%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU736^2 : TPTP v9.2.1. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n005.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 08:52:57 AM UTC 2026 % Result : Theorem 0.39s 0.59s % Output : Proof 0.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU736^2 : TPTP v9.2.1. Released v3.7.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n005.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 17:49:33 EDT 2026 % 0.17/0.34 % CPUTime : % 0.30/0.50 %----Proving TH0 % 0.39/0.59 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.39/0.59 % SZS status Theorem % 0.39/0.59 % SZS output start Proof % 0.39/0.59 ( % 0.39/0.59 (declare-sort $$unsorted 0) % 0.39/0.59 (declare-const tptp.contrasubsetT Bool) % 0.39/0.59 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 0.39/0.59 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.39/0.59 (declare-const tptp.setminusI Bool) % 0.39/0.59 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.39/0.59 (declare-const tptp.setminus (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.59 (define @t1 () (@var "B" $$unsorted)) % 0.39/0.59 (define @t2 () (@var "A" $$unsorted)) % 0.39/0.59 (define @t3 () (_ tptp.setminus @t2)) % 0.39/0.59 (define @t4 () (_ @t3 @t1)) % 0.39/0.59 (define @t5 () (@var "Xx" $$unsorted)) % 0.39/0.59 (define @t6 () (_ tptp.in @t5)) % 0.39/0.59 (define @t7 () (_ @t6 @t4)) % 0.39/0.59 (define @t8 () (_ @t6 @t1)) % 0.39/0.59 (define @t9 () (not @t8)) % 0.39/0.59 (define @t10 () (=> @t9 @t7)) % 0.39/0.59 (define @t11 () (_ @t6 @t2)) % 0.39/0.59 (define @t12 () (@list @t2 @t1 @t5)) % 0.39/0.59 (define @t13 () (forall @t12 (=> @t11 @t10))) % 0.39/0.59 (define @t14 () (= tptp.setminusI @t13)) % 0.39/0.59 (define @t15 () (@var "X" $$unsorted)) % 0.39/0.59 (define @t16 () (_ @t6 @t15)) % 0.39/0.59 (define @t17 () (not @t16)) % 0.39/0.59 (define @t18 () (@var "Y" $$unsorted)) % 0.39/0.59 (define @t19 () (_ @t6 @t18)) % 0.39/0.59 (define @t20 () (=> @t19 @t17)) % 0.39/0.59 (define @t21 () (_ @t3 @t18)) % 0.39/0.59 (define @t22 () (_ tptp.subset @t15)) % 0.39/0.59 (define @t23 () (_ @t22 @t21)) % 0.39/0.59 (define @t24 () (=> @t23 @t20)) % 0.39/0.59 (define @t25 () (@list @t5)) % 0.39/0.59 (define @t26 () (forall @t25 (=> @t11 @t24))) % 0.39/0.59 (define @t27 () (_ tptp.powerset @t2)) % 0.39/0.59 (define @t28 () (_ tptp.in @t18)) % 0.39/0.59 (define @t29 () (_ @t28 @t27)) % 0.39/0.59 (define @t30 () (=> @t29 @t26)) % 0.39/0.59 (define @t31 () (@list @t18)) % 0.39/0.59 (define @t32 () (forall @t31 @t30)) % 0.39/0.59 (define @t33 () (_ tptp.in @t15)) % 0.39/0.59 (define @t34 () (_ @t33 @t27)) % 0.39/0.59 (define @t35 () (=> @t34 @t32)) % 0.39/0.59 (define @t36 () (@list @t2 @t15)) % 0.39/0.59 (define @t37 () (forall @t36 @t35)) % 0.39/0.59 (define @t38 () (= tptp.contrasubsetT @t37)) % 0.39/0.59 (define @t39 () (_ @t3 @t15)) % 0.39/0.59 (define @t40 () (_ @t6 @t39)) % 0.39/0.59 (define @t41 () (=> @t19 @t40)) % 0.39/0.59 (define @t42 () (forall @t25 (=> @t11 @t41))) % 0.39/0.59 (define @t43 () (=> @t23 @t42)) % 0.39/0.59 (define @t44 () (=> @t29 @t43)) % 0.39/0.59 (define @t45 () (forall @t31 @t44)) % 0.39/0.59 (define @t46 () (=> @t34 @t45)) % 0.39/0.59 (define @t47 () (forall @t36 @t46)) % 0.39/0.59 (define @t48 () (=> tptp.contrasubsetT @t47)) % 0.39/0.59 (define @t49 () (=> tptp.setminusI @t48)) % 0.39/0.59 (define @t50 () (not @t49)) % 0.39/0.59 (define @t51 () (tptp.setminus @t2 @t15)) % 0.39/0.59 (define @t52 () (@var "BOUND_VARIABLE_7598" $$unsorted)) % 0.39/0.59 (define @t53 () (tptp.in @t52 @t51)) % 0.39/0.59 (define @t54 () (@var "BOUND_VARIABLE_7596" $$unsorted)) % 0.39/0.59 (define @t55 () (not (tptp.in @t52 @t54))) % 0.39/0.59 (define @t56 () (not (tptp.in @t52 @t2))) % 0.39/0.59 (define @t57 () (not (tptp.subset @t15 (tptp.setminus @t2 @t54)))) % 0.39/0.59 (define @t58 () (tptp.powerset @t2)) % 0.39/0.59 (define @t59 () (not (tptp.in @t54 @t58))) % 0.39/0.59 (define @t60 () (tptp.in @t15 @t58)) % 0.39/0.59 (define @t61 () (not @t60)) % 0.39/0.59 (define @t62 () (or @t61 @t59 @t57 @t56 @t55 @t53)) % 0.39/0.59 (define @t63 () (@list @t2 @t15 @t54 @t52)) % 0.39/0.59 (define @t64 () (forall @t63 @t62)) % 0.39/0.59 (define @t65 () (@var "BOUND_VARIABLE_7540" $$unsorted)) % 0.39/0.59 (define @t66 () (not (tptp.in @t65 @t15))) % 0.39/0.59 (define @t67 () (@var "BOUND_VARIABLE_7538" $$unsorted)) % 0.39/0.59 (define @t68 () (not (tptp.in @t65 @t67))) % 0.39/0.59 (define @t69 () (not (tptp.in @t65 @t2))) % 0.39/0.59 (define @t70 () (not (tptp.subset @t15 (tptp.setminus @t2 @t67)))) % 0.39/0.59 (define @t71 () (not (tptp.in @t67 @t58))) % 0.39/0.59 (define @t72 () (or @t61 @t71 @t70 @t69 @t68 @t66)) % 0.39/0.59 (define @t73 () (or @t71 @t70 @t69 @t68 @t66)) % 0.39/0.59 (define @t74 () (or @t61 @t73)) % 0.39/0.59 (define @t75 () (@list @t2 @t15 @t67 @t65)) % 0.39/0.59 (define @t76 () (forall @t75 @t74)) % 0.39/0.59 (define @t77 () (@list @t67 @t65)) % 0.39/0.59 (define @t78 () (forall @t77 @t74)) % 0.39/0.59 (define @t79 () (forall @t77 @t73)) % 0.39/0.59 (define @t80 () (@var "BOUND_VARIABLE_7514" $$unsorted)) % 0.39/0.59 (define @t81 () (or @t61 @t79)) % 0.39/0.59 (define @t82 () (not (tptp.in @t80 @t15))) % 0.39/0.59 (define @t83 () (not (tptp.in @t80 @t18))) % 0.39/0.59 (define @t84 () (not (tptp.in @t80 @t2))) % 0.39/0.59 (define @t85 () (tptp.setminus @t2 @t18)) % 0.39/0.59 (define @t86 () (tptp.subset @t15 @t85)) % 0.39/0.59 (define @t87 () (not @t86)) % 0.39/0.59 (define @t88 () (tptp.in @t18 @t58)) % 0.39/0.59 (define @t89 () (not @t88)) % 0.39/0.59 (define @t90 () (or @t89 @t87 @t84 @t83 @t82)) % 0.39/0.59 (define @t91 () (@list @t18 @t80)) % 0.39/0.59 (define @t92 () (forall @t91 @t90)) % 0.39/0.59 (define @t93 () (not @t34)) % 0.39/0.59 (define @t94 () (or @t93 @t92)) % 0.39/0.59 (define @t95 () (or @t84 @t83 @t82)) % 0.39/0.59 (define @t96 () (or @t89 @t87 @t95)) % 0.39/0.59 (define @t97 () (forall @t91 @t96)) % 0.39/0.59 (define @t98 () (@list @t80)) % 0.39/0.59 (define @t99 () (forall @t98 @t96)) % 0.39/0.59 (define @t100 () (forall @t98 @t95)) % 0.39/0.59 (define @t101 () (@list @t5)) % 0.39/0.59 (define @t102 () (or @t89 @t87 @t100)) % 0.39/0.59 (define @t103 () (tptp.in @t5 @t15)) % 0.39/0.59 (define @t104 () (tptp.in @t5 @t18)) % 0.39/0.59 (define @t105 () (not @t104)) % 0.39/0.59 (define @t106 () (tptp.in @t5 @t2)) % 0.39/0.59 (define @t107 () (not @t106)) % 0.39/0.59 (define @t108 () (forall @t25 (or @t107 @t105 (not @t103)))) % 0.39/0.59 (define @t109 () (not @t23)) % 0.39/0.59 (define @t110 () (not @t29)) % 0.39/0.59 (define @t111 () (or @t110 @t109 @t108)) % 0.39/0.59 (define @t112 () (or @t109 @t108)) % 0.39/0.59 (define @t113 () (not @t19)) % 0.39/0.59 (define @t114 () (not @t11)) % 0.39/0.59 (define @t115 () (or @t114 @t113 @t17)) % 0.39/0.59 (define @t116 () (forall @t25 @t115)) % 0.39/0.59 (define @t117 () (or @t109 @t116)) % 0.39/0.59 (define @t118 () (or @t109 @t115)) % 0.39/0.59 (define @t119 () (or @t114 @t109 @t113 @t17)) % 0.39/0.59 (define @t120 () (or @t109 @t113 @t17)) % 0.39/0.59 (define @t121 () (=> tptp.contrasubsetT @t64)) % 0.39/0.59 (define @t122 () (tptp.setminus @t2 @t1)) % 0.39/0.59 (define @t123 () (tptp.in @t5 @t122)) % 0.39/0.59 (define @t124 () (tptp.in @t5 @t1)) % 0.39/0.59 (define @t125 () (or @t114 @t8 @t7)) % 0.39/0.59 (define @t126 () (=> tptp.setminusI @t121)) % 0.39/0.59 (define @t127 () (or @t59 @t57 @t56 @t55 @t53)) % 0.39/0.59 (define @t128 () (or @t61 @t127)) % 0.39/0.59 (define @t129 () (forall @t63 @t128)) % 0.39/0.59 (define @t130 () (@list @t54 @t52)) % 0.39/0.59 (define @t131 () (forall @t130 @t128)) % 0.39/0.59 (define @t132 () (forall @t130 @t127)) % 0.39/0.59 (define @t133 () (@var "BOUND_VARIABLE_7577" $$unsorted)) % 0.39/0.59 (define @t134 () (or @t61 @t132)) % 0.39/0.59 (define @t135 () (tptp.in @t133 @t51)) % 0.39/0.59 (define @t136 () (not (tptp.in @t133 @t18))) % 0.39/0.59 (define @t137 () (not (tptp.in @t133 @t2))) % 0.39/0.59 (define @t138 () (or @t89 @t87 @t137 @t136 @t135)) % 0.39/0.59 (define @t139 () (@list @t18 @t133)) % 0.39/0.59 (define @t140 () (forall @t139 @t138)) % 0.39/0.59 (define @t141 () (or @t93 @t140)) % 0.39/0.59 (define @t142 () (or @t137 @t136 @t135)) % 0.39/0.59 (define @t143 () (or @t89 @t87 @t142)) % 0.39/0.59 (define @t144 () (forall @t139 @t143)) % 0.39/0.59 (define @t145 () (@list @t133)) % 0.39/0.59 (define @t146 () (forall @t145 @t143)) % 0.39/0.59 (define @t147 () (forall @t145 @t142)) % 0.39/0.59 (define @t148 () (or @t89 @t87 @t147)) % 0.39/0.59 (define @t149 () (tptp.in @t5 @t51)) % 0.39/0.59 (define @t150 () (forall @t25 (or @t107 @t105 @t149))) % 0.39/0.59 (define @t151 () (or @t110 @t109 @t150)) % 0.39/0.59 (define @t152 () (=> @t23 @t150)) % 0.39/0.59 (define @t153 () (or @t114 @t113 @t40)) % 0.39/0.59 (define @t154 () (@quantifiers_skolemize @t64 3)) % 0.39/0.59 (define @t155 () (@quantifiers_skolemize @t64 1)) % 0.39/0.59 (define @t156 () (@quantifiers_skolemize @t64 0)) % 0.39/0.59 (define @t157 () (tptp.in @t154 (tptp.setminus @t156 @t155))) % 0.39/0.59 (define @t158 () (@quantifiers_skolemize @t64 2)) % 0.39/0.59 (define @t159 () (tptp.in @t154 @t158)) % 0.39/0.59 (define @t160 () (not @t159)) % 0.39/0.59 (define @t161 () (tptp.in @t154 @t156)) % 0.39/0.59 (define @t162 () (not @t161)) % 0.39/0.59 (define @t163 () (tptp.subset @t155 (tptp.setminus @t156 @t158))) % 0.39/0.59 (define @t164 () (not @t163)) % 0.39/0.59 (define @t165 () (tptp.powerset @t156)) % 0.39/0.59 (define @t166 () (tptp.in @t158 @t165)) % 0.39/0.59 (define @t167 () (not @t166)) % 0.39/0.59 (define @t168 () (tptp.in @t155 @t165)) % 0.39/0.59 (define @t169 () (not @t168)) % 0.39/0.59 (define @t170 () (or @t169 @t167 @t164 @t162 @t160 @t157)) % 0.39/0.59 (define @t171 () (@list true)) % 0.39/0.59 (define @t172 () (@list @t170)) % 0.39/0.59 (define @t173 () (tptp.in @t154 @t155)) % 0.39/0.59 (define @t174 () (or @t162 @t173 @t157)) % 0.39/0.59 (define @t175 () (not @t173)) % 0.39/0.59 (define @t176 () (or @t169 @t167 @t164 @t162 @t160 @t175)) % 0.39/0.59 (define @t177 () (not @t176)) % 0.39/0.59 (define @t178 () (forall @t75 @t72)) % 0.39/0.59 (assume @p1 @t14) % 0.39/0.59 (assume @p2 @t38) % 0.39/0.59 (assume @p3 @t50) % 0.39/0.59 (assume @p4 true) % 0.39/0.59 (step @p5 :rule refl :args (@t64)) % 0.39/0.59 (step @p6 :rule aci_norm :args ((= @t74 @t72))) % 0.39/0.59 (step @p7 :rule cong :premises (@p6) :args (@t76)) % 0.39/0.59 (step @p8 :rule quant-merge-prenex :args ((= (forall @t36 @t78) @t76))) % 0.39/0.59 (step @p9 :rule alpha_equiv :args (@t79 (@list @t67 @t65) (@list @t18 @t80))) % 0.39/0.59 (step @p10 :rule refl :args (@t61)) % 0.39/0.59 (step @p11 :rule nary_cong :premises (@p10 @p9) :args (@t81)) % 0.39/0.59 (step @p12 :rule quant-miniscope-or :args ((= @t78 @t81))) % 0.39/0.59 (step @p13 :rule trans :premises (@p12 @p11)) % 0.39/0.59 (step @p14 :rule symm :premises (@p13)) % 0.39/0.59 (step @p15 :rule cong :premises (@p14) :args ((forall @t36 (or @t61 @t92)))) % 0.39/0.59 (step @p16 :rule trans :premises (@p15 @p8)) % 0.39/0.59 (step @p17 :rule trans :premises (@p16 @p7)) % 0.39/0.59 (step @p18 :rule refl :args (@t92)) % 0.39/0.59 (step @p19 :rule refl :args ((tptp.in @t15 @t27))) % 0.39/0.59 (step @p20 :rule refl :args (@t58)) % 0.39/0.59 (step @p21 :rule refl :args (@t15)) % 0.39/0.59 (step @p22 :rule cong :premises (@p21 @p20) :args (@t60)) % 0.39/0.59 (step @p23 :rule trans :premises (@p22 @p19)) % 0.39/0.59 (step @p24 :rule refl :args (@t33)) % 0.39/0.59 (step @p25 :rule ho_cong :premises (@p24 @p20)) % 0.39/0.59 (step @p26 :rule cong :premises (@p25 @p23) :args ((= (_ @t33 @t58) @t60))) % 0.39/0.59 (step @p27 :rule symm :premises (@p26)) % 0.39/0.59 (step @p28 :rule refl :args (@t34)) % 0.39/0.59 (step @p29 :rule eq_resolve :premises (@p28 @p27)) % 0.39/0.59 (step @p30 :rule refl :args (@t27)) % 0.39/0.59 (step @p31 :rule cong :premises (@p30 @p20) :args ((= @t27 @t58))) % 0.39/0.59 (step @p32 :rule symm :premises (@p31)) % 0.39/0.59 (step @p33 :rule eq_resolve :premises (@p30 @p32)) % 0.39/0.59 (step @p34 :rule ho_cong :premises (@p24 @p33)) % 0.39/0.59 (step @p35 :rule trans :premises (@p34 @p29)) % 0.39/0.59 (step @p36 :rule cong :premises (@p35) :args (@t93)) % 0.39/0.59 (step @p37 :rule nary_cong :premises (@p36 @p18) :args (@t94)) % 0.39/0.59 (step @p38 :rule cong :premises (@p37) :args ((forall @t36 @t94))) % 0.39/0.59 (step @p39 :rule trans :premises (@p38 @p17)) % 0.39/0.59 (step @p40 :rule bool-impl-elim :args (@t34 @t92)) % 0.39/0.59 (step @p41 :rule cong :premises (@p40) :args ((forall @t36 (=> @t34 @t92)))) % 0.39/0.59 (step @p42 :rule trans :premises (@p41 @p39)) % 0.39/0.59 (step @p43 :rule aci_norm :args ((= @t96 @t90))) % 0.39/0.59 (step @p44 :rule cong :premises (@p43) :args (@t97)) % 0.39/0.59 (step @p45 :rule quant-merge-prenex :args ((= (forall @t31 @t99) @t97))) % 0.39/0.59 (step @p46 :rule alpha_equiv :args (@t100 (@list @t80) @t101)) % 0.39/0.59 (step @p47 :rule refl :args (@t87)) % 0.39/0.59 (step @p48 :rule refl :args (@t89)) % 0.39/0.59 (step @p49 :rule nary_cong :premises (@p48 @p47 @p46) :args (@t102)) % 0.39/0.59 (step @p50 :rule quant-miniscope-or :args ((= @t99 @t102))) % 0.39/0.59 (step @p51 :rule trans :premises (@p50 @p49)) % 0.39/0.59 (step @p52 :rule symm :premises (@p51)) % 0.39/0.59 (step @p53 :rule cong :premises (@p52) :args ((forall @t31 (or @t89 @t87 @t108)))) % 0.39/0.59 (step @p54 :rule trans :premises (@p53 @p45)) % 0.39/0.59 (step @p55 :rule trans :premises (@p54 @p44)) % 0.39/0.59 (step @p56 :rule refl :args (@t108)) % 0.39/0.59 (step @p57 :rule refl :args ((tptp.subset @t15 @t21))) % 0.39/0.59 (step @p58 :rule refl :args (@t85)) % 0.39/0.59 (step @p59 :rule cong :premises (@p21 @p58) :args (@t86)) % 0.39/0.59 (step @p60 :rule trans :premises (@p59 @p57)) % 0.39/0.59 (step @p61 :rule refl :args (@t22)) % 0.39/0.59 (step @p62 :rule ho_cong :premises (@p61 @p58)) % 0.39/0.59 (step @p63 :rule cong :premises (@p62 @p60) :args ((= (_ @t22 @t85) @t86))) % 0.39/0.59 (step @p64 :rule symm :premises (@p63)) % 0.39/0.59 (step @p65 :rule refl :args (@t23)) % 0.39/0.59 (step @p66 :rule eq_resolve :premises (@p65 @p64)) % 0.39/0.59 (step @p67 :rule refl :args (@t21)) % 0.39/0.59 (step @p68 :rule cong :premises (@p67 @p58) :args ((= @t21 @t85))) % 0.39/0.59 (step @p69 :rule symm :premises (@p68)) % 0.39/0.59 (step @p70 :rule eq_resolve :premises (@p67 @p69)) % 0.39/0.59 (step @p71 :rule ho_cong :premises (@p61 @p70)) % 0.39/0.59 (step @p72 :rule trans :premises (@p71 @p66)) % 0.39/0.59 (step @p73 :rule cong :premises (@p72) :args (@t109)) % 0.39/0.59 (step @p74 :rule refl :args ((tptp.in @t18 @t27))) % 0.39/0.59 (step @p75 :rule refl :args (@t18)) % 0.39/0.59 (step @p76 :rule cong :premises (@p75 @p20) :args (@t88)) % 0.39/0.59 (step @p77 :rule trans :premises (@p76 @p74)) % 0.39/0.59 (step @p78 :rule refl :args (@t28)) % 0.39/0.59 (step @p79 :rule ho_cong :premises (@p78 @p20)) % 0.39/0.59 (step @p80 :rule cong :premises (@p79 @p77) :args ((= (_ @t28 @t58) @t88))) % 0.39/0.59 (step @p81 :rule symm :premises (@p80)) % 0.39/0.59 (step @p82 :rule refl :args (@t29)) % 0.39/0.59 (step @p83 :rule eq_resolve :premises (@p82 @p81)) % 0.39/0.59 (step @p84 :rule ho_cong :premises (@p78 @p33)) % 0.39/0.59 (step @p85 :rule trans :premises (@p84 @p83)) % 0.39/0.59 (step @p86 :rule cong :premises (@p85) :args (@t110)) % 0.39/0.59 (step @p87 :rule nary_cong :premises (@p86 @p73 @p56) :args (@t111)) % 0.39/0.59 (step @p88 :rule cong :premises (@p87) :args ((forall @t31 @t111))) % 0.39/0.59 (step @p89 :rule trans :premises (@p88 @p55)) % 0.39/0.59 (step @p90 :rule aci_norm :args ((= (or @t110 @t112) @t111))) % 0.39/0.59 (step @p91 :rule bool-impl-elim :args (@t29 @t112)) % 0.39/0.59 (step @p92 :rule trans :premises (@p91 @p90)) % 0.39/0.59 (step @p93 :rule cong :premises (@p92) :args ((forall @t31 (=> @t29 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% 0.39/0.59 (step @p140 :rule trans :premises (@p139 @p94)) % 0.39/0.59 (step @p141 :rule refl :args (@t34)) % 0.39/0.59 (step @p142 :rule cong :premises (@p141 @p140) :args (@t35)) % 0.39/0.59 (step @p143 :rule cong :premises (@p142) :args (@t37)) % 0.39/0.59 (step @p144 :rule trans :premises (@p143 @p42)) % 0.39/0.59 (step @p145 :rule refl :args (tptp.contrasubsetT)) % 0.39/0.59 (step @p146 :rule cong :premises (@p145 @p144) :args (@t38)) % 0.39/0.59 (step @p147 :rule eq_resolve :premises (@p2 @p146)) % 0.39/0.59 (step @p148 :rule cong :premises (@p147 @p5) :args (@t121)) % 0.39/0.59 (step @p149 :rule refl :args ((tptp.in @t5 @t4))) % 0.39/0.59 (step @p150 :rule refl :args (@t122)) % 0.39/0.59 (step @p151 :rule refl :args (@t5)) % 0.39/0.59 (step @p152 :rule cong :premises (@p151 @p150) :args (@t123)) % 0.39/0.59 (step @p153 :rule trans :premises (@p152 @p149)) % 0.39/0.59 (step @p154 :rule refl :args (@t6)) % 0.39/0.59 (step @p155 :rule ho_cong :premises (@p154 @p150)) % 0.39/0.59 (step @p156 :rule cong :premises (@p155 @p153) :args ((= (_ @t6 @t122) @t123))) % 0.39/0.59 (step @p157 :rule symm :premises (@p156)) % 0.39/0.59 (step @p158 :rule refl :args (@t7)) % 0.39/0.59 (step @p159 :rule eq_resolve :premises (@p158 @p157)) % 0.39/0.59 (step @p160 :rule refl :args (@t4)) % 0.39/0.59 (step @p161 :rule cong :premises (@p160 @p150) :args ((= @t4 @t122))) % 0.39/0.59 (step @p162 :rule symm :premises (@p161)) % 0.39/0.59 (step @p163 :rule eq_resolve :premises (@p160 @p162)) % 0.39/0.59 (step @p164 :rule ho_cong :premises (@p154 @p163)) % 0.39/0.59 (step @p165 :rule trans :premises (@p164 @p159)) % 0.39/0.59 (step @p166 :rule refl :args (@t124)) % 0.39/0.59 (step @p167 :rule refl :args (@t8)) % 0.39/0.59 (step @p168 :rule cong :premises (@p167 @p166) :args ((= @t8 @t124))) % 0.39/0.59 (step @p169 :rule symm :premises (@p168)) % 0.39/0.59 (step @p170 :rule eq_resolve :premises (@p167 @p169)) % 0.39/0.59 (step @p171 :rule nary_cong :premises (@p112 @p170 @p165) :args (@t125)) % 0.39/0.59 (step @p172 :rule cong :premises (@p171) :args ((forall @t12 @t125))) % 0.39/0.59 (step @p173 :rule aci_norm :args ((= (or @t114 (or @t8 @t7)) @t125))) % 0.39/0.59 (step @p174 :rule bool-double-not-elim :args (@t8)) % 0.39/0.59 (step @p175 :rule nary_cong :premises (@p174 @p158) :args ((or (not @t9) @t7))) % 0.39/0.59 (step @p176 :rule bool-impl-elim :args (@t9 @t7)) % 0.39/0.59 (step @p177 :rule trans :premises (@p176 @p175)) % 0.39/0.59 (step @p178 :rule nary_cong :premises (@p130 @p177) :args ((or @t114 @t10))) % 0.39/0.59 (step @p179 :rule trans :premises (@p178 @p173)) % 0.39/0.59 (step @p180 :rule bool-impl-elim :args (@t11 @t10)) % 0.39/0.59 (step @p181 :rule trans :premises (@p180 @p179)) % 0.39/0.59 (step @p182 :rule cong :premises (@p181) :args (@t13)) % 0.39/0.59 (step @p183 :rule trans :premises (@p182 @p172)) % 0.39/0.59 (step @p184 :rule refl :args (tptp.setminusI)) % 0.39/0.59 (step @p185 :rule cong :premises (@p184 @p183) :args (@t14)) % 0.39/0.59 (step @p186 :rule eq_resolve :premises (@p1 @p185)) % 0.39/0.59 (step @p187 :rule cong :premises (@p186 @p148) :args (@t126)) % 0.39/0.59 (step @p188 :rule cong :premises (@p187) :args ((not @t126))) % 0.39/0.59 (step @p189 :rule aci_norm :args ((= @t128 @t62))) % 0.39/0.59 (step @p190 :rule cong :premises (@p189) :args (@t129)) % 0.39/0.59 (step @p191 :rule quant-merge-prenex :args ((= (forall @t36 @t131) @t129))) % 0.39/0.59 (step @p192 :rule alpha_equiv :args (@t132 (@list @t54 @t52) (@list @t18 @t133))) % 0.39/0.59 (step @p193 :rule nary_cong :premises (@p10 @p192) :args (@t134)) % 0.39/0.59 (step @p194 :rule quant-miniscope-or :args ((= @t131 @t134))) % 0.39/0.59 (step @p195 :rule trans :premises (@p194 @p193)) % 0.39/0.59 (step @p196 :rule symm :premises (@p195)) % 0.39/0.59 (step @p197 :rule cong :premises (@p196) :args ((forall @t36 (or @t61 @t140)))) % 0.39/0.59 (step @p198 :rule trans :premises (@p197 @p191)) % 0.39/0.59 (step @p199 :rule trans :premises (@p198 @p190)) % 0.39/0.59 (step @p200 :rule refl :args (@t140)) % 0.39/0.59 (step @p201 :rule nary_cong :premises (@p36 @p200) :args (@t141)) % 0.39/0.59 (step @p202 :rule cong :premises (@p201) :args ((forall @t36 @t141))) % 0.39/0.59 (step @p203 :rule trans :premises (@p202 @p199)) % 0.39/0.59 (step @p204 :rule bool-impl-elim :args (@t34 @t140)) % 0.39/0.59 (step @p205 :rule cong :premises (@p204) :args ((forall @t36 (=> @t34 @t140)))) % 0.39/0.59 (step @p206 :rule trans :premises (@p205 @p203)) % 0.39/0.59 (step @p207 :rule aci_norm :args ((= @t143 @t138))) % 0.39/0.59 (step @p208 :rule cong :premises (@p207) :args (@t144)) % 0.39/0.59 (step @p209 :rule quant-merge-prenex :args ((= (forall @t31 @t146) @t144))) % 0.39/0.59 (step @p210 :rule alpha_equiv :args (@t147 (@list @t133) @t101)) % 0.39/0.59 (step @p211 :rule nary_cong :premises (@p48 @p47 @p210) :args (@t148)) % 0.39/0.60 (step @p212 :rule quant-miniscope-or :args ((= @t146 @t148))) % 0.39/0.60 (step @p213 :rule trans :premises (@p212 @p211)) % 0.39/0.60 (step @p214 :rule symm :premises (@p213)) % 0.39/0.60 (step @p215 :rule cong :premises (@p214) :args ((forall @t31 (or @t89 @t87 @t150)))) % 0.39/0.60 (step @p216 :rule trans :premises (@p215 @p209)) % 0.39/0.60 (step @p217 :rule trans :premises (@p216 @p208)) % 0.39/0.60 (step @p218 :rule refl :args (@t150)) % 0.39/0.60 (step @p219 :rule nary_cong :premises (@p86 @p73 @p218) :args (@t151)) % 0.39/0.60 (step @p220 :rule cong :premises (@p219) :args ((forall @t31 @t151))) % 0.39/0.60 (step @p221 :rule trans :premises (@p220 @p217)) % 0.39/0.60 (step @p222 :rule aci_norm :args ((= (or @t110 (or @t109 @t150)) @t151))) % 0.39/0.60 (step @p223 :rule bool-impl-elim :args (@t23 @t150)) % 0.39/0.60 (step @p224 :rule refl :args (@t110)) % 0.39/0.60 (step @p225 :rule nary_cong :premises (@p224 @p223) :args ((or @t110 @t152))) % 0.39/0.60 (step @p226 :rule trans :premises (@p225 @p222)) % 0.39/0.60 (step @p227 :rule bool-impl-elim :args (@t29 @t152)) % 0.39/0.60 (step @p228 :rule trans :premises (@p227 @p226)) % 0.39/0.60 (step @p229 :rule cong :premises (@p228) :args ((forall @t31 (=> @t29 @t152)))) % 0.39/0.60 (step @p230 :rule trans :premises (@p229 @p221)) % 0.39/0.60 (step @p231 :rule refl :args ((tptp.in @t5 @t39))) % 0.39/0.60 (step @p232 :rule refl :args (@t51)) % 0.39/0.60 (step @p233 :rule cong :premises (@p151 @p232) :args (@t149)) % 0.39/0.60 (step @p234 :rule trans :premises (@p233 @p231)) % 0.39/0.60 (step @p235 :rule ho_cong :premises (@p154 @p232)) % 0.39/0.60 (step @p236 :rule cong :premises (@p235 @p234) :args ((= (_ @t6 @t51) @t149))) % 0.39/0.60 (step @p237 :rule symm :premises (@p236)) % 0.39/0.60 (step @p238 :rule refl :args (@t40)) % 0.39/0.60 (step @p239 :rule eq_resolve :premises (@p238 @p237)) % 0.39/0.60 (step @p240 :rule refl :args (@t39)) % 0.39/0.60 (step @p241 :rule cong :premises (@p240 @p232) :args ((= @t39 @t51))) % 0.39/0.60 (step @p242 :rule symm :premises (@p241)) % 0.39/0.60 (step @p243 :rule eq_resolve :premises (@p240 @p242)) % 0.39/0.60 (step @p244 :rule ho_cong :premises (@p154 @p243)) % 0.39/0.60 (step @p245 :rule trans :premises (@p244 @p239)) % 0.39/0.60 (step @p246 :rule nary_cong :premises (@p112 @p106 @p245) :args (@t153)) % 0.39/0.60 (step @p247 :rule cong :premises (@p246) :args ((forall @t25 @t153))) % 0.39/0.60 (step @p248 :rule aci_norm :args ((= (or @t114 (or @t113 @t40)) @t153))) % 0.39/0.60 (step @p249 :rule bool-impl-elim :args (@t19 @t40)) % 0.39/0.60 (step @p250 :rule nary_cong :premises (@p130 @p249) :args ((or @t114 @t41))) % 0.39/0.60 (step @p251 :rule trans :premises (@p250 @p248)) % 0.39/0.60 (step @p252 :rule bool-impl-elim :args (@t11 @t41)) % 0.39/0.60 (step @p253 :rule trans :premises (@p252 @p251)) % 0.39/0.60 (step @p254 :rule cong :premises (@p253) :args (@t42)) % 0.39/0.60 (step @p255 :rule trans :premises (@p254 @p247)) % 0.39/0.60 (step @p256 :rule refl :args (@t23)) % 0.39/0.60 (step @p257 :rule cong :premises (@p256 @p255) :args (@t43)) % 0.39/0.60 (step @p258 :rule cong :premises (@p137 @p257) :args (@t44)) % 0.39/0.60 (step @p259 :rule cong :premises (@p258) :args (@t45)) % 0.39/0.60 (step @p260 :rule trans :premises (@p259 @p230)) % 0.39/0.60 (step @p261 :rule cong :premises (@p141 @p260) :args (@t46)) % 0.39/0.60 (step @p262 :rule cong :premises (@p261) :args (@t47)) % 0.39/0.60 (step @p263 :rule trans :premises (@p262 @p206)) % 0.39/0.60 (step @p264 :rule cong :premises (@p145 @p263) :args (@t48)) % 0.39/0.60 (step @p265 :rule cong :premises (@p184 @p264) :args (@t49)) % 0.39/0.60 (step @p266 :rule cong :premises (@p265) :args (@t50)) % 0.39/0.60 (step @p267 :rule trans :premises (@p266 @p188)) % 0.39/0.60 (step @p268 :rule eq_resolve :premises (@p3 @p267)) % 0.39/0.60 (step @p269 :rule not_implies_elim2 :premises (@p268)) % 0.39/0.60 (step @p270 :rule not_implies_elim1 :premises (@p269)) % 0.39/0.60 (step @p271 :rule not_implies_elim1 :premises (@p268)) % 0.39/0.60 (step @p272 :rule instantiate :premises (@p271) :args ((@list @t156 @t155 @t154))) % 0.39/0.60 (step @p273 :rule not_implies_elim2 :premises (@p269)) % 0.39/0.60 (step @p274 :rule skolemize :premises (@p273)) % 0.39/0.60 (step @p275 :rule cnf_or_neg :args (@t170 5)) % 0.39/0.60 (step @p276 :rule chain_m_resolution :premises (@p275 @p274) :args ((not @t157) @t171 @t172)) % 0.39/0.60 (step @p277 :rule bool-double-not-elim :args (@t161)) % 0.39/0.60 (step @p278 :rule refl :args (@t170)) % 0.39/0.60 (step @p279 :rule nary_cong :premises (@p278 @p277) :args ((or @t170 (not @t162)))) % 0.39/0.60 (step @p280 :rule cnf_or_neg :args (@t170 3)) % 0.39/0.60 (step @p281 :rule eq_resolve :premises (@p280 @p279)) % 0.39/0.60 (step @p282 :rule reordering :premises (@p281) :args ((or @t161 @t170))) % 0.39/0.60 (step @p283 :rule chain_m_resolution :premises (@p282 @p274) :args (@t161 @t171 @t172)) % 0.39/0.60 (step @p284 :rule cnf_or_pos :args (@t174)) % 0.39/0.60 (step @p285 :rule reordering :premises (@p284) :args ((or @t162 @t157 @t173 (not @t174)))) % 0.39/0.60 (step @p286 :rule chain_m_resolution :premises (@p285 @p283 @p276 @p272) :args (@t173 (@list false true false) (@list @t161 @t157 @t174))) % 0.39/0.60 (step @p287 :rule bool-double-not-elim :args (@t159)) % 0.39/0.60 (step @p288 :rule nary_cong :premises (@p278 @p287) :args ((or @t170 (not @t160)))) % 0.39/0.60 (step @p289 :rule cnf_or_neg :args (@t170 4)) % 0.39/0.60 (step @p290 :rule eq_resolve :premises (@p289 @p288)) % 0.39/0.60 (step @p291 :rule reordering :premises (@p290) :args ((or @t159 @t170))) % 0.39/0.60 (step @p292 :rule chain_m_resolution :premises (@p291 @p274) :args (@t159 @t171 @t172)) % 0.39/0.60 (step @p293 :rule bool-double-not-elim :args (@t163)) % 0.39/0.60 (step @p294 :rule nary_cong :premises (@p278 @p293) :args ((or @t170 (not @t164)))) % 0.39/0.60 (step @p295 :rule cnf_or_neg :args (@t170 2)) % 0.39/0.60 (step @p296 :rule eq_resolve :premises (@p295 @p294)) % 0.39/0.60 (step @p297 :rule reordering :premises (@p296) :args ((or @t163 @t170))) % 0.39/0.60 (step @p298 :rule chain_m_resolution :premises (@p297 @p274) :args (@t163 @t171 @t172)) % 0.39/0.60 (step @p299 :rule bool-double-not-elim :args (@t166)) % 0.39/0.60 (step @p300 :rule nary_cong :premises (@p278 @p299) :args ((or @t170 (not @t167)))) % 0.39/0.60 (step @p301 :rule cnf_or_neg :args (@t170 1)) % 0.39/0.60 (step @p302 :rule eq_resolve :premises (@p301 @p300)) % 0.39/0.60 (step @p303 :rule reordering :premises (@p302) :args ((or @t166 @t170))) % 0.39/0.60 (step @p304 :rule chain_m_resolution :premises (@p303 @p274) :args (@t166 @t171 @t172)) % 0.39/0.60 (step @p305 :rule bool-double-not-elim :args (@t168)) % 0.39/0.60 (step @p306 :rule nary_cong :premises (@p278 @p305) :args ((or @t170 (not @t169)))) % 0.39/0.60 (step @p307 :rule cnf_or_neg :args (@t170 0)) % 0.39/0.60 (step @p308 :rule eq_resolve :premises (@p307 @p306)) % 0.39/0.60 (step @p309 :rule reordering :premises (@p308) :args ((or @t168 @t170))) % 0.39/0.60 (step @p310 :rule chain_m_resolution :premises (@p309 @p274) :args (@t168 @t171 @t172)) % 0.39/0.60 (step @p311 :rule cnf_or_pos :args (@t176)) % 0.39/0.60 (step @p312 :rule reordering :premises (@p311) :args ((or @t169 @t167 @t164 @t162 @t160 @t175 @t177))) % 0.39/0.60 (step @p313 :rule chain_m_resolution :premises (@p312 @p310 @p304 @p298 @p283 @p292 @p286) :args (@t177 (@list false false false false false false) (@list @t168 @t166 @t163 @t161 @t159 @t173))) % 0.39/0.60 (assume-push @p320 @t178) % 0.39/0.60 (step @p315 :rule instantiate :premises (@p270) :args ((@list @t156 @t155 @t158 @t154))) % 0.39/0.60 (step-pop @p321 :rule scope :premises (@p315)) % 0.39/0.60 (step @p316 :rule process_scope :premises (@p321) :args (@t176)) % 0.39/0.60 (step @p318 :rule implies_elim :premises (@p316)) % 0.39/0.60 (step @p319 false :rule chain_m_resolution :premises (@p318 @p313 @p270) :args (false (@list true false) (@list @t176 @t178))) % 0.39/0.60 ) % 0.39/0.60 % SZS output end Proof % 0.39/0.60 % cvc5 exiting %------------------------------------------------------------------------------