%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU813^2 : 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 : n013.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 08:53:19 AM UTC 2026 % Result : Theorem 0.37s 0.59s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU813^2 : 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 : n013.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 17:54:00 EDT 2026 % 0.17/0.34 % CPUTime : % 0.31/0.49 %----Proving TH0 % 0.37/0.59 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.37/0.59 % SZS status Theorem % 0.37/0.59 % SZS output start Proof % 0.37/0.59 ( % 0.37/0.59 (declare-sort $$unsorted 0) % 0.37/0.59 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.37/0.59 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.37/0.59 (declare-const tptp.transitivesetOp1 Bool) % 0.37/0.59 (declare-const tptp.binintersectER Bool) % 0.37/0.59 (declare-const tptp.binintersectEL Bool) % 0.37/0.59 (declare-const tptp.binintersectSubset5 Bool) % 0.37/0.59 (declare-const tptp.binintersect (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.59 (define tptp.transitiveset () (let ((_let_1 (@var "A" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (lambda (@list _let_1) (forall (@list _let_2) (=> (_ (_ tptp.in _let_2) _let_1) (_ (_ tptp.subset _let_2) _let_1))))))) % 0.37/0.59 (define @t1 () (@var "B" $$unsorted)) % 0.37/0.59 (define @t2 () (@var "A" $$unsorted)) % 0.37/0.59 (define @t3 () (_ (_ tptp.binintersect @t2) @t1)) % 0.37/0.59 (define @t4 () (@var "C" $$unsorted)) % 0.37/0.59 (define @t5 () (_ tptp.subset @t4)) % 0.37/0.59 (define @t6 () (_ @t5 @t3)) % 0.37/0.59 (define @t7 () (_ @t5 @t1)) % 0.37/0.59 (define @t8 () (=> @t7 @t6)) % 0.37/0.59 (define @t9 () (_ @t5 @t2)) % 0.37/0.59 (define @t10 () (@list @t2 @t1 @t4)) % 0.37/0.59 (define @t11 () (forall @t10 (=> @t9 @t8))) % 0.37/0.59 (define @t12 () (= tptp.binintersectSubset5 @t11)) % 0.37/0.59 (define @t13 () (@var "Xx" $$unsorted)) % 0.37/0.59 (define @t14 () (_ tptp.in @t13)) % 0.37/0.59 (define @t15 () (_ @t14 @t2)) % 0.37/0.59 (define @t16 () (_ @t14 @t3)) % 0.37/0.59 (define @t17 () (@list @t2 @t1 @t13)) % 0.37/0.59 (define @t18 () (forall @t17 (=> @t16 @t15))) % 0.37/0.59 (define @t19 () (= tptp.binintersectEL @t18)) % 0.37/0.59 (define @t20 () (_ @t14 @t1)) % 0.37/0.59 (define @t21 () (forall @t17 (=> @t16 @t20))) % 0.37/0.59 (define @t22 () (= tptp.binintersectER @t21)) % 0.37/0.59 (define @t23 () (@var "X" $$unsorted)) % 0.37/0.59 (define @t24 () (_ (_ tptp.subset @t2) @t23)) % 0.37/0.59 (define @t25 () (_ (_ tptp.in @t2) @t23)) % 0.37/0.59 (define @t26 () (@list @t2)) % 0.37/0.59 (define @t27 () (forall @t26 (=> @t25 @t24))) % 0.37/0.59 (define @t28 () (_ tptp.transitiveset @t23)) % 0.37/0.59 (define @t29 () (=> @t28 @t27)) % 0.37/0.59 (define @t30 () (@list @t23)) % 0.37/0.59 (define @t31 () (forall @t30 @t29)) % 0.37/0.59 (define @t32 () (= tptp.transitivesetOp1 @t31)) % 0.37/0.59 (define @t33 () (@var "Y" $$unsorted)) % 0.37/0.59 (define @t34 () (_ (_ tptp.binintersect @t23) @t33)) % 0.37/0.59 (define @t35 () (=> (_ tptp.transitiveset @t33) (_ tptp.transitiveset @t34))) % 0.37/0.59 (define @t36 () (@list @t33)) % 0.37/0.59 (define @t37 () (forall @t36 @t35)) % 0.37/0.59 (define @t38 () (=> @t28 @t37)) % 0.37/0.59 (define @t39 () (forall @t30 @t38)) % 0.37/0.59 (define @t40 () (=> tptp.transitivesetOp1 @t39)) % 0.37/0.59 (define @t41 () (=> tptp.binintersectER @t40)) % 0.37/0.59 (define @t42 () (=> tptp.binintersectEL @t41)) % 0.37/0.59 (define @t43 () (=> tptp.binintersectSubset5 @t42)) % 0.37/0.59 (define @t44 () (not @t43)) % 0.37/0.59 (define @t45 () (_ (_ tptp.subset @t23) @t2)) % 0.37/0.59 (define @t46 () (_ (_ tptp.in @t23) @t2)) % 0.37/0.59 (define @t47 () (forall @t30 (=> @t46 @t45))) % 0.37/0.59 (define @t48 () (lambda @t26 @t47)) % 0.37/0.59 (define @t49 () (@var "BOUND_VARIABLE_7647" $$unsorted)) % 0.37/0.59 (define @t50 () (tptp.binintersect @t23 @t49)) % 0.37/0.59 (define @t51 () (@var "BOUND_VARIABLE_7649" $$unsorted)) % 0.37/0.59 (define @t52 () (tptp.subset @t51 @t50)) % 0.37/0.59 (define @t53 () (not (tptp.in @t51 @t50))) % 0.37/0.59 (define @t54 () (@var "BOUND_VARIABLE_7632" $$unsorted)) % 0.37/0.59 (define @t55 () (@list @t54)) % 0.37/0.59 (define @t56 () (not (forall @t55 (or (not (tptp.in @t54 @t49)) (tptp.subset @t54 @t49))))) % 0.37/0.59 (define @t57 () (@var "BOUND_VARIABLE_7536" $$unsorted)) % 0.37/0.59 (define @t58 () (@list @t57)) % 0.37/0.59 (define @t59 () (forall @t58 (or (not (tptp.in @t57 @t23)) (tptp.subset @t57 @t23)))) % 0.37/0.59 (define @t60 () (not @t59)) % 0.37/0.59 (define @t61 () (or @t60 @t56 @t53 @t52)) % 0.37/0.59 (define @t62 () (@list @t23 @t49 @t51)) % 0.37/0.59 (define @t63 () (forall @t62 @t61)) % 0.37/0.59 (define @t64 () (@var "BOUND_VARIABLE_7564" $$unsorted)) % 0.37/0.59 (define @t65 () (tptp.subset @t64 @t23)) % 0.37/0.59 (define @t66 () (not (tptp.in @t64 @t23))) % 0.37/0.59 (define @t67 () (or @t66 @t65)) % 0.37/0.59 (define @t68 () (or @t60 @t67)) % 0.37/0.59 (define @t69 () (forall (@list @t23 @t64) @t68)) % 0.37/0.59 (define @t70 () (@list @t64)) % 0.37/0.59 (define @t71 () (forall @t70 @t68)) % 0.37/0.59 (define @t72 () (forall @t70 @t67)) % 0.37/0.59 (define @t73 () (or @t60 @t72)) % 0.37/0.59 (define @t74 () (tptp.subset @t2 @t23)) % 0.37/0.59 (define @t75 () (tptp.in @t2 @t23)) % 0.37/0.59 (define @t76 () (forall @t26 (or (not @t75) @t74))) % 0.37/0.59 (define @t77 () (not @t25)) % 0.37/0.59 (define @t78 () (or @t77 @t24)) % 0.37/0.59 (define @t79 () (tptp.subset @t23 @t2)) % 0.37/0.59 (define @t80 () (tptp.in @t23 @t2)) % 0.37/0.59 (define @t81 () (forall @t30 (or (not @t80) @t79))) % 0.37/0.59 (define @t82 () (@list @t23)) % 0.37/0.59 (define @t83 () (lambda @t26 @t81)) % 0.37/0.59 (define @t84 () (_ @t83 @t23)) % 0.37/0.59 (define @t85 () (=> @t84 @t27)) % 0.37/0.59 (define @t86 () (forall @t30 @t85)) % 0.37/0.59 (define @t87 () (not @t46)) % 0.37/0.59 (define @t88 () (or @t87 @t45)) % 0.37/0.59 (define @t89 () (=> tptp.transitivesetOp1 @t63)) % 0.37/0.59 (define @t90 () (tptp.in @t13 @t1)) % 0.37/0.59 (define @t91 () (tptp.binintersect @t2 @t1)) % 0.37/0.59 (define @t92 () (tptp.in @t13 @t91)) % 0.37/0.59 (define @t93 () (not @t16)) % 0.37/0.59 (define @t94 () (or @t93 @t20)) % 0.37/0.59 (define @t95 () (=> tptp.binintersectER @t89)) % 0.37/0.59 (define @t96 () (tptp.in @t13 @t2)) % 0.37/0.59 (define @t97 () (or @t93 @t15)) % 0.37/0.59 (define @t98 () (=> tptp.binintersectEL @t95)) % 0.37/0.59 (define @t99 () (tptp.subset @t4 @t91)) % 0.37/0.59 (define @t100 () (tptp.subset @t4 @t1)) % 0.37/0.59 (define @t101 () (not @t7)) % 0.37/0.59 (define @t102 () (tptp.subset @t4 @t2)) % 0.37/0.59 (define @t103 () (not @t9)) % 0.37/0.59 (define @t104 () (or @t103 @t101 @t6)) % 0.37/0.59 (define @t105 () (=> tptp.binintersectSubset5 @t98)) % 0.37/0.59 (define @t106 () (or @t56 @t53 @t52)) % 0.37/0.59 (define @t107 () (or @t60 @t106)) % 0.37/0.59 (define @t108 () (forall @t62 @t107)) % 0.37/0.59 (define @t109 () (@list @t49 @t51)) % 0.37/0.59 (define @t110 () (forall @t109 @t107)) % 0.37/0.59 (define @t111 () (forall @t109 @t106)) % 0.37/0.59 (define @t112 () (@var "BOUND_VARIABLE_7619" $$unsorted)) % 0.37/0.59 (define @t113 () (or @t60 @t111)) % 0.37/0.59 (define @t114 () (tptp.binintersect @t23 @t33)) % 0.37/0.59 (define @t115 () (tptp.subset @t112 @t114)) % 0.37/0.59 (define @t116 () (not (tptp.in @t112 @t114))) % 0.37/0.59 (define @t117 () (@list @t33 @t112)) % 0.37/0.59 (define @t118 () (forall @t117 (or (not (forall @t55 (or (not (tptp.in @t54 @t33)) (tptp.subset @t54 @t33)))) @t116 @t115))) % 0.37/0.59 (define @t119 () (forall @t30 (or (not (tptp.in @t23 @t33)) (tptp.subset @t23 @t33)))) % 0.37/0.59 (define @t120 () (not @t119)) % 0.37/0.59 (define @t121 () (or @t120 @t116 @t115)) % 0.37/0.59 (define @t122 () (forall @t117 @t121)) % 0.37/0.59 (define @t123 () (=> @t59 @t122)) % 0.37/0.59 (define @t124 () (or @t116 @t115)) % 0.37/0.59 (define @t125 () (or @t120 @t124)) % 0.37/0.59 (define @t126 () (forall @t117 @t125)) % 0.37/0.59 (define @t127 () (@list @t112)) % 0.37/0.59 (define @t128 () (forall @t127 @t125)) % 0.37/0.59 (define @t129 () (forall @t127 @t124)) % 0.37/0.59 (define @t130 () (@var "BOUND_VARIABLE_7593" $$unsorted)) % 0.37/0.59 (define @t131 () (@list @t130)) % 0.37/0.59 (define @t132 () (or @t120 @t129)) % 0.37/0.59 (define @t133 () (@list @t130)) % 0.37/0.59 (define @t134 () (forall @t133 (or (not (tptp.in @t130 @t114)) (tptp.subset @t130 @t114)))) % 0.37/0.59 (define @t135 () (tptp.subset @t130 @t34)) % 0.37/0.59 (define @t136 () (tptp.in @t130 @t34)) % 0.37/0.59 (define @t137 () (not @t136)) % 0.37/0.59 (define @t138 () (or @t137 @t135)) % 0.37/0.59 (define @t139 () (forall @t133 @t138)) % 0.37/0.59 (define @t140 () (_ @t83 @t33)) % 0.37/0.59 (define @t141 () (=> @t140 (_ @t83 @t34))) % 0.37/0.59 (define @t142 () (forall @t36 @t141)) % 0.37/0.59 (define @t143 () (=> @t84 @t142)) % 0.37/0.59 (define @t144 () (forall @t30 @t143)) % 0.37/0.59 (define @t145 () (=> tptp.transitivesetOp1 @t144)) % 0.37/0.59 (define @t146 () (=> tptp.binintersectER @t145)) % 0.37/0.59 (define @t147 () (=> tptp.binintersectEL @t146)) % 0.37/0.59 (define @t148 () (=> tptp.binintersectSubset5 @t147)) % 0.37/0.59 (define @t149 () (@quantifiers_skolemize @t63 1)) % 0.37/0.59 (define @t150 () (forall @t55 (or (not (tptp.in @t54 @t149)) (tptp.subset @t54 @t149)))) % 0.37/0.59 (define @t151 () (@quantifiers_skolemize @t63 0)) % 0.37/0.59 (define @t152 () (tptp.binintersect @t151 @t149)) % 0.37/0.59 (define @t153 () (@quantifiers_skolemize @t63 2)) % 0.37/0.59 (define @t154 () (tptp.subset @t153 @t152)) % 0.37/0.59 (define @t155 () (tptp.in @t153 @t152)) % 0.37/0.59 (define @t156 () (not @t155)) % 0.37/0.59 (define @t157 () (not @t150)) % 0.37/0.59 (define @t158 () (forall @t58 (or (not (tptp.in @t57 @t151)) (tptp.subset @t57 @t151)))) % 0.37/0.59 (define @t159 () (not @t158)) % 0.37/0.59 (define @t160 () (or @t159 @t157 @t156 @t154)) % 0.37/0.59 (define @t161 () (@list true)) % 0.37/0.59 (define @t162 () (@list @t160)) % 0.37/0.59 (define @t163 () (@list @t151 @t149 @t153)) % 0.37/0.59 (define @t164 () (tptp.in @t153 @t149)) % 0.37/0.59 (define @t165 () (or @t156 @t164)) % 0.37/0.59 (define @t166 () (@list false false)) % 0.37/0.59 (define @t167 () (@list @t153)) % 0.37/0.59 (define @t168 () (tptp.in @t153 @t151)) % 0.37/0.59 (define @t169 () (or @t156 @t168)) % 0.37/0.59 (define @t170 () (tptp.subset @t153 @t151)) % 0.37/0.59 (define @t171 () (not @t168)) % 0.37/0.59 (define @t172 () (or @t171 @t170)) % 0.37/0.59 (define @t173 () (tptp.subset @t153 @t149)) % 0.37/0.59 (define @t174 () (not @t173)) % 0.37/0.59 (define @t175 () (not @t170)) % 0.37/0.59 (define @t176 () (or @t175 @t174 @t154)) % 0.37/0.59 (define @t177 () (not @t164)) % 0.37/0.59 (define @t178 () (or @t177 @t173)) % 0.37/0.59 (define @t179 () (not @t178)) % 0.37/0.59 (define @t180 () (@list true false)) % 0.37/0.59 (assume @p1 @t12) % 0.37/0.59 (assume @p2 @t19) % 0.37/0.59 (assume @p3 @t22) % 0.37/0.59 (assume @p4 @t32) % 0.37/0.59 (assume @p5 @t44) % 0.37/0.59 (assume @p6 true) % 0.37/0.59 (step @p7 (= tptp.transitiveset @t48) :rule refl :args (@t48)) % 0.37/0.59 (step @p8 :rule refl :args (@t63)) % 0.37/0.59 (step @p9 :rule aci_norm :args ((= @t68 (or @t60 @t66 @t65)))) % 0.37/0.59 (step @p10 :rule cong :premises (@p9) :args (@t69)) % 0.37/0.59 (step @p11 :rule quant-merge-prenex :args ((= (forall @t30 @t71) @t69))) % 0.37/0.59 (step @p12 :rule alpha_equiv :args (@t72 (@list @t64) (@list @t2))) % 0.37/0.59 (step @p13 :rule refl :args (@t60)) % 0.37/0.59 (step @p14 :rule nary_cong :premises (@p13 @p12) :args (@t73)) % 0.37/0.59 (step @p15 :rule quant-miniscope-or :args ((= @t71 @t73))) % 0.37/0.59 (step @p16 :rule trans :premises (@p15 @p14)) % 0.37/0.59 (step @p17 :rule symm :premises (@p16)) % 0.37/0.59 (step @p18 :rule cong :premises (@p17) :args ((forall @t30 (or @t60 @t76)))) % 0.37/0.59 (step @p19 :rule trans :premises (@p18 @p11)) % 0.37/0.59 (step @p20 :rule trans :premises (@p19 @p10)) % 0.37/0.59 (step @p21 :rule bool-impl-elim :args (@t59 @t76)) % 0.37/0.59 (step @p22 :rule cong :premises (@p21) :args ((forall @t30 (=> @t59 @t76)))) % 0.37/0.59 (step @p23 :rule trans :premises (@p22 @p20)) % 0.37/0.59 (step @p24 :rule refl :args (@t74)) % 0.37/0.59 (step @p25 :rule refl :args (@t24)) % 0.37/0.59 (step @p26 :rule cong :premises (@p25 @p24) :args ((= @t24 @t74))) % 0.37/0.59 (step @p27 :rule symm :premises (@p26)) % 0.37/0.59 (step @p28 :rule eq_resolve :premises (@p25 @p27)) % 0.37/0.59 (step @p29 :rule refl :args (@t75)) % 0.37/0.59 (step @p30 :rule refl :args (@t25)) % 0.37/0.59 (step @p31 :rule cong :premises (@p30 @p29) :args ((= @t25 @t75))) % 0.37/0.59 (step @p32 :rule symm :premises (@p31)) % 0.37/0.59 (step @p33 :rule eq_resolve :premises (@p30 @p32)) % 0.37/0.59 (step @p34 :rule cong :premises (@p33) :args (@t77)) % 0.37/0.59 (step @p35 :rule nary_cong :premises (@p34 @p28) :args (@t78)) % 0.37/0.59 (step @p36 :rule cong :premises (@p35) :args ((forall @t26 @t78))) % 0.37/0.59 (step @p37 :rule bool-impl-elim :args (@t25 @t24)) % 0.37/0.59 (step @p38 :rule cong :premises (@p37) :args (@t27)) % 0.37/0.59 (step @p39 :rule trans :premises (@p38 @p36)) % 0.37/0.59 (step @p40 :rule beta-reduce :args ((= (_ (lambda @t26 (forall @t58 (or (not (tptp.in @t57 @t2)) (tptp.subset @t57 @t2)))) @t23) @t59))) % 0.37/0.59 (step @p41 :rule refl :args (@t23)) % 0.37/0.59 (step @p42 :rule alpha_equiv :args (@t81 @t82 (@list @t57))) % 0.37/0.59 (step @p43 :rule cong :premises (@p42) :args (@t83)) % 0.37/0.59 (step @p44 :rule ho_cong :premises (@p43 @p41)) % 0.37/0.59 (step @p45 :rule trans :premises (@p44 @p40)) % 0.37/0.59 (step @p46 :rule cong :premises (@p45 @p39) :args (@t85)) % 0.37/0.59 (step @p47 :rule cong :premises (@p46) :args (@t86)) % 0.37/0.59 (step @p48 :rule trans :premises (@p47 @p23)) % 0.37/0.59 (step @p49 :rule refl :args (tptp.transitivesetOp1)) % 0.37/0.59 (step @p50 :rule cong :premises (@p49 @p48) :args ((= tptp.transitivesetOp1 @t86))) % 0.37/0.59 (step @p51 :rule refl :args (@t27)) % 0.37/0.59 (step @p52 :rule refl :args (@t23)) % 0.37/0.59 (step @p53 :rule refl :args (@t79)) % 0.37/0.59 (step @p54 :rule refl :args (@t45)) % 0.37/0.59 (step @p55 :rule cong :premises (@p54 @p53) :args ((= @t45 @t79))) % 0.37/0.59 (step @p56 :rule symm :premises (@p55)) % 0.37/0.59 (step @p57 :rule eq_resolve :premises (@p54 @p56)) % 0.37/0.59 (step @p58 :rule refl :args (@t80)) % 0.37/0.59 (step @p59 :rule refl :args (@t46)) % 0.37/0.59 (step @p60 :rule cong :premises (@p59 @p58) :args ((= @t46 @t80))) % 0.37/0.59 (step @p61 :rule symm :premises (@p60)) % 0.37/0.59 (step @p62 :rule eq_resolve :premises (@p59 @p61)) % 0.37/0.59 (step @p63 :rule cong :premises (@p62) :args (@t87)) % 0.37/0.59 (step @p64 :rule nary_cong :premises (@p63 @p57) :args (@t88)) % 0.37/0.59 (step @p65 :rule cong :premises (@p64) :args ((forall @t30 @t88))) % 0.37/0.59 (step @p66 :rule bool-impl-elim :args (@t46 @t45)) % 0.37/0.59 (step @p67 :rule cong :premises (@p66) :args (@t47)) % 0.37/0.59 (step @p68 :rule trans :premises (@p67 @p65)) % 0.37/0.59 (step @p69 :rule cong :premises (@p68) :args (@t48)) % 0.37/0.59 (step @p70 :rule trans :premises (@p7 @p69)) % 0.37/0.59 (step @p71 :rule ho_cong :premises (@p70 @p52)) % 0.37/0.59 (step @p72 :rule cong :premises (@p71 @p51) :args (@t29)) % 0.37/0.59 (step @p73 :rule cong :premises (@p72) :args (@t31)) % 0.37/0.59 (step @p74 :rule cong :premises (@p49 @p73) :args (@t32)) % 0.37/0.59 (step @p75 :rule trans :premises (@p74 @p50)) % 0.37/0.59 (step @p76 :rule eq_resolve :premises (@p4 @p75)) % 0.37/0.59 (step @p77 :rule cong :premises (@p76 @p8) :args (@t89)) % 0.37/0.59 (step @p78 :rule refl :args (@t90)) % 0.37/0.59 (step @p79 :rule refl :args (@t20)) % 0.37/0.59 (step @p80 :rule cong :premises (@p79 @p78) :args ((= @t20 @t90))) % 0.37/0.59 (step @p81 :rule symm :premises (@p80)) % 0.37/0.59 (step @p82 :rule eq_resolve :premises (@p79 @p81)) % 0.37/0.59 (step @p83 :rule refl :args ((tptp.in @t13 @t3))) % 0.37/0.59 (step @p84 :rule refl :args (@t91)) % 0.37/0.59 (step @p85 :rule refl :args (@t13)) % 0.37/0.59 (step @p86 :rule cong :premises (@p85 @p84) :args (@t92)) % 0.37/0.59 (step @p87 :rule trans :premises (@p86 @p83)) % 0.37/0.59 (step @p88 :rule refl :args (@t14)) % 0.37/0.59 (step @p89 :rule ho_cong :premises (@p88 @p84)) % 0.37/0.59 (step @p90 :rule cong :premises (@p89 @p87) :args ((= (_ @t14 @t91) @t92))) % 0.37/0.59 (step @p91 :rule symm :premises (@p90)) % 0.37/0.59 (step @p92 :rule refl :args (@t16)) % 0.37/0.59 (step @p93 :rule eq_resolve :premises (@p92 @p91)) % 0.37/0.59 (step @p94 :rule refl :args (@t3)) % 0.37/0.59 (step @p95 :rule cong :premises (@p94 @p84) :args ((= @t3 @t91))) % 0.37/0.59 (step @p96 :rule symm :premises (@p95)) % 0.37/0.59 (step @p97 :rule eq_resolve :premises (@p94 @p96)) % 0.37/0.59 (step @p98 :rule ho_cong :premises (@p88 @p97)) % 0.37/0.59 (step @p99 :rule trans :premises (@p98 @p93)) % 0.37/0.59 (step @p100 :rule cong :premises (@p99) :args (@t93)) % 0.37/0.59 (step @p101 :rule nary_cong :premises (@p100 @p82) :args (@t94)) % 0.37/0.59 (step @p102 :rule cong :premises (@p101) :args ((forall @t17 @t94))) % 0.37/0.59 (step @p103 :rule bool-impl-elim :args (@t16 @t20)) % 0.37/0.59 (step @p104 :rule cong :premises (@p103) :args (@t21)) % 0.37/0.59 (step @p105 :rule trans :premises (@p104 @p102)) % 0.37/0.59 (step @p106 :rule refl :args (tptp.binintersectER)) % 0.37/0.59 (step @p107 :rule cong :premises (@p106 @p105) :args (@t22)) % 0.37/0.59 (step @p108 :rule eq_resolve :premises (@p3 @p107)) % 0.37/0.59 (step @p109 :rule cong :premises (@p108 @p77) :args (@t95)) % 0.37/0.59 (step @p110 :rule refl :args (@t96)) % 0.37/0.59 (step @p111 :rule refl :args (@t15)) % 0.37/0.59 (step @p112 :rule cong :premises (@p111 @p110) :args ((= @t15 @t96))) % 0.37/0.59 (step @p113 :rule symm :premises (@p112)) % 0.37/0.59 (step @p114 :rule eq_resolve :premises (@p111 @p113)) % 0.37/0.59 (step @p115 :rule nary_cong :premises (@p100 @p114) :args (@t97)) % 0.37/0.59 (step @p116 :rule cong :premises (@p115) :args ((forall @t17 @t97))) % 0.37/0.59 (step @p117 :rule bool-impl-elim :args (@t16 @t15)) % 0.37/0.59 (step @p118 :rule cong :premises (@p117) :args (@t18)) % 0.37/0.59 (step @p119 :rule trans :premises (@p118 @p116)) % 0.37/0.59 (step @p120 :rule refl :args (tptp.binintersectEL)) % 0.37/0.59 (step @p121 :rule cong :premises (@p120 @p119) :args (@t19)) % 0.37/0.59 (step @p122 :rule eq_resolve :premises (@p2 @p121)) % 0.37/0.59 (step @p123 :rule cong :premises (@p122 @p109) :args (@t98)) % 0.37/0.59 (step @p124 :rule refl :args ((tptp.subset @t4 @t3))) % 0.37/0.59 (step @p125 :rule refl :args (@t4)) % 0.37/0.59 (step @p126 :rule cong :premises (@p125 @p84) :args (@t99)) % 0.37/0.59 (step @p127 :rule trans :premises (@p126 @p124)) % 0.37/0.59 (step @p128 :rule refl :args (@t5)) % 0.37/0.59 (step @p129 :rule ho_cong :premises (@p128 @p84)) % 0.37/0.59 (step @p130 :rule cong :premises (@p129 @p127) :args ((= (_ @t5 @t91) @t99))) % 0.37/0.59 (step @p131 :rule symm :premises (@p130)) % 0.37/0.59 (step @p132 :rule refl :args (@t6)) % 0.37/0.59 (step @p133 :rule eq_resolve :premises (@p132 @p131)) % 0.37/0.59 (step @p134 :rule ho_cong :premises (@p128 @p97)) % 0.37/0.59 (step @p135 :rule trans :premises (@p134 @p133)) % 0.37/0.59 (step @p136 :rule refl :args (@t100)) % 0.37/0.59 (step @p137 :rule refl :args (@t7)) % 0.37/0.59 (step @p138 :rule cong :premises (@p137 @p136) :args ((= @t7 @t100))) % 0.37/0.59 (step @p139 :rule symm :premises (@p138)) % 0.37/0.59 (step @p140 :rule eq_resolve :premises (@p137 @p139)) % 0.37/0.59 (step @p141 :rule cong :premises (@p140) :args (@t101)) % 0.37/0.59 (step @p142 :rule refl :args (@t102)) % 0.37/0.59 (step @p143 :rule refl :args (@t9)) % 0.37/0.59 (step @p144 :rule cong :premises (@p143 @p142) :args ((= @t9 @t102))) % 0.37/0.59 (step @p145 :rule symm :premises (@p144)) % 0.37/0.59 (step @p146 :rule eq_resolve :premises (@p143 @p145)) % 0.37/0.59 (step @p147 :rule cong :premises (@p146) :args (@t103)) % 0.37/0.59 (step @p148 :rule nary_cong :premises (@p147 @p141 @p135) :args (@t104)) % 0.37/0.59 (step @p149 :rule cong :premises (@p148) :args ((forall @t10 @t104))) % 0.37/0.59 (step @p150 :rule aci_norm :args ((= (or @t103 (or @t101 @t6)) @t104))) % 0.37/0.59 (step @p151 :rule bool-impl-elim :args (@t7 @t6)) % 0.37/0.59 (step @p152 :rule refl :args (@t103)) % 0.37/0.59 (step @p153 :rule nary_cong :premises (@p152 @p151) :args ((or @t103 @t8))) % 0.37/0.59 (step @p154 :rule trans :premises (@p153 @p150)) % 0.37/0.59 (step @p155 :rule bool-impl-elim :args (@t9 @t8)) % 0.37/0.59 (step @p156 :rule trans :premises (@p155 @p154)) % 0.37/0.59 (step @p157 :rule cong :premises (@p156) :args (@t11)) % 0.37/0.59 (step @p158 :rule trans :premises (@p157 @p149)) % 0.37/0.59 (step @p159 :rule refl :args (tptp.binintersectSubset5)) % 0.37/0.59 (step @p160 :rule cong :premises (@p159 @p158) :args (@t12)) % 0.37/0.59 (step @p161 :rule eq_resolve :premises (@p1 @p160)) % 0.37/0.59 (step @p162 :rule cong :premises (@p161 @p123) :args (@t105)) % 0.37/0.59 (step @p163 :rule cong :premises (@p162) :args ((not @t105))) % 0.37/0.59 (step @p164 :rule aci_norm :args ((= @t107 @t61))) % 0.37/0.59 (step @p165 :rule cong :premises (@p164) :args (@t108)) % 0.37/0.59 (step @p166 :rule quant-merge-prenex :args ((= (forall @t30 @t110) @t108))) % 0.37/0.59 (step @p167 :rule alpha_equiv :args (@t111 (@list @t49 @t51) (@list @t33 @t112))) % 0.37/0.59 (step @p168 :rule nary_cong :premises (@p13 @p167) :args (@t113)) % 0.37/0.59 (step @p169 :rule quant-miniscope-or :args ((= @t110 @t113))) % 0.37/0.59 (step @p170 :rule trans :premises (@p169 @p168)) % 0.37/0.59 (step @p171 :rule symm :premises (@p170)) % 0.37/0.59 (step @p172 :rule cong :premises (@p171) :args ((forall @t30 (or @t60 @t118)))) % 0.37/0.59 (step @p173 :rule trans :premises (@p172 @p166)) % 0.37/0.59 (step @p174 :rule trans :premises (@p173 @p165)) % 0.37/0.59 (step @p175 :rule bool-impl-elim :args (@t59 @t118)) % 0.37/0.59 (step @p176 :rule cong :premises (@p175) :args ((forall @t30 (=> @t59 @t118)))) % 0.37/0.59 (step @p177 :rule trans :premises (@p176 @p174)) % 0.37/0.59 (step @p178 :rule refl :args (@t115)) % 0.37/0.59 (step @p179 :rule refl :args (@t116)) % 0.37/0.59 (step @p180 :rule alpha_equiv :args (@t119 @t82 (@list @t54))) % 0.37/0.59 (step @p181 :rule cong :premises (@p180) :args (@t120)) % 0.37/0.59 (step @p182 :rule nary_cong :premises (@p181 @p179 @p178) :args (@t121)) % 0.37/0.59 (step @p183 :rule cong :premises (@p182) :args (@t122)) % 0.37/0.59 (step @p184 :rule refl :args (@t59)) % 0.37/0.59 (step @p185 :rule cong :premises (@p184 @p183) :args (@t123)) % 0.37/0.59 (step @p186 :rule cong :premises (@p185) :args ((forall @t30 @t123))) % 0.37/0.59 (step @p187 :rule trans :premises (@p186 @p177)) % 0.37/0.59 (step @p188 :rule aci_norm :args ((= @t125 @t121))) % 0.37/0.59 (step @p189 :rule cong :premises (@p188) :args (@t126)) % 0.37/0.59 (step @p190 :rule quant-merge-prenex :args ((= (forall @t36 @t128) @t126))) % 0.37/0.59 (step @p191 :rule alpha_equiv :args (@t129 (@list @t112) @t131)) % 0.37/0.59 (step @p192 :rule refl :args (@t120)) % 0.37/0.59 (step @p193 :rule nary_cong :premises (@p192 @p191) :args (@t132)) % 0.37/0.59 (step @p194 :rule quant-miniscope-or :args ((= @t128 @t132))) % 0.37/0.59 (step @p195 :rule trans :premises (@p194 @p193)) % 0.37/0.59 (step @p196 :rule symm :premises (@p195)) % 0.37/0.59 (step @p197 :rule cong :premises (@p196) :args ((forall @t36 (or @t120 @t134)))) % 0.37/0.59 (step @p198 :rule trans :premises (@p197 @p190)) % 0.37/0.59 (step @p199 :rule trans :premises (@p198 @p189)) % 0.37/0.59 (step @p200 :rule bool-impl-elim :args (@t119 @t134)) % 0.37/0.59 (step @p201 :rule cong :premises (@p200) :args ((forall @t36 (=> @t119 @t134)))) % 0.37/0.59 (step @p202 :rule trans :premises (@p201 @p199)) % 0.37/0.59 (step @p203 :rule refl :args (@t114)) % 0.37/0.59 (step @p204 :rule refl :args (@t34)) % 0.37/0.59 (step @p205 :rule cong :premises (@p204 @p203) :args ((= @t34 @t114))) % 0.37/0.59 (step @p206 :rule symm :premises (@p205)) % 0.37/0.59 (step @p207 :rule eq_resolve :premises (@p204 @p206)) % 0.37/0.59 (step @p208 :rule refl :args (@t130)) % 0.37/0.59 (step @p209 :rule cong :premises (@p208 @p207) :args (@t135)) % 0.37/0.59 (step @p210 :rule cong :premises (@p208 @p207) :args (@t136)) % 0.37/0.59 (step @p211 :rule cong :premises (@p210) :args (@t137)) % 0.37/0.59 (step @p212 :rule nary_cong :premises (@p211 @p209) :args (@t138)) % 0.37/0.59 (step @p213 :rule cong :premises (@p212) :args (@t139)) % 0.37/0.59 (step @p214 :rule beta-reduce :args ((= (_ (lambda @t26 (forall @t133 (or (not (tptp.in @t130 @t2)) (tptp.subset @t130 @t2)))) @t34) @t139))) % 0.37/0.59 (step @p215 :rule trans :premises (@p214 @p213)) % 0.37/0.59 (step @p216 :rule alpha_equiv :args (@t81 @t82 @t131)) % 0.37/0.59 (step @p217 :rule cong :premises (@p216) :args (@t83)) % 0.37/0.59 (step @p218 :rule ho_cong :premises (@p217 @p204)) % 0.37/0.59 (step @p219 :rule trans :premises (@p218 @p215)) % 0.37/0.59 (step @p220 :rule beta-reduce :args ((= @t140 @t119))) % 0.37/0.59 (step @p221 :rule cong :premises (@p220 @p219) :args (@t141)) % 0.37/0.59 (step @p222 :rule cong :premises (@p221) :args (@t142)) % 0.37/0.59 (step @p223 :rule trans :premises (@p222 @p202)) % 0.37/0.59 (step @p224 :rule cong :premises (@p45 @p223) :args (@t143)) % 0.37/0.59 (step @p225 :rule cong :premises (@p224) :args (@t144)) % 0.37/0.59 (step @p226 :rule trans :premises (@p225 @p187)) % 0.37/0.59 (step @p227 :rule cong :premises (@p49 @p226) :args (@t145)) % 0.37/0.59 (step @p228 :rule cong :premises (@p106 @p227) :args (@t146)) % 0.37/0.59 (step @p229 :rule cong :premises (@p120 @p228) :args (@t147)) % 0.37/0.59 (step @p230 :rule cong :premises (@p159 @p229) :args (@t148)) % 0.37/0.59 (step @p231 :rule cong :premises (@p230) :args ((not @t148))) % 0.37/0.59 (step @p232 :rule refl :args (@t34)) % 0.37/0.59 (step @p233 :rule ho_cong :premises (@p70 @p232)) % 0.37/0.59 (step @p234 :rule refl :args (@t33)) % 0.37/0.59 (step @p235 :rule ho_cong :premises (@p70 @p234)) % 0.37/0.59 (step @p236 :rule cong :premises (@p235 @p233) :args (@t35)) % 0.37/0.59 (step @p237 :rule cong :premises (@p236) :args (@t37)) % 0.37/0.59 (step @p238 :rule cong :premises (@p71 @p237) :args (@t38)) % 0.37/0.59 (step @p239 :rule cong :premises (@p238) :args (@t39)) % 0.37/0.59 (step @p240 :rule cong :premises (@p49 @p239) :args (@t40)) % 0.37/0.59 (step @p241 :rule cong :premises (@p106 @p240) :args (@t41)) % 0.37/0.59 (step @p242 :rule cong :premises (@p120 @p241) :args (@t42)) % 0.37/0.59 (step @p243 :rule cong :premises (@p159 @p242) :args (@t43)) % 0.37/0.59 (step @p244 :rule cong :premises (@p243) :args (@t44)) % 0.37/0.59 (step @p245 :rule trans :premises (@p244 @p231)) % 0.37/0.59 (step @p246 :rule trans :premises (@p245 @p163)) % 0.37/0.59 (step @p247 :rule eq_resolve :premises (@p5 @p246)) % 0.37/0.59 (step @p248 :rule not_implies_elim2 :premises (@p247)) % 0.37/0.59 (step @p249 :rule not_implies_elim2 :premises (@p248)) % 0.37/0.59 (step @p250 :rule not_implies_elim2 :premises (@p249)) % 0.37/0.59 (step @p251 :rule not_implies_elim2 :premises (@p250)) % 0.37/0.59 (step @p252 :rule skolemize :premises (@p251)) % 0.37/0.59 (step @p253 :rule bool-double-not-elim :args (@t150)) % 0.37/0.59 (step @p254 :rule refl :args (@t160)) % 0.37/0.59 (step @p255 :rule nary_cong :premises (@p254 @p253) :args ((or @t160 (not @t157)))) % 0.37/0.59 (step @p256 :rule cnf_or_neg :args (@t160 1)) % 0.37/0.59 (step @p257 :rule eq_resolve :premises (@p256 @p255)) % 0.37/0.59 (step @p258 :rule reordering :premises (@p257) :args ((or @t150 @t160))) % 0.37/0.59 (step @p259 :rule chain_m_resolution :premises (@p258 @p252) :args (@t150 @t161 @t162)) % 0.37/0.59 (step @p260 :rule not_implies_elim1 :premises (@p249)) % 0.37/0.59 (step @p261 :rule instantiate :premises (@p260) :args (@t163)) % 0.37/0.59 (step @p262 :rule bool-double-not-elim :args (@t155)) % 0.37/0.59 (step @p263 :rule nary_cong :premises (@p254 @p262) :args ((or @t160 (not @t156)))) % 0.37/0.59 (step @p264 :rule cnf_or_neg :args (@t160 2)) % 0.37/0.59 (step @p265 :rule eq_resolve :premises (@p264 @p263)) % 0.37/0.59 (step @p266 :rule reordering :premises (@p265) :args ((or @t155 @t160))) % 0.37/0.59 (step @p267 :rule chain_m_resolution :premises (@p266 @p252) :args (@t155 @t161 @t162)) % 0.37/0.59 (step @p268 :rule cnf_or_pos :args (@t165)) % 0.37/0.59 (step @p269 :rule reordering :premises (@p268) :args ((or @t156 @t164 (not @t165)))) % 0.37/0.59 (step @p270 :rule chain_m_resolution :premises (@p269 @p267 @p261) :args (@t164 @t166 (@list @t155 @t165))) % 0.37/0.59 (step @p271 :rule not_implies_elim1 :premises (@p247)) % 0.37/0.59 (step @p272 :rule instantiate :premises (@p271) :args (@t163)) % 0.37/0.59 (step @p273 :rule bool-double-not-elim :args (@t158)) % 0.37/0.59 (step @p274 :rule nary_cong :premises (@p254 @p273) :args ((or @t160 (not @t159)))) % 0.37/0.59 (step @p275 :rule cnf_or_neg :args (@t160 0)) % 0.37/0.59 (step @p276 :rule eq_resolve :premises (@p275 @p274)) % 0.37/0.59 (step @p277 :rule reordering :premises (@p276) :args ((or @t158 @t160))) % 0.37/0.59 (step @p278 :rule chain_m_resolution :premises (@p277 @p252) :args (@t158 @t161 @t162)) % 0.37/0.59 (step @p279 :rule instantiate :premises (@p278) :args (@t167)) % 0.37/0.59 (step @p280 :rule not_implies_elim1 :premises (@p248)) % 0.37/0.59 (step @p281 :rule instantiate :premises (@p280) :args (@t163)) % 0.37/0.59 (step @p282 :rule cnf_or_pos :args (@t169)) % 0.37/0.59 (step @p283 :rule reordering :premises (@p282) :args ((or @t156 @t168 (not @t169)))) % 0.37/0.59 (step @p284 :rule chain_m_resolution :premises (@p283 @p267 @p281) :args (@t168 @t166 (@list @t155 @t169))) % 0.37/0.59 (step @p285 :rule cnf_or_pos :args (@t172)) % 0.37/0.59 (step @p286 :rule reordering :premises (@p285) :args ((or @t170 @t171 (not @t172)))) % 0.37/0.59 (step @p287 :rule chain_m_resolution :premises (@p286 @p284 @p279) :args (@t170 @t166 (@list @t168 @t172))) % 0.37/0.59 (step @p288 :rule cnf_or_neg :args (@t160 3)) % 0.37/0.59 (step @p289 :rule chain_m_resolution :premises (@p288 @p252) :args ((not @t154) @t161 @t162)) % 0.37/0.59 (step @p290 :rule cnf_or_pos :args (@t176)) % 0.37/0.59 (step @p291 :rule reordering :premises (@p290) :args ((or @t154 @t175 @t174 (not @t176)))) % 0.37/0.59 (step @p292 :rule chain_m_resolution :premises (@p291 @p289 @p287 @p272) :args (@t174 (@list true false false) (@list @t154 @t170 @t176))) % 0.37/0.59 (step @p293 :rule cnf_or_pos :args (@t178)) % 0.37/0.59 (step @p294 :rule reordering :premises (@p293) :args ((or @t173 @t177 @t179))) % 0.37/0.59 (step @p295 :rule chain_m_resolution :premises (@p294 @p292 @p270) :args (@t179 @t180 (@list @t173 @t164))) % 0.37/0.59 (assume-push @p302 @t150) % 0.37/0.59 (step @p297 :rule instantiate :premises (@p259) :args (@t167)) % 0.37/0.59 (step-pop @p303 :rule scope :premises (@p297)) % 0.37/0.59 (step @p298 :rule process_scope :premises (@p303) :args (@t178)) % 0.37/0.59 (step @p300 :rule implies_elim :premises (@p298)) % 0.37/0.59 (step @p301 false :rule chain_m_resolution :premises (@p300 @p295 @p259) :args (false @t180 (@list @t178 @t150))) % 0.37/0.59 ) % 0.37/0.59 % SZS output end Proof % 0.37/0.60 % cvc5 exiting %------------------------------------------------------------------------------