%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU711^2 : 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 : n004.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 08:52:50 AM UTC 2026 % Result : Theorem 0.37s 0.57s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU711^2 : TPTP v9.2.1. Released v3.7.0. % 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n004.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 17:48:07 EDT 2026 % 0.17/0.34 % CPUTime : % 0.29/0.48 %----Proving TH0 % 0.37/0.57 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.37/0.57 % SZS status Theorem % 0.37/0.57 % SZS output start Proof % 0.37/0.57 ( % 0.37/0.57 (declare-sort $$unsorted 0) % 0.37/0.57 (declare-const tptp.binunionEcases Bool) % 0.37/0.57 (declare-const tptp.binunion (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.57 (declare-const tptp.powersetI Bool) % 0.37/0.57 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.37/0.57 (declare-const tptp.powersetE Bool) % 0.37/0.57 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 0.37/0.57 (define @t1 () (@var "A" $$unsorted)) % 0.37/0.57 (define @t2 () (_ tptp.powerset @t1)) % 0.37/0.57 (define @t3 () (@var "B" $$unsorted)) % 0.37/0.57 (define @t4 () (_ tptp.in @t3)) % 0.37/0.57 (define @t5 () (_ @t4 @t2)) % 0.37/0.57 (define @t6 () (@var "Xx" $$unsorted)) % 0.37/0.57 (define @t7 () (_ tptp.in @t6)) % 0.37/0.57 (define @t8 () (_ @t7 @t1)) % 0.37/0.57 (define @t9 () (_ @t7 @t3)) % 0.37/0.57 (define @t10 () (=> @t9 @t8)) % 0.37/0.57 (define @t11 () (@list @t6)) % 0.37/0.57 (define @t12 () (forall @t11 @t10)) % 0.37/0.57 (define @t13 () (=> @t12 @t5)) % 0.37/0.57 (define @t14 () (@list @t1 @t3)) % 0.37/0.57 (define @t15 () (forall @t14 @t13)) % 0.37/0.57 (define @t16 () (= tptp.powersetI @t15)) % 0.37/0.57 (define @t17 () (@list @t1 @t3 @t6)) % 0.37/0.57 (define @t18 () (forall @t17 (=> @t5 @t10))) % 0.37/0.57 (define @t19 () (= tptp.powersetE @t18)) % 0.37/0.57 (define @t20 () (@var "Xphi" Bool)) % 0.37/0.57 (define @t21 () (=> @t9 @t20)) % 0.37/0.57 (define @t22 () (=> @t21 @t20)) % 0.37/0.57 (define @t23 () (=> @t8 @t20)) % 0.37/0.57 (define @t24 () (=> @t23 @t22)) % 0.37/0.57 (define @t25 () (_ (_ tptp.binunion @t1) @t3)) % 0.37/0.57 (define @t26 () (_ @t7 @t25)) % 0.37/0.57 (define @t27 () (@list @t1 @t3 @t6 @t20)) % 0.37/0.57 (define @t28 () (forall @t27 (=> @t26 @t24))) % 0.37/0.57 (define @t29 () (= tptp.binunionEcases @t28)) % 0.37/0.57 (define @t30 () (@var "Y" $$unsorted)) % 0.37/0.57 (define @t31 () (@var "X" $$unsorted)) % 0.37/0.57 (define @t32 () (_ (_ tptp.binunion @t31) @t30)) % 0.37/0.57 (define @t33 () (_ (_ tptp.in @t32) @t2)) % 0.37/0.57 (define @t34 () (_ tptp.in @t30)) % 0.37/0.57 (define @t35 () (_ @t34 @t2)) % 0.37/0.57 (define @t36 () (@list @t30)) % 0.37/0.57 (define @t37 () (forall @t36 (=> @t35 @t33))) % 0.37/0.57 (define @t38 () (_ tptp.in @t31)) % 0.37/0.57 (define @t39 () (_ @t38 @t2)) % 0.37/0.57 (define @t40 () (=> @t39 @t37)) % 0.37/0.57 (define @t41 () (@list @t1 @t31)) % 0.37/0.57 (define @t42 () (forall @t41 @t40)) % 0.37/0.57 (define @t43 () (=> tptp.binunionEcases @t42)) % 0.37/0.57 (define @t44 () (=> tptp.powersetE @t43)) % 0.37/0.57 (define @t45 () (=> tptp.powersetI @t44)) % 0.37/0.57 (define @t46 () (not @t45)) % 0.37/0.57 (define @t47 () (tptp.powerset @t1)) % 0.37/0.57 (define @t48 () (@var "BOUND_VARIABLE_7547" $$unsorted)) % 0.37/0.57 (define @t49 () (tptp.in (tptp.binunion @t31 @t48) @t47)) % 0.37/0.57 (define @t50 () (not (tptp.in @t48 @t47))) % 0.37/0.57 (define @t51 () (tptp.in @t31 @t47)) % 0.37/0.57 (define @t52 () (not @t51)) % 0.37/0.57 (define @t53 () (or @t52 @t50 @t49)) % 0.37/0.57 (define @t54 () (@list @t1 @t31 @t48)) % 0.37/0.57 (define @t55 () (forall @t54 @t53)) % 0.37/0.57 (define @t56 () (tptp.in @t6 @t3)) % 0.37/0.57 (define @t57 () (not false)) % 0.37/0.57 (define @t58 () (and @t56 @t57)) % 0.37/0.57 (define @t59 () (tptp.in @t6 @t1)) % 0.37/0.57 (define @t60 () (and @t59 @t57)) % 0.37/0.57 (define @t61 () (tptp.binunion @t1 @t3)) % 0.37/0.57 (define @t62 () (tptp.in @t6 @t61)) % 0.37/0.57 (define @t63 () (not @t62)) % 0.37/0.57 (define @t64 () (or @t63 @t60 @t58)) % 0.37/0.57 (define @t65 () (or @t63 @t60 @t58 false)) % 0.37/0.57 (define @t66 () (not @t20)) % 0.37/0.57 (define @t67 () (and @t56 @t66)) % 0.37/0.57 (define @t68 () (and @t59 @t66)) % 0.37/0.57 (define @t69 () (@list @t20)) % 0.37/0.57 (define @t70 () (or @t20 @t63 @t68 @t67 @t20)) % 0.37/0.57 (define @t71 () (or @t63 @t68 @t67 @t20)) % 0.37/0.57 (define @t72 () (forall @t69 @t71)) % 0.37/0.57 (define @t73 () (forall @t17 @t72)) % 0.37/0.57 (define @t74 () (and @t9 @t66)) % 0.37/0.57 (define @t75 () (and @t8 @t66)) % 0.37/0.57 (define @t76 () (not @t26)) % 0.37/0.57 (define @t77 () (or @t76 @t75 @t74 @t20)) % 0.37/0.57 (define @t78 () (or @t75 @t74 @t20)) % 0.37/0.57 (define @t79 () (=> tptp.binunionEcases @t55)) % 0.37/0.57 (define @t80 () (not @t9)) % 0.37/0.57 (define @t81 () (tptp.in @t3 @t47)) % 0.37/0.57 (define @t82 () (not @t5)) % 0.37/0.57 (define @t83 () (or @t82 @t80 @t8)) % 0.37/0.57 (define @t84 () (or @t80 @t8)) % 0.37/0.57 (define @t85 () (=> tptp.powersetE @t79)) % 0.37/0.57 (define @t86 () (not @t56)) % 0.37/0.57 (define @t87 () (forall @t11 (or @t86 @t59))) % 0.37/0.57 (define @t88 () (not @t87)) % 0.37/0.57 (define @t89 () (or @t88 @t5)) % 0.37/0.57 (define @t90 () (=> tptp.powersetI @t85)) % 0.37/0.57 (define @t91 () (or @t50 @t49)) % 0.37/0.57 (define @t92 () (or @t52 @t91)) % 0.37/0.57 (define @t93 () (forall @t54 @t92)) % 0.37/0.57 (define @t94 () (@list @t48)) % 0.37/0.57 (define @t95 () (forall @t94 @t92)) % 0.37/0.57 (define @t96 () (forall @t94 @t91)) % 0.37/0.57 (define @t97 () (or @t52 @t96)) % 0.37/0.57 (define @t98 () (tptp.binunion @t31 @t30)) % 0.37/0.57 (define @t99 () (tptp.in @t98 @t47)) % 0.37/0.57 (define @t100 () (tptp.in @t30 @t47)) % 0.37/0.57 (define @t101 () (forall @t36 (or (not @t100) @t99))) % 0.37/0.57 (define @t102 () (not @t39)) % 0.37/0.57 (define @t103 () (or @t102 @t101)) % 0.37/0.57 (define @t104 () (not @t35)) % 0.37/0.57 (define @t105 () (or @t104 @t33)) % 0.37/0.57 (define @t106 () (@quantifiers_skolemize @t55 0)) % 0.37/0.57 (define @t107 () (@quantifiers_skolemize @t55 2)) % 0.37/0.57 (define @t108 () (@quantifiers_skolemize @t55 1)) % 0.37/0.57 (define @t109 () (tptp.binunion @t108 @t107)) % 0.37/0.57 (define @t110 () (forall @t11 (or (not (tptp.in @t6 @t109)) (tptp.in @t6 @t106)))) % 0.37/0.57 (define @t111 () (@quantifiers_skolemize @t110 0)) % 0.37/0.57 (define @t112 () (tptp.powerset @t106)) % 0.37/0.57 (define @t113 () (tptp.in @t109 @t112)) % 0.37/0.57 (define @t114 () (tptp.in @t107 @t112)) % 0.37/0.57 (define @t115 () (not @t114)) % 0.37/0.57 (define @t116 () (tptp.in @t108 @t112)) % 0.37/0.57 (define @t117 () (not @t116)) % 0.37/0.57 (define @t118 () (or @t117 @t115 @t113)) % 0.37/0.57 (define @t119 () (@list true)) % 0.37/0.57 (define @t120 () (@list @t118)) % 0.37/0.57 (define @t121 () (not @t110)) % 0.37/0.57 (define @t122 () (or @t121 @t113)) % 0.37/0.57 (define @t123 () (@list true false)) % 0.37/0.57 (define @t124 () (tptp.in @t111 @t106)) % 0.37/0.57 (define @t125 () (tptp.in @t111 @t109)) % 0.37/0.57 (define @t126 () (not @t125)) % 0.37/0.57 (define @t127 () (or @t126 @t124)) % 0.37/0.57 (define @t128 () (@list @t127)) % 0.37/0.57 (define @t129 () (tptp.in @t111 @t108)) % 0.37/0.57 (define @t130 () (not @t129)) % 0.37/0.57 (define @t131 () (or @t117 @t130 @t124)) % 0.37/0.57 (define @t132 () (@list false true false)) % 0.37/0.57 (define @t133 () (tptp.in @t111 @t107)) % 0.37/0.57 (define @t134 () (or @t126 @t129 @t133)) % 0.37/0.57 (define @t135 () (not @t133)) % 0.37/0.57 (define @t136 () (or @t115 @t135 @t124)) % 0.37/0.57 (define @t137 () (not @t136)) % 0.37/0.57 (define @t138 () (forall @t17 (or (not @t81) @t86 @t59))) % 0.37/0.57 (assume @p1 @t16) % 0.37/0.57 (assume @p2 @t19) % 0.37/0.57 (assume @p3 @t29) % 0.37/0.57 (assume @p4 @t46) % 0.37/0.57 (assume @p5 true) % 0.37/0.57 (step @p6 :rule refl :args (@t55)) % 0.37/0.57 (step @p7 :rule aci_norm :args ((= (and @t56 true) @t56))) % 0.37/0.57 (step @p8 :rule evaluate :args (@t57)) % 0.37/0.57 (step @p9 :rule refl :args (@t56)) % 0.37/0.57 (step @p10 :rule nary_cong :premises (@p9 @p8) :args (@t58)) % 0.37/0.57 (step @p11 :rule trans :premises (@p10 @p7)) % 0.37/0.57 (step @p12 :rule aci_norm :args ((= (and @t59 true) @t59))) % 0.37/0.57 (step @p13 :rule refl :args (@t59)) % 0.37/0.57 (step @p14 :rule nary_cong :premises (@p13 @p8) :args (@t60)) % 0.37/0.57 (step @p15 :rule trans :premises (@p14 @p12)) % 0.37/0.57 (step @p16 :rule refl :args (@t63)) % 0.37/0.57 (step @p17 :rule nary_cong :premises (@p16 @p15 @p11) :args (@t64)) % 0.37/0.57 (step @p18 :rule aci_norm :args ((= @t65 @t64))) % 0.37/0.57 (step @p19 :rule trans :premises (@p18 @p17)) % 0.37/0.57 (step @p20 :rule cong :premises (@p19) :args ((forall @t17 @t65))) % 0.37/0.57 (step @p21 :rule quant-var-elim-eq :args ((= (forall @t69 (or (not (= @t20 false)) @t63 @t68 @t67 @t20)) @t65))) % 0.37/0.57 (step @p22 :rule refl :args (@t20)) % 0.37/0.57 (step @p23 :rule refl :args (@t67)) % 0.37/0.57 (step @p24 :rule refl :args (@t68)) % 0.37/0.57 (step @p25 :rule refl :args (@t63)) % 0.37/0.57 (step @p26 :rule bool-eq-false :args (@t20)) % 0.37/0.57 (step @p27 :rule symm :premises (@p26)) % 0.37/0.57 (step @p28 :rule cong :premises (@p27) :args ((not @t66))) % 0.37/0.57 (step @p29 :rule bool-double-not-elim :args (@t20)) % 0.37/0.57 (step @p30 :rule symm :premises (@p29)) % 0.37/0.57 (step @p31 :rule trans :premises (@p30 @p28)) % 0.37/0.57 (step @p32 :rule nary_cong :premises (@p31 @p25 @p24 @p23 @p22) :args (@t70)) % 0.37/0.57 (step @p33 :rule aci_norm :args ((= @t71 @t70))) % 0.37/0.57 (step @p34 :rule trans :premises (@p33 @p32)) % 0.37/0.57 (step @p35 :rule cong :premises (@p34) :args (@t72)) % 0.37/0.57 (step @p36 :rule trans :premises (@p35 @p21)) % 0.37/0.57 (step @p37 :rule cong :premises (@p36) :args (@t73)) % 0.37/0.57 (step @p38 :rule quant-merge-prenex :args ((= @t73 (forall @t27 @t71)))) % 0.37/0.57 (step @p39 :rule symm :premises (@p38)) % 0.37/0.57 (step @p40 :rule trans :premises (@p39 @p37)) % 0.37/0.57 (step @p41 :rule trans :premises (@p40 @p20)) % 0.37/0.57 (step @p42 :rule refl :args (@t66)) % 0.37/0.57 (step @p43 :rule refl :args (@t56)) % 0.37/0.57 (step @p44 :rule refl :args (@t9)) % 0.37/0.57 (step @p45 :rule cong :premises (@p44 @p43) :args ((= @t9 @t56))) % 0.37/0.57 (step @p46 :rule symm :premises (@p45)) % 0.37/0.57 (step @p47 :rule eq_resolve :premises (@p44 @p46)) % 0.37/0.57 (step @p48 :rule nary_cong :premises (@p47 @p42) :args (@t74)) % 0.37/0.57 (step @p49 :rule refl :args (@t59)) % 0.37/0.57 (step @p50 :rule refl :args (@t8)) % 0.37/0.57 (step @p51 :rule cong :premises (@p50 @p49) :args ((= @t8 @t59))) % 0.37/0.57 (step @p52 :rule symm :premises (@p51)) % 0.37/0.57 (step @p53 :rule eq_resolve :premises (@p50 @p52)) % 0.37/0.57 (step @p54 :rule nary_cong :premises (@p53 @p42) :args (@t75)) % 0.37/0.57 (step @p55 :rule refl :args ((tptp.in @t6 @t25))) % 0.37/0.57 (step @p56 :rule refl :args (@t61)) % 0.37/0.57 (step @p57 :rule refl :args (@t6)) % 0.37/0.57 (step @p58 :rule cong :premises (@p57 @p56) :args (@t62)) % 0.37/0.57 (step @p59 :rule trans :premises (@p58 @p55)) % 0.37/0.57 (step @p60 :rule refl :args (@t7)) % 0.37/0.57 (step @p61 :rule ho_cong :premises (@p60 @p56)) % 0.37/0.57 (step @p62 :rule cong :premises (@p61 @p59) :args ((= (_ @t7 @t61) @t62))) % 0.37/0.57 (step @p63 :rule symm :premises (@p62)) % 0.37/0.57 (step @p64 :rule refl :args (@t26)) % 0.37/0.57 (step @p65 :rule eq_resolve :premises (@p64 @p63)) % 0.37/0.57 (step @p66 :rule refl :args (@t25)) % 0.37/0.57 (step @p67 :rule cong :premises (@p66 @p56) :args ((= @t25 @t61))) % 0.37/0.57 (step @p68 :rule symm :premises (@p67)) % 0.37/0.57 (step @p69 :rule eq_resolve :premises (@p66 @p68)) % 0.37/0.57 (step @p70 :rule ho_cong :premises (@p60 @p69)) % 0.37/0.57 (step @p71 :rule trans :premises (@p70 @p65)) % 0.37/0.57 (step @p72 :rule cong :premises (@p71) :args (@t76)) % 0.37/0.57 (step @p73 :rule nary_cong :premises (@p72 @p54 @p48 @p22) :args (@t77)) % 0.37/0.57 (step @p74 :rule cong :premises (@p73) :args ((forall @t27 @t77))) % 0.37/0.57 (step @p75 :rule trans :premises (@p74 @p41)) % 0.37/0.57 (step @p76 :rule aci_norm :args ((= (or @t76 @t78) @t77))) % 0.37/0.57 (step @p77 :rule aci_norm :args ((= (or @t75 (or @t74 @t20)) @t78))) % 0.37/0.57 (step @p78 :rule bool-implies-de-morgan :args (@t9 @t20)) % 0.37/0.57 (step @p79 :rule nary_cong :premises (@p78 @p22) :args ((or (not @t21) @t20))) % 0.37/0.57 (step @p80 :rule bool-impl-elim :args (@t21 @t20)) % 0.37/0.57 (step @p81 :rule trans :premises (@p80 @p79)) % 0.37/0.57 (step @p82 :rule bool-implies-de-morgan :args (@t8 @t20)) % 0.37/0.57 (step @p83 :rule nary_cong :premises (@p82 @p81) :args ((or (not @t23) @t22))) % 0.37/0.57 (step @p84 :rule trans :premises (@p83 @p77)) % 0.37/0.57 (step @p85 :rule bool-impl-elim :args (@t23 @t22)) % 0.37/0.57 (step @p86 :rule trans :premises (@p85 @p84)) % 0.37/0.57 (step @p87 :rule refl :args (@t76)) % 0.37/0.57 (step @p88 :rule nary_cong :premises (@p87 @p86) :args ((or @t76 @t24))) % 0.37/0.57 (step @p89 :rule trans :premises (@p88 @p76)) % 0.37/0.57 (step @p90 :rule bool-impl-elim :args (@t26 @t24)) % 0.37/0.57 (step @p91 :rule trans :premises (@p90 @p89)) % 0.37/0.57 (step @p92 :rule cong :premises (@p91) :args (@t28)) % 0.37/0.57 (step @p93 :rule trans :premises (@p92 @p75)) % 0.37/0.57 (step @p94 :rule refl :args (tptp.binunionEcases)) % 0.37/0.57 (step @p95 :rule cong :premises (@p94 @p93) :args (@t29)) % 0.37/0.57 (step @p96 :rule eq_resolve :premises (@p3 @p95)) % 0.37/0.57 (step @p97 :rule cong :premises (@p96 @p6) :args (@t79)) % 0.37/0.57 (step @p98 :rule cong :premises (@p47) :args (@t80)) % 0.37/0.57 (step @p99 :rule refl :args ((tptp.in @t3 @t2))) % 0.37/0.57 (step @p100 :rule refl :args (@t47)) % 0.37/0.57 (step @p101 :rule refl :args (@t3)) % 0.37/0.57 (step @p102 :rule cong :premises (@p101 @p100) :args (@t81)) % 0.37/0.57 (step @p103 :rule trans :premises (@p102 @p99)) % 0.37/0.57 (step @p104 :rule refl :args (@t4)) % 0.37/0.57 (step @p105 :rule ho_cong :premises (@p104 @p100)) % 0.37/0.57 (step @p106 :rule cong :premises (@p105 @p103) :args ((= (_ @t4 @t47) @t81))) % 0.37/0.57 (step @p107 :rule symm :premises (@p106)) % 0.37/0.57 (step @p108 :rule refl :args (@t5)) % 0.37/0.57 (step @p109 :rule eq_resolve :premises (@p108 @p107)) % 0.37/0.57 (step @p110 :rule refl :args (@t2)) % 0.37/0.57 (step @p111 :rule cong :premises (@p110 @p100) :args ((= @t2 @t47))) % 0.37/0.57 (step @p112 :rule symm :premises (@p111)) % 0.37/0.57 (step @p113 :rule eq_resolve :premises (@p110 @p112)) % 0.37/0.57 (step @p114 :rule ho_cong :premises (@p104 @p113)) % 0.37/0.57 (step @p115 :rule trans :premises (@p114 @p109)) % 0.37/0.57 (step @p116 :rule cong :premises (@p115) :args (@t82)) % 0.37/0.57 (step @p117 :rule nary_cong :premises (@p116 @p98 @p53) :args (@t83)) % 0.37/0.57 (step @p118 :rule cong :premises (@p117) :args ((forall @t17 @t83))) % 0.37/0.57 (step @p119 :rule aci_norm :args ((= (or @t82 @t84) @t83))) % 0.37/0.57 (step @p120 :rule bool-impl-elim :args (@t9 @t8)) % 0.37/0.57 (step @p121 :rule refl :args (@t82)) % 0.37/0.57 (step @p122 :rule nary_cong :premises (@p121 @p120) :args ((or @t82 @t10))) % 0.37/0.57 (step @p123 :rule trans :premises (@p122 @p119)) % 0.37/0.57 (step @p124 :rule bool-impl-elim :args (@t5 @t10)) % 0.37/0.57 (step @p125 :rule trans :premises (@p124 @p123)) % 0.37/0.57 (step @p126 :rule cong :premises (@p125) :args (@t18)) % 0.37/0.57 (step @p127 :rule trans :premises (@p126 @p118)) % 0.37/0.57 (step @p128 :rule refl :args (tptp.powersetE)) % 0.37/0.57 (step @p129 :rule cong :premises (@p128 @p127) :args (@t19)) % 0.37/0.57 (step @p130 :rule eq_resolve :premises (@p2 @p129)) % 0.37/0.57 (step @p131 :rule cong :premises (@p130 @p97) :args (@t85)) % 0.37/0.57 (step @p132 :rule refl :args (@t88)) % 0.37/0.57 (step @p133 :rule nary_cong :premises (@p132 @p115) :args (@t89)) % 0.37/0.57 (step @p134 :rule cong :premises (@p133) :args ((forall @t14 @t89))) % 0.37/0.57 (step @p135 :rule bool-impl-elim :args (@t87 @t5)) % 0.37/0.57 (step @p136 :rule cong :premises (@p135) :args ((forall @t14 (=> @t87 @t5)))) % 0.37/0.57 (step @p137 :rule trans :premises (@p136 @p134)) % 0.37/0.57 (step @p138 :rule refl :args (@t5)) % 0.37/0.57 (step @p139 :rule nary_cong :premises (@p98 @p53) :args (@t84)) % 0.37/0.57 (step @p140 :rule cong :premises (@p139) :args ((forall @t11 @t84))) % 0.37/0.57 (step @p141 :rule cong :premises (@p120) :args (@t12)) % 0.37/0.57 (step @p142 :rule trans :premises (@p141 @p140)) % 0.37/0.57 (step @p143 :rule cong :premises (@p142 @p138) :args (@t13)) % 0.37/0.57 (step @p144 :rule cong :premises (@p143) :args (@t15)) % 0.37/0.57 (step @p145 :rule trans :premises (@p144 @p137)) % 0.37/0.57 (step @p146 :rule refl :args (tptp.powersetI)) % 0.37/0.57 (step @p147 :rule cong :premises (@p146 @p145) :args (@t16)) % 0.37/0.57 (step @p148 :rule eq_resolve :premises (@p1 @p147)) % 0.37/0.57 (step @p149 :rule cong :premises (@p148 @p131) :args (@t90)) % 0.37/0.57 (step @p150 :rule cong :premises (@p149) :args ((not @t90))) % 0.37/0.57 (step @p151 :rule aci_norm :args ((= @t92 @t53))) % 0.37/0.57 (step @p152 :rule cong :premises (@p151) :args (@t93)) % 0.37/0.57 (step @p153 :rule quant-merge-prenex :args ((= (forall @t41 @t95) @t93))) % 0.37/0.57 (step @p154 :rule alpha_equiv :args (@t96 (@list @t48) (@list @t30))) % 0.37/0.57 (step @p155 :rule refl :args (@t52)) % 0.37/0.57 (step @p156 :rule nary_cong :premises (@p155 @p154) :args (@t97)) % 0.37/0.57 (step @p157 :rule quant-miniscope-or :args ((= @t95 @t97))) % 0.37/0.57 (step @p158 :rule trans :premises (@p157 @p156)) % 0.37/0.57 (step @p159 :rule symm :premises (@p158)) % 0.37/0.57 (step @p160 :rule cong :premises (@p159) :args ((forall @t41 (or @t52 @t101)))) % 0.37/0.57 (step @p161 :rule trans :premises (@p160 @p153)) % 0.37/0.57 (step @p162 :rule trans :premises (@p161 @p152)) % 0.37/0.57 (step @p163 :rule refl :args (@t101)) % 0.37/0.57 (step @p164 :rule refl :args ((tptp.in @t31 @t2))) % 0.37/0.57 (step @p165 :rule refl :args (@t31)) % 0.37/0.57 (step @p166 :rule cong :premises (@p165 @p100) :args (@t51)) % 0.37/0.57 (step @p167 :rule trans :premises (@p166 @p164)) % 0.37/0.57 (step @p168 :rule refl :args (@t38)) % 0.37/0.57 (step @p169 :rule ho_cong :premises (@p168 @p100)) % 0.37/0.57 (step @p170 :rule cong :premises (@p169 @p167) :args ((= (_ @t38 @t47) @t51))) % 0.37/0.57 (step @p171 :rule symm :premises (@p170)) % 0.37/0.57 (step @p172 :rule refl :args (@t39)) % 0.37/0.57 (step @p173 :rule eq_resolve :premises (@p172 @p171)) % 0.37/0.57 (step @p174 :rule ho_cong :premises (@p168 @p113)) % 0.37/0.57 (step @p175 :rule trans :premises (@p174 @p173)) % 0.37/0.57 (step @p176 :rule cong :premises (@p175) :args (@t102)) % 0.37/0.57 (step @p177 :rule nary_cong :premises (@p176 @p163) :args (@t103)) % 0.37/0.57 (step @p178 :rule cong :premises (@p177) :args ((forall @t41 @t103))) % 0.37/0.57 (step @p179 :rule trans :premises (@p178 @p162)) % 0.37/0.57 (step @p180 :rule bool-impl-elim :args (@t39 @t101)) % 0.37/0.57 (step @p181 :rule cong :premises (@p180) :args ((forall @t41 (=> @t39 @t101)))) % 0.37/0.57 (step @p182 :rule trans :premises (@p181 @p179)) % 0.37/0.57 (step @p183 :rule refl :args ((tptp.in @t32 @t2))) % 0.37/0.57 (step @p184 :rule refl :args (@t98)) % 0.37/0.57 (step @p185 :rule cong :premises (@p184 @p100) :args (@t99)) % 0.37/0.57 (step @p186 :rule trans :premises (@p185 @p183)) % 0.37/0.57 (step @p187 :rule refl :args (tptp.in)) % 0.37/0.57 (step @p188 :rule ho_cong :premises (@p187 @p184)) % 0.37/0.57 (step @p189 :rule ho_cong :premises (@p188 @p100)) % 0.37/0.57 (step @p190 :rule cong :premises (@p189 @p186) :args ((= (_ (_ tptp.in @t98) @t47) @t99))) % 0.37/0.57 (step @p191 :rule symm :premises (@p190)) % 0.37/0.57 (step @p192 :rule refl :args (@t33)) % 0.37/0.57 (step @p193 :rule eq_resolve :premises (@p192 @p191)) % 0.37/0.57 (step @p194 :rule refl :args (@t32)) % 0.37/0.57 (step @p195 :rule cong :premises (@p194 @p184) :args ((= @t32 @t98))) % 0.37/0.57 (step @p196 :rule symm :premises (@p195)) % 0.37/0.57 (step @p197 :rule eq_resolve :premises (@p194 @p196)) % 0.37/0.57 (step @p198 :rule ho_cong :premises (@p187 @p197)) % 0.37/0.57 (step @p199 :rule ho_cong :premises (@p198 @p113)) % 0.37/0.57 (step @p200 :rule trans :premises (@p199 @p193)) % 0.37/0.57 (step @p201 :rule refl :args ((tptp.in @t30 @t2))) % 0.37/0.57 (step @p202 :rule refl :args (@t30)) % 0.37/0.57 (step @p203 :rule cong :premises (@p202 @p100) :args (@t100)) % 0.37/0.57 (step @p204 :rule trans :premises (@p203 @p201)) % 0.37/0.57 (step @p205 :rule refl :args (@t34)) % 0.37/0.57 (step @p206 :rule ho_cong :premises (@p205 @p100)) % 0.37/0.57 (step @p207 :rule cong :premises (@p206 @p204) :args ((= (_ @t34 @t47) @t100))) % 0.37/0.57 (step @p208 :rule symm :premises (@p207)) % 0.37/0.57 (step @p209 :rule refl :args (@t35)) % 0.37/0.57 (step @p210 :rule eq_resolve :premises (@p209 @p208)) % 0.37/0.57 (step @p211 :rule ho_cong :premises (@p205 @p113)) % 0.37/0.57 (step @p212 :rule trans :premises (@p211 @p210)) % 0.37/0.57 (step @p213 :rule cong :premises (@p212) :args (@t104)) % 0.37/0.57 (step @p214 :rule nary_cong :premises (@p213 @p200) :args (@t105)) % 0.37/0.57 (step @p215 :rule cong :premises (@p214) :args ((forall @t36 @t105))) % 0.37/0.57 (step @p216 :rule bool-impl-elim :args (@t35 @t33)) % 0.37/0.57 (step @p217 :rule cong :premises (@p216) :args (@t37)) % 0.37/0.57 (step @p218 :rule trans :premises (@p217 @p215)) % 0.37/0.57 (step @p219 :rule refl :args (@t39)) % 0.37/0.57 (step @p220 :rule cong :premises (@p219 @p218) :args (@t40)) % 0.37/0.57 (step @p221 :rule cong :premises (@p220) :args (@t42)) % 0.37/0.57 (step @p222 :rule trans :premises (@p221 @p182)) % 0.37/0.57 (step @p223 :rule cong :premises (@p94 @p222) :args (@t43)) % 0.37/0.57 (step @p224 :rule cong :premises (@p128 @p223) :args (@t44)) % 0.37/0.57 (step @p225 :rule cong :premises (@p146 @p224) :args (@t45)) % 0.37/0.57 (step @p226 :rule cong :premises (@p225) :args (@t46)) % 0.37/0.57 (step @p227 :rule trans :premises (@p226 @p150)) % 0.37/0.57 (step @p228 :rule eq_resolve :premises (@p4 @p227)) % 0.37/0.57 (step @p229 :rule not_implies_elim2 :premises (@p228)) % 0.37/0.57 (step @p230 :rule not_implies_elim1 :premises (@p229)) % 0.37/0.57 (step @p231 :rule not_implies_elim2 :premises (@p229)) % 0.37/0.57 (step @p232 :rule not_implies_elim1 :premises (@p231)) % 0.37/0.57 (step @p233 :rule instantiate :premises (@p232) :args ((@list @t108 @t107 @t111))) % 0.37/0.57 (step @p234 :rule instantiate :premises (@p230) :args ((@list @t106 @t108 @t111))) % 0.37/0.57 (step @p235 :rule not_implies_elim1 :premises (@p228)) % 0.37/0.57 (step @p236 :rule instantiate :premises (@p235) :args ((@list @t106 @t109))) % 0.37/0.57 (step @p237 :rule not_implies_elim2 :premises (@p231)) % 0.37/0.57 (step @p238 :rule skolemize :premises (@p237)) % 0.37/0.57 (step @p239 :rule cnf_or_neg :args (@t118 2)) % 0.37/0.57 (step @p240 :rule chain_m_resolution :premises (@p239 @p238) :args ((not @t113) @t119 @t120)) % 0.37/0.57 (step @p241 :rule cnf_or_pos :args (@t122)) % 0.37/0.57 (step @p242 :rule reordering :premises (@p241) :args ((or @t113 @t121 (not @t122)))) % 0.37/0.57 (step @p243 :rule chain_m_resolution :premises (@p242 @p240 @p236) :args (@t121 @t123 (@list @t113 @t122))) % 0.37/0.57 (step @p244 :rule skolemize :premises (@p243)) % 0.37/0.57 (step @p245 :rule cnf_or_neg :args (@t127 1)) % 0.37/0.57 (step @p246 :rule chain_m_resolution :premises (@p245 @p244) :args ((not @t124) @t119 @t128)) % 0.37/0.57 (step @p247 :rule bool-double-not-elim :args (@t116)) % 0.37/0.57 (step @p248 :rule refl :args (@t118)) % 0.37/0.57 (step @p249 :rule nary_cong :premises (@p248 @p247) :args ((or @t118 (not @t117)))) % 0.37/0.57 (step @p250 :rule cnf_or_neg :args (@t118 0)) % 0.37/0.57 (step @p251 :rule eq_resolve :premises (@p250 @p249)) % 0.37/0.57 (step @p252 :rule reordering :premises (@p251) :args ((or @t116 @t118))) % 0.37/0.57 (step @p253 :rule chain_m_resolution :premises (@p252 @p238) :args (@t116 @t119 @t120)) % 0.37/0.57 (step @p254 :rule cnf_or_pos :args (@t131)) % 0.37/0.57 (step @p255 :rule reordering :premises (@p254) :args ((or @t117 @t124 @t130 (not @t131)))) % 0.37/0.57 (step @p256 :rule chain_m_resolution :premises (@p255 @p253 @p246 @p234) :args (@t130 @t132 (@list @t116 @t124 @t131))) % 0.37/0.57 (step @p257 :rule bool-double-not-elim :args (@t125)) % 0.37/0.57 (step @p258 :rule refl :args (@t127)) % 0.37/0.57 (step @p259 :rule nary_cong :premises (@p258 @p257) :args ((or @t127 (not @t126)))) % 0.37/0.57 (step @p260 :rule cnf_or_neg :args (@t127 0)) % 0.37/0.57 (step @p261 :rule eq_resolve :premises (@p260 @p259)) % 0.37/0.57 (step @p262 :rule reordering :premises (@p261) :args ((or @t125 @t127))) % 0.37/0.57 (step @p263 :rule chain_m_resolution :premises (@p262 @p244) :args (@t125 @t119 @t128)) % 0.37/0.57 (step @p264 :rule cnf_or_pos :args (@t134)) % 0.37/0.57 (step @p265 :rule reordering :premises (@p264) :args ((or @t126 @t129 @t133 (not @t134)))) % 0.37/0.57 (step @p266 :rule chain_m_resolution :premises (@p265 @p263 @p256 @p233) :args (@t133 @t132 (@list @t125 @t129 @t134))) % 0.37/0.57 (step @p267 :rule bool-double-not-elim :args (@t114)) % 0.37/0.57 (step @p268 :rule nary_cong :premises (@p248 @p267) :args ((or @t118 (not @t115)))) % 0.37/0.57 (step @p269 :rule cnf_or_neg :args (@t118 1)) % 0.37/0.57 (step @p270 :rule eq_resolve :premises (@p269 @p268)) % 0.37/0.57 (step @p271 :rule reordering :premises (@p270) :args ((or @t114 @t118))) % 0.37/0.57 (step @p272 :rule chain_m_resolution :premises (@p271 @p238) :args (@t114 @t119 @t120)) % 0.37/0.57 (step @p273 :rule cnf_or_pos :args (@t136)) % 0.37/0.57 (step @p274 :rule reordering :premises (@p273) :args ((or @t115 @t124 @t135 @t137))) % 0.37/0.57 (step @p275 :rule chain_m_resolution :premises (@p274 @p272 @p246 @p266) :args (@t137 @t132 (@list @t114 @t124 @t133))) % 0.37/0.57 (assume-push @p282 @t138) % 0.37/0.57 (step @p277 :rule instantiate :premises (@p230) :args ((@list @t106 @t107 @t111))) % 0.37/0.57 (step-pop @p283 :rule scope :premises (@p277)) % 0.37/0.57 (step @p278 :rule process_scope :premises (@p283) :args (@t136)) % 0.37/0.57 (step @p280 :rule implies_elim :premises (@p278)) % 0.37/0.57 (step @p281 false :rule chain_m_resolution :premises (@p280 @p275 @p230) :args (false @t123 (@list @t136 @t138))) % 0.37/0.57 ) % 0.37/0.57 % SZS output end Proof % 0.37/0.57 % cvc5 exiting %------------------------------------------------------------------------------