%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU625^2 : 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 : n025.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:52:28 AM UTC 2026 % Result : Theorem 0.36s 0.57s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU625^2 : 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 % 0.16/0.34 % Computer : n025.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 17:43:31 EDT 2026 % 0.16/0.34 % CPUTime : % 0.30/0.48 %----Proving TH0 % 0.36/0.57 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.36/0.57 % SZS status Theorem % 0.36/0.57 % SZS output start Proof % 0.36/0.57 ( % 0.36/0.57 (declare-sort $$unsorted 0) % 0.36/0.57 (declare-const tptp.emptyset $$unsorted) % 0.36/0.57 (declare-const tptp.binunionLsub Bool) % 0.36/0.57 (declare-const tptp.upairset2E Bool) % 0.36/0.57 (declare-const tptp.binunion (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.57 (declare-const tptp.setadjoin (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.57 (declare-const tptp.binunionRsub Bool) % 0.36/0.57 (declare-const tptp.subsetE Bool) % 0.36/0.57 (declare-const tptp.subsetI2 Bool) % 0.36/0.57 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.36/0.57 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.36/0.57 (define @t1 () (@var "B" $$unsorted)) % 0.36/0.57 (define @t2 () (@var "A" $$unsorted)) % 0.36/0.57 (define @t3 () (_ tptp.subset @t2)) % 0.36/0.57 (define @t4 () (_ @t3 @t1)) % 0.36/0.57 (define @t5 () (@var "Xx" $$unsorted)) % 0.36/0.57 (define @t6 () (_ tptp.in @t5)) % 0.36/0.57 (define @t7 () (_ @t6 @t1)) % 0.36/0.57 (define @t8 () (_ @t6 @t2)) % 0.36/0.57 (define @t9 () (=> @t8 @t7)) % 0.36/0.57 (define @t10 () (@list @t5)) % 0.36/0.57 (define @t11 () (forall @t10 @t9)) % 0.36/0.57 (define @t12 () (=> @t11 @t4)) % 0.36/0.57 (define @t13 () (@list @t2 @t1)) % 0.36/0.57 (define @t14 () (forall @t13 @t12)) % 0.36/0.57 (define @t15 () (= tptp.subsetI2 @t14)) % 0.36/0.57 (define @t16 () (@list @t2 @t1 @t5)) % 0.36/0.57 (define @t17 () (forall @t16 (=> @t4 @t9))) % 0.36/0.57 (define @t18 () (= tptp.subsetE @t17)) % 0.36/0.57 (define @t19 () (_ (_ tptp.binunion @t2) @t1)) % 0.36/0.57 (define @t20 () (_ @t3 @t19)) % 0.36/0.57 (define @t21 () (forall @t13 @t20)) % 0.36/0.57 (define @t22 () (= tptp.binunionLsub @t21)) % 0.36/0.57 (define @t23 () (_ tptp.subset @t1)) % 0.36/0.57 (define @t24 () (_ @t23 @t19)) % 0.36/0.57 (define @t25 () (forall @t13 @t24)) % 0.36/0.57 (define @t26 () (= tptp.binunionRsub @t25)) % 0.36/0.57 (define @t27 () (@var "Xy" $$unsorted)) % 0.36/0.57 (define @t28 () (@var "Xz" $$unsorted)) % 0.36/0.57 (define @t29 () (or (= @t28 @t5) (= @t28 @t27))) % 0.36/0.57 (define @t30 () (_ (_ tptp.setadjoin @t27) tptp.emptyset)) % 0.36/0.57 (define @t31 () (_ tptp.setadjoin @t5)) % 0.36/0.57 (define @t32 () (_ @t31 @t30)) % 0.36/0.57 (define @t33 () (_ tptp.in @t28)) % 0.36/0.57 (define @t34 () (_ @t33 @t32)) % 0.36/0.57 (define @t35 () (=> @t34 @t29)) % 0.36/0.57 (define @t36 () (@list @t5 @t27 @t28)) % 0.36/0.57 (define @t37 () (forall @t36 @t35)) % 0.36/0.57 (define @t38 () (= tptp.upairset2E @t37)) % 0.36/0.57 (define @t39 () (_ (_ tptp.subset @t32) @t19)) % 0.36/0.57 (define @t40 () (_ (_ tptp.in @t27) @t1)) % 0.36/0.57 (define @t41 () (@list @t27)) % 0.36/0.57 (define @t42 () (forall @t41 (=> @t40 @t39))) % 0.36/0.57 (define @t43 () (=> @t8 @t42)) % 0.36/0.57 (define @t44 () (forall @t16 @t43)) % 0.36/0.57 (define @t45 () (=> tptp.upairset2E @t44)) % 0.36/0.57 (define @t46 () (=> tptp.binunionRsub @t45)) % 0.36/0.57 (define @t47 () (=> tptp.binunionLsub @t46)) % 0.36/0.57 (define @t48 () (=> tptp.subsetE @t47)) % 0.36/0.57 (define @t49 () (=> tptp.subsetI2 @t48)) % 0.36/0.57 (define @t50 () (not @t49)) % 0.36/0.57 (define @t51 () (tptp.binunion @t2 @t1)) % 0.36/0.57 (define @t52 () (@var "BOUND_VARIABLE_7549" $$unsorted)) % 0.36/0.57 (define @t53 () (tptp.subset (tptp.setadjoin @t5 (tptp.setadjoin @t52 tptp.emptyset)) @t51)) % 0.36/0.57 (define @t54 () (not (tptp.in @t52 @t1))) % 0.36/0.57 (define @t55 () (tptp.in @t5 @t2)) % 0.36/0.57 (define @t56 () (not @t55)) % 0.36/0.57 (define @t57 () (or @t56 @t54 @t53)) % 0.36/0.57 (define @t58 () (@list @t2 @t1 @t5 @t52)) % 0.36/0.57 (define @t59 () (forall @t58 @t57)) % 0.36/0.57 (define @t60 () (= @t27 @t28)) % 0.36/0.57 (define @t61 () (= @t5 @t28)) % 0.36/0.57 (define @t62 () (tptp.setadjoin @t27 tptp.emptyset)) % 0.36/0.57 (define @t63 () (tptp.setadjoin @t5 @t62)) % 0.36/0.57 (define @t64 () (tptp.in @t28 @t63)) % 0.36/0.57 (define @t65 () (not @t34)) % 0.36/0.57 (define @t66 () (or @t65 @t61 @t60)) % 0.36/0.57 (define @t67 () (or @t61 @t60)) % 0.36/0.57 (define @t68 () (=> tptp.upairset2E @t59)) % 0.36/0.57 (define @t69 () (tptp.subset @t1 @t51)) % 0.36/0.57 (define @t70 () (=> tptp.binunionRsub @t68)) % 0.36/0.57 (define @t71 () (tptp.subset @t2 @t51)) % 0.36/0.57 (define @t72 () (=> tptp.binunionLsub @t70)) % 0.36/0.57 (define @t73 () (tptp.in @t5 @t1)) % 0.36/0.57 (define @t74 () (not @t8)) % 0.36/0.57 (define @t75 () (tptp.subset @t2 @t1)) % 0.36/0.57 (define @t76 () (not @t4)) % 0.36/0.57 (define @t77 () (or @t76 @t74 @t7)) % 0.36/0.57 (define @t78 () (or @t74 @t7)) % 0.36/0.57 (define @t79 () (=> tptp.subsetE @t72)) % 0.36/0.57 (define @t80 () (forall @t10 (or @t56 @t73))) % 0.36/0.57 (define @t81 () (not @t80)) % 0.36/0.57 (define @t82 () (or @t81 @t4)) % 0.36/0.57 (define @t83 () (=> tptp.subsetI2 @t79)) % 0.36/0.57 (define @t84 () (or @t54 @t53)) % 0.36/0.57 (define @t85 () (or @t56 @t84)) % 0.36/0.57 (define @t86 () (forall @t58 @t85)) % 0.36/0.57 (define @t87 () (@list @t52)) % 0.36/0.57 (define @t88 () (forall @t87 @t85)) % 0.36/0.57 (define @t89 () (forall @t87 @t84)) % 0.36/0.57 (define @t90 () (or @t56 @t89)) % 0.36/0.57 (define @t91 () (tptp.subset @t63 @t51)) % 0.36/0.57 (define @t92 () (tptp.in @t27 @t1)) % 0.36/0.57 (define @t93 () (forall @t41 (or (not @t92) @t91))) % 0.36/0.57 (define @t94 () (or @t74 @t93)) % 0.36/0.57 (define @t95 () (not @t40)) % 0.36/0.57 (define @t96 () (or @t95 @t39)) % 0.36/0.57 (define @t97 () (@quantifiers_skolemize @t59 1)) % 0.36/0.57 (define @t98 () (@quantifiers_skolemize @t59 0)) % 0.36/0.57 (define @t99 () (tptp.binunion @t98 @t97)) % 0.36/0.57 (define @t100 () (@quantifiers_skolemize @t59 3)) % 0.36/0.57 (define @t101 () (@quantifiers_skolemize @t59 2)) % 0.36/0.57 (define @t102 () (tptp.setadjoin @t101 (tptp.setadjoin @t100 tptp.emptyset))) % 0.36/0.57 (define @t103 () (forall @t10 (or (not (tptp.in @t5 @t102)) (tptp.in @t5 @t99)))) % 0.36/0.57 (define @t104 () (@quantifiers_skolemize @t103 0)) % 0.36/0.57 (define @t105 () (@list @t98 @t97)) % 0.36/0.57 (define @t106 () (tptp.in @t101 @t98)) % 0.36/0.57 (define @t107 () (tptp.subset @t102 @t99)) % 0.36/0.57 (define @t108 () (tptp.in @t100 @t97)) % 0.36/0.57 (define @t109 () (not @t108)) % 0.36/0.57 (define @t110 () (not @t106)) % 0.36/0.57 (define @t111 () (or @t110 @t109 @t107)) % 0.36/0.57 (define @t112 () (@list true)) % 0.36/0.57 (define @t113 () (@list @t111)) % 0.36/0.57 (define @t114 () (tptp.in @t101 @t99)) % 0.36/0.57 (define @t115 () (tptp.subset @t98 @t99)) % 0.36/0.57 (define @t116 () (not @t115)) % 0.36/0.57 (define @t117 () (or @t116 @t110 @t114)) % 0.36/0.57 (define @t118 () (not @t103)) % 0.36/0.57 (define @t119 () (or @t118 @t107)) % 0.36/0.57 (define @t120 () (@list true false)) % 0.36/0.57 (define @t121 () (tptp.in @t104 @t99)) % 0.36/0.57 (define @t122 () (tptp.in @t104 @t102)) % 0.36/0.57 (define @t123 () (not @t122)) % 0.36/0.57 (define @t124 () (or @t123 @t121)) % 0.36/0.57 (define @t125 () (not @t121)) % 0.36/0.57 (define @t126 () (@list @t124)) % 0.36/0.57 (define @t127 () (not @t114)) % 0.36/0.57 (define @t128 () (= @t101 @t104)) % 0.36/0.57 (define @t129 () (not @t128)) % 0.36/0.57 (define @t130 () (not @t125)) % 0.36/0.57 (define @t131 () (= @t100 @t104)) % 0.36/0.57 (define @t132 () (or @t123 @t128 @t131)) % 0.36/0.57 (define @t133 () (tptp.in @t100 @t99)) % 0.36/0.57 (define @t134 () (not @t133)) % 0.36/0.57 (define @t135 () (not @t131)) % 0.36/0.57 (define @t136 () (and @t125 @t131)) % 0.36/0.57 (define @t137 () (tptp.subset @t97 @t99)) % 0.36/0.57 (define @t138 () (not @t137)) % 0.36/0.57 (define @t139 () (or @t138 @t109 @t133)) % 0.36/0.57 (define @t140 () (not @t139)) % 0.36/0.57 (define @t141 () (forall @t16 (or (not @t75) @t56 @t73))) % 0.36/0.57 (assume @p1 @t15) % 0.36/0.57 (assume @p2 @t18) % 0.36/0.57 (assume @p3 @t22) % 0.36/0.57 (assume @p4 @t26) % 0.36/0.57 (assume @p5 @t38) % 0.36/0.57 (assume @p6 @t50) % 0.36/0.57 (assume @p7 true) % 0.36/0.57 (step @p8 :rule refl :args (@t59)) % 0.36/0.57 (step @p9 :rule refl :args (@t60)) % 0.36/0.57 (step @p10 :rule refl :args (@t61)) % 0.36/0.57 (step @p11 :rule refl :args ((tptp.in @t28 @t32))) % 0.36/0.57 (step @p12 :rule refl :args ((tptp.setadjoin @t5 @t30))) % 0.36/0.57 (step @p13 :rule refl :args (@t62)) % 0.36/0.57 (step @p14 :rule refl :args (@t5)) % 0.36/0.57 (step @p15 :rule cong :premises (@p14 @p13) :args (@t63)) % 0.36/0.57 (step @p16 :rule trans :premises (@p15 @p12)) % 0.36/0.57 (step @p17 :rule refl :args (@t28)) % 0.36/0.57 (step @p18 :rule cong :premises (@p17 @p16) :args (@t64)) % 0.36/0.57 (step @p19 :rule trans :premises (@p18 @p11)) % 0.36/0.57 (step @p20 :rule refl :args (@t33)) % 0.36/0.57 (step @p21 :rule ho_cong :premises (@p20 @p16)) % 0.36/0.57 (step @p22 :rule cong :premises (@p21 @p19) :args ((= (_ @t33 @t63) @t64))) % 0.36/0.57 (step @p23 :rule symm :premises (@p22)) % 0.36/0.57 (step @p24 :rule refl :args (@t34)) % 0.36/0.57 (step @p25 :rule eq_resolve :premises (@p24 @p23)) % 0.36/0.57 (step @p26 :rule refl :args (@t31)) % 0.36/0.57 (step @p27 :rule ho_cong :premises (@p26 @p13)) % 0.36/0.57 (step @p28 :rule cong :premises (@p27 @p16) :args ((= (_ @t31 @t62) @t63))) % 0.36/0.57 (step @p29 :rule symm :premises (@p28)) % 0.36/0.57 (step @p30 :rule refl :args (@t32)) % 0.36/0.57 (step @p31 :rule eq_resolve :premises (@p30 @p29)) % 0.36/0.57 (step @p32 :rule refl :args (@t30)) % 0.36/0.57 (step @p33 :rule cong :premises (@p32 @p13) :args ((= @t30 @t62))) % 0.36/0.57 (step @p34 :rule symm :premises (@p33)) % 0.36/0.57 (step @p35 :rule eq_resolve :premises (@p32 @p34)) % 0.36/0.57 (step @p36 :rule ho_cong :premises (@p26 @p35)) % 0.36/0.57 (step @p37 :rule trans :premises (@p36 @p31)) % 0.36/0.57 (step @p38 :rule ho_cong :premises (@p20 @p37)) % 0.36/0.57 (step @p39 :rule trans :premises (@p38 @p25)) % 0.36/0.57 (step @p40 :rule cong :premises (@p39) :args (@t65)) % 0.36/0.57 (step @p41 :rule nary_cong :premises (@p40 @p10 @p9) :args (@t66)) % 0.36/0.57 (step @p42 :rule cong :premises (@p41) :args ((forall @t36 @t66))) % 0.36/0.57 (step @p43 :rule aci_norm :args ((= (or @t65 @t67) @t66))) % 0.36/0.57 (step @p44 :rule bool-impl-elim :args (@t34 @t67)) % 0.36/0.57 (step @p45 :rule trans :premises (@p44 @p43)) % 0.36/0.57 (step @p46 :rule cong :premises (@p45) :args ((forall @t36 (=> @t34 @t67)))) % 0.36/0.57 (step @p47 :rule trans :premises (@p46 @p42)) % 0.36/0.57 (step @p48 :rule eq-symm :args (@t28 @t27)) % 0.36/0.57 (step @p49 :rule eq-symm :args (@t28 @t5)) % 0.36/0.57 (step @p50 :rule nary_cong :premises (@p49 @p48) :args (@t29)) % 0.36/0.57 (step @p51 :rule refl :args (@t34)) % 0.36/0.57 (step @p52 :rule cong :premises (@p51 @p50) :args (@t35)) % 0.36/0.57 (step @p53 :rule cong :premises (@p52) :args (@t37)) % 0.36/0.57 (step @p54 :rule trans :premises (@p53 @p47)) % 0.36/0.57 (step @p55 :rule refl :args (tptp.upairset2E)) % 0.36/0.57 (step @p56 :rule cong :premises (@p55 @p54) :args (@t38)) % 0.36/0.57 (step @p57 :rule eq_resolve :premises (@p5 @p56)) % 0.36/0.57 (step @p58 :rule cong :premises (@p57 @p8) :args (@t68)) % 0.36/0.57 (step @p59 :rule refl :args ((tptp.subset @t1 @t19))) % 0.36/0.57 (step @p60 :rule refl :args (@t51)) % 0.36/0.57 (step @p61 :rule refl :args (@t1)) % 0.36/0.57 (step @p62 :rule cong :premises (@p61 @p60) :args (@t69)) % 0.36/0.57 (step @p63 :rule trans :premises (@p62 @p59)) % 0.36/0.57 (step @p64 :rule refl :args (@t23)) % 0.36/0.57 (step @p65 :rule ho_cong :premises (@p64 @p60)) % 0.36/0.57 (step @p66 :rule cong :premises (@p65 @p63) :args ((= (_ @t23 @t51) @t69))) % 0.36/0.57 (step @p67 :rule symm :premises (@p66)) % 0.36/0.57 (step @p68 :rule refl :args (@t24)) % 0.36/0.57 (step @p69 :rule eq_resolve :premises (@p68 @p67)) % 0.36/0.57 (step @p70 :rule refl :args (@t19)) % 0.36/0.57 (step @p71 :rule cong :premises (@p70 @p60) :args ((= @t19 @t51))) % 0.36/0.57 (step @p72 :rule symm :premises (@p71)) % 0.36/0.57 (step @p73 :rule eq_resolve :premises (@p70 @p72)) % 0.36/0.57 (step @p74 :rule ho_cong :premises (@p64 @p73)) % 0.36/0.57 (step @p75 :rule trans :premises (@p74 @p69)) % 0.36/0.57 (step @p76 :rule cong :premises (@p75) :args (@t25)) % 0.36/0.57 (step @p77 :rule refl :args (tptp.binunionRsub)) % 0.36/0.57 (step @p78 :rule cong :premises (@p77 @p76) :args (@t26)) % 0.36/0.57 (step @p79 :rule eq_resolve :premises (@p4 @p78)) % 0.36/0.57 (step @p80 :rule cong :premises (@p79 @p58) :args (@t70)) % 0.36/0.57 (step @p81 :rule refl :args ((tptp.subset @t2 @t19))) % 0.36/0.57 (step @p82 :rule refl :args (@t2)) % 0.36/0.57 (step @p83 :rule cong :premises (@p82 @p60) :args (@t71)) % 0.36/0.57 (step @p84 :rule trans :premises (@p83 @p81)) % 0.36/0.57 (step @p85 :rule refl :args (@t3)) % 0.36/0.57 (step @p86 :rule ho_cong :premises (@p85 @p60)) % 0.36/0.57 (step @p87 :rule cong :premises (@p86 @p84) :args ((= (_ @t3 @t51) @t71))) % 0.36/0.57 (step @p88 :rule symm :premises (@p87)) % 0.36/0.57 (step @p89 :rule refl :args (@t20)) % 0.36/0.57 (step @p90 :rule eq_resolve :premises (@p89 @p88)) % 0.36/0.57 (step @p91 :rule ho_cong :premises (@p85 @p73)) % 0.36/0.57 (step @p92 :rule trans :premises (@p91 @p90)) % 0.36/0.57 (step @p93 :rule cong :premises (@p92) :args (@t21)) % 0.36/0.57 (step @p94 :rule refl :args (tptp.binunionLsub)) % 0.36/0.57 (step @p95 :rule cong :premises (@p94 @p93) :args (@t22)) % 0.36/0.57 (step @p96 :rule eq_resolve :premises (@p3 @p95)) % 0.36/0.57 (step @p97 :rule cong :premises (@p96 @p80) :args (@t72)) % 0.36/0.57 (step @p98 :rule refl :args (@t73)) % 0.36/0.57 (step @p99 :rule refl :args (@t7)) % 0.36/0.57 (step @p100 :rule cong :premises (@p99 @p98) :args ((= @t7 @t73))) % 0.36/0.57 (step @p101 :rule symm :premises (@p100)) % 0.36/0.57 (step @p102 :rule eq_resolve :premises (@p99 @p101)) % 0.36/0.57 (step @p103 :rule refl :args (@t55)) % 0.36/0.57 (step @p104 :rule refl :args (@t8)) % 0.36/0.57 (step @p105 :rule cong :premises (@p104 @p103) :args ((= @t8 @t55))) % 0.36/0.57 (step @p106 :rule symm :premises (@p105)) % 0.36/0.57 (step @p107 :rule eq_resolve :premises (@p104 @p106)) % 0.36/0.57 (step @p108 :rule cong :premises (@p107) :args (@t74)) % 0.36/0.57 (step @p109 :rule refl :args (@t75)) % 0.36/0.57 (step @p110 :rule refl :args (@t4)) % 0.36/0.57 (step @p111 :rule cong :premises (@p110 @p109) :args ((= @t4 @t75))) % 0.36/0.57 (step @p112 :rule symm :premises (@p111)) % 0.36/0.57 (step @p113 :rule eq_resolve :premises (@p110 @p112)) % 0.36/0.57 (step @p114 :rule cong :premises (@p113) :args (@t76)) % 0.36/0.57 (step @p115 :rule nary_cong :premises (@p114 @p108 @p102) :args (@t77)) % 0.36/0.57 (step @p116 :rule cong :premises (@p115) :args ((forall @t16 @t77))) % 0.36/0.57 (step @p117 :rule aci_norm :args ((= (or @t76 @t78) @t77))) % 0.36/0.57 (step @p118 :rule bool-impl-elim :args (@t8 @t7)) % 0.36/0.57 (step @p119 :rule refl :args (@t76)) % 0.36/0.57 (step @p120 :rule nary_cong :premises (@p119 @p118) :args ((or @t76 @t9))) % 0.36/0.57 (step @p121 :rule trans :premises (@p120 @p117)) % 0.36/0.57 (step @p122 :rule bool-impl-elim :args (@t4 @t9)) % 0.36/0.57 (step @p123 :rule trans :premises (@p122 @p121)) % 0.36/0.57 (step @p124 :rule cong :premises (@p123) :args (@t17)) % 0.36/0.57 (step @p125 :rule trans :premises (@p124 @p116)) % 0.36/0.57 (step @p126 :rule refl :args (tptp.subsetE)) % 0.36/0.57 (step @p127 :rule cong :premises (@p126 @p125) :args (@t18)) % 0.36/0.57 (step @p128 :rule eq_resolve :premises (@p2 @p127)) % 0.36/0.57 (step @p129 :rule cong :premises (@p128 @p97) :args (@t79)) % 0.36/0.57 (step @p130 :rule refl :args (@t81)) % 0.36/0.57 (step @p131 :rule nary_cong :premises (@p130 @p113) :args (@t82)) % 0.36/0.57 (step @p132 :rule cong :premises (@p131) :args ((forall @t13 @t82))) % 0.36/0.57 (step @p133 :rule bool-impl-elim :args (@t80 @t4)) % 0.36/0.57 (step @p134 :rule cong :premises (@p133) :args ((forall @t13 (=> @t80 @t4)))) % 0.36/0.57 (step @p135 :rule trans :premises (@p134 @p132)) % 0.36/0.57 (step @p136 :rule refl :args (@t4)) % 0.36/0.57 (step @p137 :rule nary_cong :premises (@p108 @p102) :args (@t78)) % 0.36/0.57 (step @p138 :rule cong :premises (@p137) :args ((forall @t10 @t78))) % 0.36/0.57 (step @p139 :rule cong :premises (@p118) :args (@t11)) % 0.36/0.57 (step @p140 :rule trans :premises (@p139 @p138)) % 0.36/0.57 (step @p141 :rule cong :premises (@p140 @p136) :args (@t12)) % 0.36/0.57 (step @p142 :rule cong :premises (@p141) :args (@t14)) % 0.36/0.57 (step @p143 :rule trans :premises (@p142 @p135)) % 0.36/0.57 (step @p144 :rule refl :args (tptp.subsetI2)) % 0.36/0.57 (step @p145 :rule cong :premises (@p144 @p143) :args (@t15)) % 0.36/0.57 (step @p146 :rule eq_resolve :premises (@p1 @p145)) % 0.36/0.57 (step @p147 :rule cong :premises (@p146 @p129) :args (@t83)) % 0.36/0.57 (step @p148 :rule cong :premises (@p147) :args ((not @t83))) % 0.36/0.57 (step @p149 :rule aci_norm :args ((= @t85 @t57))) % 0.36/0.57 (step @p150 :rule cong :premises (@p149) :args (@t86)) % 0.36/0.57 (step @p151 :rule quant-merge-prenex :args ((= (forall @t16 @t88) @t86))) % 0.36/0.57 (step @p152 :rule alpha_equiv :args (@t89 (@list @t52) (@list @t27))) % 0.36/0.57 (step @p153 :rule refl :args (@t56)) % 0.36/0.57 (step @p154 :rule nary_cong :premises (@p153 @p152) :args (@t90)) % 0.36/0.57 (step @p155 :rule quant-miniscope-or :args ((= @t88 @t90))) % 0.36/0.57 (step @p156 :rule trans :premises (@p155 @p154)) % 0.36/0.57 (step @p157 :rule symm :premises (@p156)) % 0.36/0.57 (step @p158 :rule cong :premises (@p157) :args ((forall @t16 (or @t56 @t93)))) % 0.36/0.57 (step @p159 :rule trans :premises (@p158 @p151)) % 0.36/0.57 (step @p160 :rule trans :premises (@p159 @p150)) % 0.36/0.57 (step @p161 :rule refl :args (@t93)) % 0.36/0.57 (step @p162 :rule nary_cong :premises (@p108 @p161) :args (@t94)) % 0.36/0.57 (step @p163 :rule cong :premises (@p162) :args ((forall @t16 @t94))) % 0.36/0.57 (step @p164 :rule trans :premises (@p163 @p160)) % 0.36/0.57 (step @p165 :rule bool-impl-elim :args (@t8 @t93)) % 0.36/0.57 (step @p166 :rule cong :premises (@p165) :args ((forall @t16 (=> @t8 @t93)))) % 0.36/0.57 (step @p167 :rule trans :premises (@p166 @p164)) % 0.36/0.57 (step @p168 :rule refl :args ((tptp.subset @t32 @t19))) % 0.36/0.57 (step @p169 :rule cong :premises (@p16 @p60) :args (@t91)) % 0.36/0.57 (step @p170 :rule trans :premises (@p169 @p168)) % 0.36/0.57 (step @p171 :rule refl :args (tptp.subset)) % 0.36/0.57 (step @p172 :rule ho_cong :premises (@p171 @p16)) % 0.36/0.57 (step @p173 :rule ho_cong :premises (@p172 @p60)) % 0.36/0.57 (step @p174 :rule cong :premises (@p173 @p170) :args ((= (_ (_ tptp.subset @t63) @t51) @t91))) % 0.36/0.57 (step @p175 :rule symm :premises (@p174)) % 0.36/0.57 (step @p176 :rule refl :args (@t39)) % 0.36/0.57 (step @p177 :rule eq_resolve :premises (@p176 @p175)) % 0.36/0.57 (step @p178 :rule ho_cong :premises (@p171 @p37)) % 0.36/0.57 (step @p179 :rule ho_cong :premises (@p178 @p73)) % 0.36/0.57 (step @p180 :rule trans :premises (@p179 @p177)) % 0.36/0.57 (step @p181 :rule refl :args (@t92)) % 0.36/0.57 (step @p182 :rule refl :args (@t40)) % 0.36/0.57 (step @p183 :rule cong :premises (@p182 @p181) :args ((= @t40 @t92))) % 0.36/0.57 (step @p184 :rule symm :premises (@p183)) % 0.36/0.57 (step @p185 :rule eq_resolve :premises (@p182 @p184)) % 0.36/0.57 (step @p186 :rule cong :premises (@p185) :args (@t95)) % 0.36/0.57 (step @p187 :rule nary_cong :premises (@p186 @p180) :args (@t96)) % 0.36/0.57 (step @p188 :rule cong :premises (@p187) :args ((forall @t41 @t96))) % 0.36/0.57 (step @p189 :rule bool-impl-elim :args (@t40 @t39)) % 0.36/0.57 (step @p190 :rule cong :premises (@p189) :args (@t42)) % 0.36/0.57 (step @p191 :rule trans :premises (@p190 @p188)) % 0.36/0.57 (step @p192 :rule refl :args (@t8)) % 0.36/0.57 (step @p193 :rule cong :premises (@p192 @p191) :args (@t43)) % 0.36/0.57 (step @p194 :rule cong :premises (@p193) :args (@t44)) % 0.36/0.57 (step @p195 :rule trans :premises (@p194 @p167)) % 0.36/0.57 (step @p196 :rule cong :premises (@p55 @p195) :args (@t45)) % 0.36/0.57 (step @p197 :rule cong :premises (@p77 @p196) :args (@t46)) % 0.36/0.57 (step @p198 :rule cong :premises (@p94 @p197) :args (@t47)) % 0.36/0.57 (step @p199 :rule cong :premises (@p126 @p198) :args (@t48)) % 0.36/0.57 (step @p200 :rule cong :premises (@p144 @p199) :args (@t49)) % 0.36/0.57 (step @p201 :rule cong :premises (@p200) :args (@t50)) % 0.36/0.57 (step @p202 :rule trans :premises (@p201 @p148)) % 0.36/0.57 (step @p203 :rule eq_resolve :premises (@p6 @p202)) % 0.36/0.57 (step @p204 :rule not_implies_elim2 :premises (@p203)) % 0.36/0.57 (step @p205 :rule not_implies_elim1 :premises (@p204)) % 0.36/0.57 (step @p206 :rule not_implies_elim2 :premises (@p204)) % 0.36/0.57 (step @p207 :rule not_implies_elim2 :premises (@p206)) % 0.36/0.57 (step @p208 :rule not_implies_elim2 :premises (@p207)) % 0.36/0.57 (step @p209 :rule not_implies_elim1 :premises (@p208)) % 0.36/0.57 (step @p210 :rule instantiate :premises (@p209) :args ((@list @t101 @t100 @t104))) % 0.36/0.57 (step @p211 :rule instantiate :premises (@p205) :args ((@list @t98 @t99 @t101))) % 0.36/0.57 (step @p212 :rule not_implies_elim1 :premises (@p206)) % 0.36/0.57 (step @p213 :rule instantiate :premises (@p212) :args (@t105)) % 0.36/0.57 (step @p214 :rule not_implies_elim2 :premises (@p208)) % 0.36/0.57 (step @p215 :rule skolemize :premises (@p214)) % 0.36/0.57 (step @p216 :rule bool-double-not-elim :args (@t106)) % 0.36/0.57 (step @p217 :rule refl :args (@t111)) % 0.36/0.57 (step @p218 :rule nary_cong :premises (@p217 @p216) :args ((or @t111 (not @t110)))) % 0.36/0.57 (step @p219 :rule cnf_or_neg :args (@t111 0)) % 0.36/0.57 (step @p220 :rule eq_resolve :premises (@p219 @p218)) % 0.36/0.57 (step @p221 :rule reordering :premises (@p220) :args ((or @t106 @t111))) % 0.36/0.57 (step @p222 :rule chain_m_resolution :premises (@p221 @p215) :args (@t106 @t112 @t113)) % 0.36/0.57 (step @p223 :rule cnf_or_pos :args (@t117)) % 0.36/0.57 (step @p224 :rule reordering :premises (@p223) :args ((or @t110 @t116 @t114 (not @t117)))) % 0.36/0.57 (step @p225 :rule chain_m_resolution :premises (@p224 @p222 @p213 @p211) :args (@t114 (@list false false false) (@list @t106 @t115 @t117))) % 0.36/0.57 (step @p226 :rule not_implies_elim1 :premises (@p203)) % 0.36/0.57 (step @p227 :rule instantiate :premises (@p226) :args ((@list @t102 @t99))) % 0.36/0.57 (step @p228 :rule cnf_or_neg :args (@t111 2)) % 0.36/0.57 (step @p229 :rule chain_m_resolution :premises (@p228 @p215) :args ((not @t107) @t112 @t113)) % 0.36/0.57 (step @p230 :rule cnf_or_pos :args (@t119)) % 0.36/0.57 (step @p231 :rule reordering :premises (@p230) :args ((or @t107 @t118 (not @t119)))) % 0.36/0.57 (step @p232 :rule chain_m_resolution :premises (@p231 @p229 @p227) :args (@t118 @t120 (@list @t107 @t119))) % 0.36/0.57 (step @p233 :rule skolemize :premises (@p232)) % 0.36/0.57 (step @p234 :rule cnf_or_neg :args (@t124 1)) % 0.36/0.57 (step @p235 :rule chain_m_resolution :premises (@p234 @p233) :args (@t125 @t112 @t126)) % 0.36/0.57 (step @p236 :rule refl :args (@t127)) % 0.36/0.57 (step @p237 :rule refl :args (@t129)) % 0.36/0.57 (step @p238 :rule bool-double-not-elim :args (@t121)) % 0.36/0.57 (step @p239 :rule nary_cong :premises (@p238 @p237 @p236) :args ((or @t130 @t129 @t127))) % 0.36/0.57 (assume-push @p308 @t125) % 0.36/0.57 (assume-push @p309 @t128) % 0.36/0.57 (assume-push @p310 @t114) % 0.36/0.57 (step @p243 :rule evaluate :args ((= true false))) % 0.36/0.57 (step @p244 :rule false_intro :premises (@p235)) % 0.36/0.57 (step @p245 :rule refl :args (@t99)) % 0.36/0.57 (step @p246 :rule cong :premises (@p309 @p245) :args (@t114)) % 0.36/0.57 (step @p247 :rule true_intro :premises (@p225)) % 0.36/0.57 (step @p248 :rule symm :premises (@p247)) % 0.36/0.57 (step @p249 :rule trans :premises (@p248 @p246 @p244)) % 0.36/0.57 (step @p250 false :rule eq_resolve :premises (@p249 @p243)) % 0.36/0.57 (step-pop @p311 :rule scope :premises (@p250)) % 0.36/0.57 (step-pop @p312 :rule scope :premises (@p311)) % 0.36/0.57 (step-pop @p313 :rule scope :premises (@p312)) % 0.36/0.57 (step @p251 :rule process_scope :premises (@p313) :args (false)) % 0.36/0.57 (step @p255 :rule not_and :premises (@p251)) % 0.36/0.57 (step @p256 :rule eq_resolve :premises (@p255 @p239)) % 0.36/0.57 (step @p257 :rule chain_m_resolution :premises (@p256 @p235 @p225) :args (@t129 @t120 (@list @t121 @t114))) % 0.36/0.57 (step @p258 :rule bool-double-not-elim :args (@t122)) % 0.36/0.57 (step @p259 :rule refl :args (@t124)) % 0.36/0.57 (step @p260 :rule nary_cong :premises (@p259 @p258) :args ((or @t124 (not @t123)))) % 0.36/0.57 (step @p261 :rule cnf_or_neg :args (@t124 0)) % 0.36/0.57 (step @p262 :rule eq_resolve :premises (@p261 @p260)) % 0.36/0.57 (step @p263 :rule reordering :premises (@p262) :args ((or @t122 @t124))) % 0.36/0.57 (step @p264 :rule chain_m_resolution :premises (@p263 @p233) :args (@t122 @t112 @t126)) % 0.36/0.57 (step @p265 :rule cnf_or_pos :args (@t132)) % 0.36/0.57 (step @p266 :rule reordering :premises (@p265) :args ((or @t123 @t128 @t131 (not @t132)))) % 0.36/0.57 (step @p267 :rule chain_m_resolution :premises (@p266 @p264 @p257 @p210) :args (@t131 (@list false true false) (@list @t122 @t128 @t132))) % 0.36/0.57 (step @p268 :rule refl :args (@t134)) % 0.36/0.57 (step @p269 :rule refl :args (@t135)) % 0.36/0.57 (step @p270 :rule nary_cong :premises (@p238 @p269 @p268) :args ((or @t130 @t135 @t134))) % 0.36/0.57 (assume-push @p314 @t125) % 0.36/0.57 (assume-push @p315 @t131) % 0.36/0.57 (assume-push @p316 @t125) % 0.36/0.57 (assume-push @p317 @t131) % 0.36/0.57 (step @p244 :rule false_intro :premises (@p235)) % 0.36/0.57 (step @p245 :rule refl :args (@t99)) % 0.36/0.57 (step @p275 :rule cong :premises (@p315 @p245) :args (@t133)) % 0.36/0.57 (step @p276 :rule trans :premises (@p275 @p244)) % 0.36/0.57 (step @p277 :rule false_elim :premises (@p276)) % 0.36/0.57 (step-pop @p318 :rule scope :premises (@p277)) % 0.36/0.57 (step-pop @p319 :rule scope :premises (@p318)) % 0.36/0.57 (step @p278 :rule process_scope :premises (@p319) :args (@t134)) % 0.36/0.57 (step @p281 :rule and_intro :premises (@p235 @p315)) % 0.36/0.57 (step @p282 :rule modus_ponens :premises (@p281 @p278)) % 0.36/0.57 (step-pop @p320 :rule scope :premises (@p282)) % 0.36/0.57 (step-pop @p321 :rule scope :premises (@p320)) % 0.36/0.57 (step @p283 :rule process_scope :premises (@p321) :args (@t134)) % 0.36/0.57 (step @p286 :rule implies_elim :premises (@p283)) % 0.36/0.57 (step @p287 :rule cnf_and_neg :args (@t136)) % 0.36/0.57 (step @p288 :rule resolution :premises (@p287 @p286) :args (true @t136)) % 0.36/0.57 (step @p289 :rule eq_resolve :premises (@p288 @p270)) % 0.36/0.57 (step @p290 :rule chain_m_resolution :premises (@p289 @p235 @p267) :args (@t134 @t120 (@list @t121 @t131))) % 0.36/0.57 (step @p291 :rule not_implies_elim1 :premises (@p207)) % 0.36/0.57 (step @p292 :rule instantiate :premises (@p291) :args (@t105)) % 0.36/0.57 (step @p293 :rule bool-double-not-elim :args (@t108)) % 0.36/0.57 (step @p294 :rule nary_cong :premises (@p217 @p293) :args ((or @t111 (not @t109)))) % 0.36/0.57 (step @p295 :rule cnf_or_neg :args (@t111 1)) % 0.36/0.57 (step @p296 :rule eq_resolve :premises (@p295 @p294)) % 0.36/0.57 (step @p297 :rule reordering :premises (@p296) :args ((or @t108 @t111))) % 0.36/0.57 (step @p298 :rule chain_m_resolution :premises (@p297 @p215) :args (@t108 @t112 @t113)) % 0.36/0.57 (step @p299 :rule cnf_or_pos :args (@t139)) % 0.36/0.57 (step @p300 :rule reordering :premises (@p299) :args ((or @t109 @t138 @t133 @t140))) % 0.36/0.57 (step @p301 :rule chain_m_resolution :premises (@p300 @p298 @p292 @p290) :args (@t140 (@list false false true) (@list @t108 @t137 @t133))) % 0.36/0.57 (assume-push @p322 @t141) % 0.36/0.57 (step @p303 :rule instantiate :premises (@p205) :args ((@list @t97 @t99 @t100))) % 0.36/0.57 (step-pop @p323 :rule scope :premises (@p303)) % 0.36/0.57 (step @p304 :rule process_scope :premises (@p323) :args (@t139)) % 0.36/0.57 (step @p306 :rule implies_elim :premises (@p304)) % 0.36/0.57 (step @p307 false :rule chain_m_resolution :premises (@p306 @p301 @p205) :args (false @t120 (@list @t139 @t141))) % 0.36/0.57 ) % 0.36/0.57 % SZS output end Proof % 0.36/0.57 % cvc5 exiting %------------------------------------------------------------------------------