @t97)) % 237.58/237.88 (define @t99 () (=> tptp.subsetI1 @t98)) % 237.58/237.88 (define @t100 () (@quantifiers_skolemize @t48 1)) % 237.58/237.88 (define @t101 () (tptp.in @t4 @t100)) % 237.58/237.88 (define @t102 () (lambda @t9 @t101)) % 237.58/237.88 (define @t103 () (@purify @t102)) % 237.58/237.88 (define @t104 () (@quantifiers_skolemize @t48 0)) % 237.58/237.88 (define @t105 () (tptp.dsetconstr @t104 @t103)) % 237.58/237.88 (define @t106 () (tptp.subset @t104 @t105)) % 237.58/237.88 (define @t107 () (not @t106)) % 237.58/237.88 (define @t108 () (tptp.subset @t105 @t104)) % 237.58/237.88 (define @t109 () (not @t108)) % 237.58/237.88 (define @t110 () (or @t109 @t107 (= @t105 @t104))) % 237.58/237.88 (define @t111 () (forall @t12 (or @t47 (not @t77) @t18))) % 237.58/237.88 (define @t112 () (= @t104 @t105)) % 237.58/237.88 (define @t113 () (or @t109 @t107 @t112)) % 237.58/237.88 (define @t114 () (@list false)) % 237.58/237.88 (define @t115 () (tptp.dsetconstr @t104 @t102)) % 237.58/237.88 (define @t116 () (tptp.subset @t115 @t104)) % 237.58/237.88 (define @t117 () (forall @t12 @t49)) % 237.58/237.88 (define @t118 () (tptp.subset @t104 @t100)) % 237.58/237.88 (define @t119 () (not @t118)) % 237.58/237.88 (define @t120 () (or @t119 @t112)) % 237.58/237.88 (define @t121 () (not @t120)) % 237.58/237.88 (define @t122 () (not @t48)) % 237.58/237.88 (define @t123 () (= @t104 @t115)) % 237.58/237.88 (define @t124 () (or @t119 @t123)) % 237.58/237.88 (define @t125 () (not @t124)) % 237.58/237.88 (define @t126 () (@list true)) % 237.58/237.88 (define @t127 () (@list @t120)) % 237.58/237.88 (define @t128 () (forall @t9 (or (not (tptp.in @t4 @t104)) (tptp.in @t4 @t105)))) % 237.58/237.88 (define @t129 () (not @t128)) % 237.58/237.88 (define @t130 () (or @t129 @t106)) % 237.58/237.88 (define @t131 () (@quantifiers_skolemize @t128 0)) % 237.58/237.88 (define @t132 () (tptp.in @t131 @t105)) % 237.58/237.88 (define @t133 () (tptp.in @t131 @t104)) % 237.58/237.88 (define @t134 () (not @t133)) % 237.58/237.88 (define @t135 () (or @t134 @t132)) % 237.58/237.88 (define @t136 () (@list @t135)) % 237.58/237.88 (define @t137 () (@const 0 $$unsorted)) % 237.58/237.88 (define @t138 () (tptp.in @t56 @t100)) % 237.58/237.88 (define @t139 () (lambda @t58 @t138)) % 237.58/237.88 (define @t140 () (@purify @t139)) % 237.58/237.88 (define @t141 () (_ @t140 @t137)) % 237.58/237.88 (define @t142 () (_ @t103 @t137)) % 237.58/237.88 (define @t143 () (= @t142 @t141)) % 237.58/237.88 (define @t144 () (_ @t103 @t4)) % 237.58/237.88 (define @t145 () (_ @t102 @t4)) % 237.58/237.88 (define @t146 () (= @t144 @t145)) % 237.58/237.88 (define @t147 () (forall @t9 @t146)) % 237.58/237.88 (define @t148 () (tptp.in @t137 @t100)) % 237.58/237.88 (define @t149 () (forall @t9 (= @t101 @t144))) % 237.58/237.88 (define @t150 () (= @t148 @t142)) % 237.58/237.88 (define @t151 () (@list @t137)) % 237.58/237.88 (define @t152 () (= @t142 @t148)) % 237.58/237.88 (define @t153 () (not @t152)) % 237.58/237.88 (define @t154 () (not @t142)) % 237.58/237.88 (define @t155 () (_ @t140 @t56)) % 237.58/237.88 (define @t156 () (_ @t139 @t56)) % 237.58/237.88 (define @t157 () (= @t155 @t156)) % 237.58/237.88 (define @t158 () (forall @t58 @t157)) % 237.58/237.88 (define @t159 () (forall @t58 (= @t138 @t155))) % 237.58/237.88 (define @t160 () (= @t148 @t141)) % 237.58/237.88 (define @t161 () (= @t141 @t148)) % 237.58/237.88 (define @t162 () (not @t161)) % 237.58/237.88 (define @t163 () (not @t148)) % 237.58/237.88 (define @t164 () (= @t103 @t140)) % 237.58/237.88 (define @t165 () (tptp.dsetconstr @t104 @t140)) % 237.58/237.88 (define @t166 () (tptp.in @t131 @t165)) % 237.58/237.88 (define @t167 () (tptp.dsetconstr @t104 @t139)) % 237.58/237.88 (define @t168 () (tptp.in @t131 @t167)) % 237.58/237.88 (define @t169 () (tptp.in @t131 @t100)) % 237.58/237.88 (define @t170 () (not @t169)) % 237.58/237.88 (define @t171 () (or @t134 @t170 @t168)) % 237.58/237.88 (define @t172 () (forall @t15 (or @t85 (not @t43) @t64))) % 237.58/237.88 (define @t173 () (@list @t104 @t100 @t131)) % 237.58/237.88 (define @t174 () (or @t134 @t170 @t166)) % 237.58/237.88 (define @t175 () (or @t119 @t134 @t169)) % 237.58/237.88 (define @t176 () (@list false false false)) % 237.58/237.88 (assume @p1 @t14) % 237.58/237.88 (assume @p2 @t17) % 237.58/237.88 (assume @p3 @t22) % 237.58/237.88 (assume @p4 @t27) % 237.58/237.88 (assume @p5 @t29) % 237.58/237.88 (assume @p6 @t38) % 237.58/237.88 (assume @p7 true) % 237.58/237.88 (step @p8 (= tptp.binintersect @t42) :rule refl :args (@t42)) % 237.58/237.88 (step @p9 :rule evaluate :args ((= true false))) % 237.58/237.88 (step @p10 :rule refl :args (@t48)) % 237.58/237.88 (step @p11 :rule refl :args ((tptp.subset @t41 @t2))) % 237.58/237.88 (step @p12 :rule refl :args (@t2)) % 237.58/237.88 (step @p13 :rule refl :args ((tptp.dsetconstr @t2 @t39))) % 237.58/237.88 (step @p14 :rule refl :args (@t43)) % 237.58/237.88 (step @p15 :rule cong :premises (@p14) :args (@t44)) % 237.58/237.88 (step @p16 :rule cong :premises (@p12 @p15) :args (@t45)) % 237.58/237.88 (step @p17 :rule trans :premises (@p16 @p13)) % 237.58/237.88 (step @p18 :rule cong :premises (@p17 @p12) :args (@t49)) % 237.58/237.88 (step @p19 :rule trans :premises (@p18 @p11)) % 237.58/237.88 (step @p20 :rule refl :args (tptp.subset)) % 237.58/237.88 (step @p21 :rule ho_cong :premises (@p20 @p17)) % 237.58/237.88 (step @p22 :rule ho_cong :premises (@p21 @p12)) % 237.58/237.88 (step @p23 :rule cong :premises (@p22 @p19) :args ((= (_ (_ tptp.subset @t45) @t2) @t49))) % 237.58/237.88 (step @p24 :rule symm :premises (@p23)) % 237.58/237.88 (step @p25 :rule refl :args (@t50)) % 237.58/237.88 (step @p26 :rule eq_resolve :premises (@p25 @p24)) % 237.58/237.88 (step @p27 :rule refl :args (@t40)) % 237.58/237.88 (step @p28 :rule ho_cong :premises (@p27 @p15)) % 237.58/237.88 (step @p29 :rule cong :premises (@p28 @p17) :args ((= (_ @t40 @t44) @t45))) % 237.58/237.88 (step @p30 :rule symm :premises (@p29)) % 237.58/237.88 (step @p31 :rule refl :args (@t41)) % 237.58/237.88 (step @p32 :rule eq_resolve :premises (@p31 @p30)) % 237.58/237.88 (step @p33 :rule refl :args (@t6)) % 237.58/237.88 (step @p34 :rule cong :premises (@p33 @p14) :args ((= @t6 @t43))) % 237.58/237.88 (step @p35 :rule symm :premises (@p34)) % 237.58/237.88 (step @p36 :rule eq_resolve :premises (@p33 @p35)) % 237.58/237.88 (step @p37 :rule cong :premises (@p36) :args (@t39)) % 237.58/237.88 (step @p38 :rule ho_cong :premises (@p27 @p37)) % 237.58/237.88 (step @p39 :rule trans :premises (@p38 @p32)) % 237.58/237.88 (step @p40 :rule ho_cong :premises (@p20 @p39)) % 237.58/237.88 (step @p41 :rule ho_cong :premises (@p40 @p12)) % 237.58/237.88 (step @p42 :rule trans :premises (@p41 @p26)) % 237.58/237.88 (step @p43 :rule cong :premises (@p42) :args ((forall @t12 @t50))) % 237.58/237.88 (step @p44 :rule refl :args (@t2)) % 237.58/237.88 (step @p45 :rule beta-reduce :args ((= (_ @t51 @t1) @t41))) % 237.58/237.88 (step @p46 :rule refl :args (@t1)) % 237.58/237.88 (step @p47 :rule beta-reduce :args ((= @t52 @t51))) % 237.58/237.88 (step @p48 :rule ho_cong :premises (@p47 @p46)) % 237.58/237.88 (step @p49 :rule trans :premises (@p48 @p45)) % 237.58/237.88 (step @p50 :rule refl :args (tptp.subset)) % 237.58/237.88 (step @p51 :rule ho_cong :premises (@p50 @p49)) % 237.58/237.88 (step @p52 :rule ho_cong :premises (@p51 @p44)) % 237.58/237.88 (step @p53 :rule cong :premises (@p52) :args (@t54)) % 237.58/237.88 (step @p54 :rule trans :premises (@p53 @p43)) % 237.58/237.88 (step @p55 :rule refl :args (tptp.binintersectLsub)) % 237.58/237.88 (step @p56 :rule cong :premises (@p55 @p54) :args ((= tptp.binintersectLsub @t54))) % 237.58/237.88 (step @p57 :rule ho_cong :premises (@p8 @p44)) % 237.58/237.88 (step @p58 :rule ho_cong :premises (@p57 @p46)) % 237.58/237.88 (step @p59 :rule ho_cong :premises (@p50 @p58)) % 237.58/237.88 (step @p60 :rule ho_cong :premises (@p59 @p44)) % 237.58/237.88 (step @p61 :rule cong :premises (@p60) :args (@t28)) % 237.58/237.88 (step @p62 :rule cong :premises (@p55 @p61) :args (@t29)) % 237.58/237.88 (step @p63 :rule trans :premises (@p62 @p56)) % 237.58/237.88 (step @p64 :rule eq_resolve :premises (@p5 @p63)) % 237.58/237.88 (step @p65 :rule cong :premises (@p64 @p10) :args (@t55)) % 237.58/237.88 (step @p66 :rule refl :args ((tptp.in @t4 @t60))) % 237.58/237.88 (step @p67 :rule refl :args ((tptp.dsetconstr @t2 @t59))) % 237.58/237.88 (step @p68 :rule refl :args (@t61)) % 237.58/237.88 (step @p69 :rule cong :premises (@p68) :args (@t62)) % 237.58/237.88 (step @p70 :rule cong :premises (@p12 @p69) :args (@t63)) % 237.58/237.88 (step @p71 :rule trans :premises (@p70 @p67)) % 237.58/237.88 (step @p72 :rule refl :args (@t4)) % 237.58/237.88 (step @p73 :rule cong :premises (@p72 @p71) :args (@t64)) % 237.58/237.88 (step @p74 :rule trans :premises (@p73 @p66)) % 237.58/237.88 (step @p75 :rule refl :args (@t5)) % 237.58/237.88 (step @p76 :rule ho_cong :premises (@p75 @p71)) % 237.58/237.88 (step @p77 :rule cong :premises (@p76 @p74) 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:args ((not @t112) @t126 @t127)) % 237.58/237.88 (step @p288 :rule cnf_or_pos :args (@t113)) % 237.58/237.88 (step @p289 :rule reordering :premises (@p288) :args ((or @t112 @t109 @t107 (not @t113)))) % 237.58/237.88 (step @p290 :rule chain_m_resolution :premises (@p289 @p287 @p267 @p246) :args (@t107 (@list true false false) (@list @t112 @t108 @t113))) % 237.58/237.88 (step @p291 :rule cnf_or_pos :args (@t130)) % 237.58/237.88 (step @p292 :rule reordering :premises (@p291) :args ((or @t106 @t129 (not @t130)))) % 237.58/237.88 (step @p293 :rule chain_m_resolution :premises (@p292 @p290 @p230) :args (@t129 (@list true false) (@list @t106 @t130))) % 237.58/237.88 (step @p294 :rule skolemize :premises (@p293)) % 237.58/237.88 (step @p295 :rule cnf_or_neg :args (@t135 1)) % 237.58/237.88 (step @p296 :rule chain_m_resolution :premises (@p295 @p294) :args ((not @t132) @t126 @t136)) % 237.58/237.88 (step @p297 :rule false_intro :premises (@p296)) % 237.58/237.88 (step @p298 :rule cnf_equiv_neg2 :args (@t143)) % 237.58/237.88 (step @p299 :rule eq-symm :args (@t144 @t101)) % 237.58/237.88 (step @p300 :rule beta-reduce :args ((= @t145 @t101))) % 237.58/237.88 (step @p301 :rule refl :args (@t144)) % 237.58/237.88 (step @p302 :rule cong :premises (@p301 @p300) :args (@t146)) % 237.58/237.88 (step @p303 :rule trans :premises (@p302 @p299)) % 237.58/237.88 (step @p304 :rule cong :premises (@p303) :args (@t147)) % 237.58/237.88 (step @p305 :rule quant-unused-vars :args ((= (forall @t9 true) true))) % 237.58/237.88 (step @p306 :rule eq-refl :args (@t145)) % 237.58/237.88 (step @p307 :rule cong :premises (@p306) :args ((forall @t9 (= @t145 @t145)))) % 237.58/237.88 (step @p308 :rule trans :premises (@p307 @p305)) % 237.58/237.88 (step @p309 :rule refl :args (@t145)) % 237.58/237.88 (step @p310 :rule refl :args (@t4)) % 237.58/237.88 (step @p311 :rule ho_cong :premises (@p252 @p310)) % 237.58/237.88 (step @p312 :rule cong :premises (@p311 @p309) :args (@t146)) % 237.58/237.88 (step @p313 :rule cong :premises (@p312) :args (@t147)) % 237.58/237.88 (step @p314 :rule trans :premises (@p313 @p308)) % 237.58/237.88 (step @p315 :rule true_elim :premises (@p314)) % 237.58/237.88 (step @p316 :rule eq_resolve :premises (@p315 @p304)) % 237.58/237.88 (step @p317 :rule eq-symm :args (@t148 @t142)) % 237.58/237.88 (step @p318 :rule refl :args (@t149)) % 237.58/237.88 (step @p319 :rule cong :premises (@p318 @p317) :args ((=> @t149 @t150))) % 237.58/237.88 (assume-push @p426 @t149) % 237.58/237.88 (step @p321 :rule instantiate :premises (@p316) :args (@t151)) % 237.58/237.88 (step-pop @p427 :rule scope :premises (@p321)) % 237.58/237.88 (step @p322 :rule process_scope :premises (@p427) :args (@t150)) % 237.58/237.88 (step @p324 :rule eq_resolve :premises (@p322 @p319)) % 237.58/237.88 (step @p325 :rule implies_elim :premises (@p324)) % 237.58/237.88 (step @p326 :rule chain_m_resolution :premises (@p325 @p316) :args (@t152 @t114 (@list @t149))) % 237.58/237.88 (step @p327 :rule cnf_equiv_pos1 :args (@t152)) % 237.58/237.88 (step @p328 :rule reordering :premises (@p327) :args ((or @t154 @t148 @t153))) % 237.58/237.88 (step @p329 :rule eq-symm :args (@t155 @t138)) % 237.58/237.88 (step @p330 :rule beta-reduce :args ((= @t156 @t138))) % 237.58/237.88 (step @p331 :rule refl :args (@t155)) % 237.58/237.88 (step @p332 :rule cong :premises (@p331 @p330) :args (@t157)) % 237.58/237.88 (step @p333 :rule trans :premises (@p332 @p329)) % 237.58/237.88 (step @p334 :rule cong :premises (@p333) :args (@t158)) % 237.58/237.88 (step @p335 :rule quant-unused-vars :args ((= (forall @t58 true) true))) % 237.58/237.88 (step @p336 :rule eq-refl :args (@t156)) % 237.58/237.88 (step @p337 :rule cong :premises (@p336) :args ((forall @t58 (= @t156 @t156)))) % 237.58/237.88 (step @p338 :rule trans :premises (@p337 @p335)) % 237.58/237.88 (step @p339 :rule refl :args (@t156)) % 237.58/237.88 (step @p340 :rule refl :args (@t56)) % 237.58/237.88 (step @p341 :rule skolem_intro :args (@t140)) % 237.58/237.88 (step @p342 :rule ho_cong :premises (@p341 @p340)) % 237.58/237.88 (step @p343 :rule cong :premises (@p342 @p339) :args (@t157)) % 237.58/237.88 (step @p344 :rule cong :premises (@p343) :args (@t158)) % 237.58/237.88 (step @p345 :rule trans :premises (@p344 @p338)) % 237.58/237.88 (step @p346 :rule true_elim :premises (@p345)) % 237.58/237.88 (step @p347 :rule eq_resolve :premises (@p346 @p334)) % 237.58/237.88 (step @p348 :rule eq-symm :args (@t148 @t141)) % 237.58/237.88 (step @p349 :rule refl :args (@t159)) % 237.58/237.88 (step @p350 :rule cong :premises (@p349 @p348) :args ((=> @t159 @t160))) % 237.58/237.88 (assume-push @p428 @t159) % 237.58/237.88 (step @p352 :rule instantiate :premises (@p347) :args (@t151)) % 237.58/237.88 (step-pop @p429 :rule scope :premises (@p352)) % 237.58/237.88 (step @p353 :rule process_scope :premises (@p429) :args (@t160)) % 237.58/237.88 (step @p355 :rule eq_resolve :premises (@p353 @p350)) % 237.58/237.88 (step @p356 :rule implies_elim :premises (@p355)) % 237.58/237.88 (step @p357 :rule chain_m_resolution :premises (@p356 @p347) :args (@t161 @t114 (@list @t159))) % 237.58/237.88 (step @p358 :rule cnf_equiv_pos2 :args (@t161)) % 237.58/237.88 (step @p359 :rule reordering :premises (@p358) :args ((or @t141 @t163 @t162))) % 237.58/237.88 (step @p360 :rule chain_m_resolution :premises (@p359 @p357 @p328 @p326 @p298) :args ((or @t143 @t154) (@list false false false true) (@list @t161 @t148 @t152 @t141))) % 237.58/237.88 (step @p361 :rule cnf_equiv_neg1 :args (@t143)) % 237.58/237.88 (step @p362 :rule reordering :premises (@p361) :args ((or @t142 @t141 @t143))) % 237.58/237.88 (step @p363 :rule cnf_equiv_pos2 :args (@t152)) % 237.58/237.88 (step @p364 :rule reordering :premises (@p363) :args ((or @t142 @t163 @t153))) % 237.58/237.88 (step @p365 :rule cnf_equiv_pos1 :args (@t161)) % 237.58/237.88 (step @p366 :rule reordering :premises (@p365) :args ((or (not @t141) @t148 @t162))) % 237.58/237.88 (step @p367 :rule chain_m_resolution :premises (@p366 @p357 @p364 @p326 @p362 @p360) :args (@t143 (@list false true false false true) (@list @t161 @t148 @t152 @t141 @t142))) % 237.58/237.88 ; WARNING: add trust step for TRUST % 237.58/237.88 ; trust TRUST THEORY_LEMMA % 237.58/237.88 (step @p368 :rule trust :premises () :args ((or @t164 (not @t143)))) % 237.58/237.88 (step @p369 :rule chain_m_resolution :premises (@p368 @p367) :args (@t164 @t114 (@list @t143))) % 237.58/237.88 (step @p370 :rule symm :premises (@p369)) % 237.58/237.89 (step @p371 :rule cong :premises (@p250 @p370) :args (@t165)) % 237.58/237.89 (step @p372 :rule refl :args (@t131)) % 237.58/237.89 (step @p373 :rule cong :premises (@p372 @p371) :args (@t166)) % 237.58/237.89 (step @p374 :rule not_implies_elim1 :premises (@p247)) % 237.58/237.89 (step @p375 :rule eq-refl :args (@t139)) % 237.58/237.89 (step @p376 :rule refl :args (@t139)) % 237.58/237.89 (step @p377 :rule cong :premises (@p376 @p341) :args ((= @t139 @t140))) % 237.58/237.89 (step @p378 :rule trans :premises (@p377 @p375)) % 237.58/237.89 (step @p379 :rule true_elim :premises (@p378)) % 237.58/237.89 (step @p380 :rule cong :premises (@p250 @p379) :args (@t167)) % 237.58/237.89 (step @p381 :rule cong :premises (@p372 @p380) :args (@t168)) % 237.58/237.89 (step @p382 :rule refl :args (@t170)) % 237.58/237.89 (step @p383 :rule refl :args (@t134)) % 237.58/237.89 (step @p384 :rule nary_cong :premises (@p383 @p382 @p381) :args (@t171)) % 237.58/237.89 (step @p385 :rule refl :args (@t172)) % 237.58/237.89 (step @p386 :rule cong :premises (@p385 @p384) :args ((=> @t172 @t171))) % 237.58/237.89 (assume-push @p430 @t172) % 237.58/237.89 (step @p388 :rule instantiate :premises (@p374) :args (@t173)) % 237.58/237.89 (step-pop @p431 :rule scope :premises (@p388)) % 237.58/237.89 (step @p389 :rule process_scope :premises (@p431) :args (@t171)) % 237.58/237.89 (step @p391 :rule eq_resolve :premises (@p389 @p386)) % 237.58/237.89 (step @p392 :rule implies_elim :premises (@p391)) % 237.58/237.89 (step @p393 :rule chain_m_resolution :premises (@p392 @p374) :args (@t174 @t114 (@list @t172))) % 237.58/237.89 (step @p394 :rule not_implies_elim1 :premises (@p231)) % 237.58/237.89 (step @p395 :rule instantiate :premises (@p394) :args (@t173)) % 237.58/237.89 (step @p396 :rule bool-double-not-elim :args (@t133)) % 237.58/237.89 (step @p397 :rule refl :args (@t135)) % 237.58/237.89 (step @p398 :rule nary_cong :premises (@p397 @p396) :args ((or @t135 (not @t134)))) % 237.58/237.89 (step @p399 :rule cnf_or_neg :args (@t135 0)) % 237.58/237.89 (step @p400 :rule eq_resolve :premises (@p399 @p398)) % 237.58/237.89 (step @p401 :rule reordering :premises (@p400) :args ((or @t133 @t135))) % 237.58/237.89 (step @p402 :rule chain_m_resolution :premises (@p401 @p294) :args (@t133 @t126 @t136)) % 237.58/237.89 (step @p403 :rule bool-double-not-elim :args (@t118)) % 237.58/237.89 (step @p404 :rule refl :args (@t120)) % 237.58/237.89 (step @p405 :rule nary_cong :premises (@p404 @p403) :args ((or @t120 (not @t119)))) % 237.58/237.89 (step @p406 :rule cnf_or_neg :args (@t120 0)) % 237.58/237.89 (step @p407 :rule eq_resolve :premises (@p406 @p405)) % 237.58/237.89 (step @p408 :rule reordering :premises (@p407) :args ((or @t118 @t120))) % 237.58/237.89 (step @p409 :rule chain_m_resolution :premises (@p408 @p285) :args (@t118 @t126 @t127)) % 237.58/237.89 (step @p410 :rule cnf_or_pos :args (@t175)) % 237.58/237.89 (step @p411 :rule reordering :premises (@p410) :args ((or @t119 @t134 @t169 (not @t175)))) % 237.58/237.89 (step @p412 :rule chain_m_resolution :premises (@p411 @p409 @p402 @p395) :args (@t169 @t176 (@list @t118 @t133 @t175))) % 237.58/237.89 (step @p413 :rule cnf_or_pos :args (@t174)) % 237.58/237.89 (step @p414 :rule reordering :premises (@p413) :args ((or @t134 @t170 @t166 (not @t174)))) % 237.58/237.89 (step @p415 :rule chain_m_resolution :premises (@p414 @p402 @p412 @p393) :args (@t166 @t176 (@list @t133 @t169 @t174))) % 237.58/237.89 (step @p416 :rule true_intro :premises (@p415)) % 237.58/237.89 (step @p417 :rule symm :premises (@p416)) % 237.58/237.89 (step @p418 :rule trans :premises (@p417 @p373 @p297)) % 237.58/237.89 (step @p419 false :rule eq_resolve :premises (@p418 @p9)) % 237.58/237.89 ) % 237.58/237.89 % SZS output end Proof % 237.58/237.89 % cvc5 exiting %------------------------------------------------------------------------------