%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU782^2 : 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 : n024.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 08:53:10 AM UTC 2026 % Result : Theorem 0.17s 0.39s % Output : Proof 0.17s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.06 % Problem : SEU782^2 : TPTP v9.2.1. Released v3.7.0. % 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.09/0.26 % Computer : n024.cluster.edu % 0.09/0.26 % Model : x86_64 x86_64 % 0.09/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.26 % Memory : 8042.1875MB % 0.09/0.26 % OS : Linux 3.10.0-693.el7.x86_64 % 0.09/0.26 % CPULimit : 300 % 0.09/0.26 % WCLimit : 300 % 0.09/0.26 % DateTime : Tue Jun 2 12:51:30 EDT 2026 % 0.09/0.26 % CPUTime : % 0.17/0.34 %----Proving TH0 % 0.17/0.39 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.17/0.39 % SZS status Theorem % 0.17/0.39 % SZS output start Proof % 0.17/0.39 ( % 0.17/0.39 (declare-sort $$unsorted 0) % 0.17/0.39 (declare-const tptp.cartprod (-> $$unsorted $$unsorted $$unsorted)) % 0.17/0.39 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.17/0.39 (declare-const tptp.binunionEcases Bool) % 0.17/0.39 (declare-const tptp.binunion (-> $$unsorted $$unsorted $$unsorted)) % 0.17/0.39 (declare-const tptp.subsetI1 Bool) % 0.17/0.39 (declare-const tptp.subsetE Bool) % 0.17/0.39 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.17/0.39 (define tptp.breln () (let ((_let_1 (@var "B" $$unsorted))) (let ((_let_2 (@var "A" $$unsorted))) (let ((_let_3 (@var "C" $$unsorted))) (lambda (@list _let_2 _let_1 _let_3) (_ (_ tptp.subset _let_3) (_ (_ tptp.cartprod _let_2) _let_1))))))) % 0.17/0.39 (define tptp.breln1 () (let ((_let_1 (@var "R" $$unsorted))) (let ((_let_2 (@var "A" $$unsorted))) (lambda (@list _let_2 _let_1) (_ (_ (_ tptp.breln _let_2) _let_2) _let_1))))) % 0.17/0.39 (define @t1 () (@var "B" $$unsorted)) % 0.17/0.39 (define @t2 () (@var "A" $$unsorted)) % 0.17/0.39 (define @t3 () (_ (_ tptp.subset @t2) @t1)) % 0.17/0.39 (define @t4 () (@var "Xx" $$unsorted)) % 0.17/0.39 (define @t5 () (_ tptp.in @t4)) % 0.17/0.39 (define @t6 () (_ @t5 @t1)) % 0.17/0.39 (define @t7 () (_ @t5 @t2)) % 0.17/0.39 (define @t8 () (=> @t7 @t6)) % 0.17/0.39 (define @t9 () (@list @t4)) % 0.17/0.39 (define @t10 () (forall @t9 @t8)) % 0.17/0.39 (define @t11 () (=> @t10 @t3)) % 0.17/0.39 (define @t12 () (@list @t2 @t1)) % 0.17/0.39 (define @t13 () (forall @t12 @t11)) % 0.17/0.39 (define @t14 () (= tptp.subsetI1 @t13)) % 0.17/0.39 (define @t15 () (@list @t2 @t1 @t4)) % 0.17/0.39 (define @t16 () (forall @t15 (=> @t3 @t8))) % 0.17/0.39 (define @t17 () (= tptp.subsetE @t16)) % 0.17/0.39 (define @t18 () (@var "Xphi" Bool)) % 0.17/0.39 (define @t19 () (=> @t6 @t18)) % 0.17/0.39 (define @t20 () (=> @t19 @t18)) % 0.17/0.39 (define @t21 () (=> @t7 @t18)) % 0.17/0.39 (define @t22 () (=> @t21 @t20)) % 0.17/0.39 (define @t23 () (_ (_ tptp.binunion @t2) @t1)) % 0.17/0.39 (define @t24 () (_ @t5 @t23)) % 0.17/0.39 (define @t25 () (@list @t2 @t1 @t4 @t18)) % 0.17/0.39 (define @t26 () (forall @t25 (=> @t24 @t22))) % 0.17/0.39 (define @t27 () (= tptp.binunionEcases @t26)) % 0.17/0.39 (define @t28 () (@var "S" $$unsorted)) % 0.17/0.39 (define @t29 () (@var "R" $$unsorted)) % 0.17/0.39 (define @t30 () (_ (_ tptp.binunion @t29) @t28)) % 0.17/0.39 (define @t31 () (_ tptp.breln1 @t2)) % 0.17/0.39 (define @t32 () (=> (_ @t31 @t28) (_ @t31 @t30))) % 0.17/0.39 (define @t33 () (@list @t28)) % 0.17/0.39 (define @t34 () (forall @t33 @t32)) % 0.17/0.39 (define @t35 () (=> (_ @t31 @t29) @t34)) % 0.17/0.39 (define @t36 () (@list @t2 @t29)) % 0.17/0.39 (define @t37 () (forall @t36 @t35)) % 0.17/0.39 (define @t38 () (=> tptp.binunionEcases @t37)) % 0.17/0.39 (define @t39 () (=> tptp.subsetE @t38)) % 0.17/0.39 (define @t40 () (=> tptp.subsetI1 @t39)) % 0.17/0.39 (define @t41 () (not @t40)) % 0.17/0.39 (define @t42 () (_ tptp.cartprod @t2)) % 0.17/0.39 (define @t43 () (@var "C" $$unsorted)) % 0.17/0.39 (define @t44 () (_ tptp.subset @t43)) % 0.17/0.39 (define @t45 () (_ @t44 (_ @t42 @t1))) % 0.17/0.39 (define @t46 () (lambda (@list @t2 @t1 @t43) @t45)) % 0.17/0.39 (define @t47 () (lambda @t36 (_ (_ (_ tptp.breln @t2) @t2) @t29))) % 0.17/0.39 (define @t48 () (tptp.cartprod @t2 @t2)) % 0.17/0.39 (define @t49 () (@var "BOUND_VARIABLE_7612" $$unsorted)) % 0.17/0.39 (define @t50 () (tptp.subset (tptp.binunion @t29 @t49) @t48)) % 0.17/0.39 (define @t51 () (not (tptp.subset @t49 @t48))) % 0.17/0.39 (define @t52 () (tptp.subset @t29 @t48)) % 0.17/0.39 (define @t53 () (not @t52)) % 0.17/0.39 (define @t54 () (or @t53 @t51 @t50)) % 0.17/0.39 (define @t55 () (@list @t2 @t29 @t49)) % 0.17/0.39 (define @t56 () (forall @t55 @t54)) % 0.17/0.39 (define @t57 () (tptp.in @t4 @t1)) % 0.17/0.39 (define @t58 () (not false)) % 0.17/0.39 (define @t59 () (and @t57 @t58)) % 0.17/0.39 (define @t60 () (tptp.in @t4 @t2)) % 0.17/0.39 (define @t61 () (and @t60 @t58)) % 0.17/0.39 (define @t62 () (tptp.binunion @t2 @t1)) % 0.17/0.39 (define @t63 () (tptp.in @t4 @t62)) % 0.17/0.39 (define @t64 () (not @t63)) % 0.17/0.39 (define @t65 () (or @t64 @t61 @t59)) % 0.17/0.39 (define @t66 () (or @t64 @t61 @t59 false)) % 0.17/0.39 (define @t67 () (not @t18)) % 0.17/0.39 (define @t68 () (and @t57 @t67)) % 0.17/0.39 (define @t69 () (and @t60 @t67)) % 0.17/0.39 (define @t70 () (@list @t18)) % 0.17/0.39 (define @t71 () (or @t18 @t64 @t69 @t68 @t18)) % 0.17/0.39 (define @t72 () (or @t64 @t69 @t68 @t18)) % 0.17/0.39 (define @t73 () (forall @t70 @t72)) % 0.17/0.39 (define @t74 () (forall @t15 @t73)) % 0.17/0.39 (define @t75 () (and @t6 @t67)) % 0.17/0.39 (define @t76 () (and @t7 @t67)) % 0.17/0.39 (define @t77 () (not @t24)) % 0.17/0.39 (define @t78 () (or @t77 @t76 @t75 @t18)) % 0.17/0.39 (define @t79 () (or @t76 @t75 @t18)) % 0.17/0.39 (define @t80 () (=> tptp.binunionEcases @t56)) % 0.17/0.39 (define @t81 () (not @t7)) % 0.17/0.39 (define @t82 () (tptp.subset @t2 @t1)) % 0.17/0.39 (define @t83 () (not @t3)) % 0.17/0.39 (define @t84 () (or @t83 @t81 @t6)) % 0.17/0.39 (define @t85 () (or @t81 @t6)) % 0.17/0.39 (define @t86 () (=> tptp.subsetE @t80)) % 0.17/0.39 (define @t87 () (not @t60)) % 0.17/0.39 (define @t88 () (forall @t9 (or @t87 @t57))) % 0.17/0.39 (define @t89 () (not @t88)) % 0.17/0.39 (define @t90 () (or @t89 @t3)) % 0.17/0.39 (define @t91 () (=> tptp.subsetI1 @t86)) % 0.17/0.39 (define @t92 () (or @t51 @t50)) % 0.17/0.39 (define @t93 () (or @t53 @t92)) % 0.17/0.39 (define @t94 () (forall @t55 @t93)) % 0.17/0.39 (define @t95 () (@list @t49)) % 0.17/0.39 (define @t96 () (forall @t95 @t93)) % 0.17/0.39 (define @t97 () (forall @t95 @t92)) % 0.17/0.39 (define @t98 () (or @t53 @t97)) % 0.17/0.39 (define @t99 () (tptp.binunion @t29 @t28)) % 0.17/0.39 (define @t100 () (tptp.subset @t99 @t48)) % 0.17/0.39 (define @t101 () (tptp.subset @t28 @t48)) % 0.17/0.39 (define @t102 () (forall @t33 (or (not @t101) @t100))) % 0.17/0.39 (define @t103 () (_ @t42 @t2)) % 0.17/0.39 (define @t104 () (_ tptp.subset @t29)) % 0.17/0.39 (define @t105 () (_ @t104 @t103)) % 0.17/0.39 (define @t106 () (not @t105)) % 0.17/0.39 (define @t107 () (or @t106 @t102)) % 0.17/0.39 (define @t108 () (_ (_ tptp.subset @t30) @t103)) % 0.17/0.39 (define @t109 () (_ tptp.subset @t28)) % 0.17/0.39 (define @t110 () (_ @t109 @t103)) % 0.17/0.39 (define @t111 () (not @t110)) % 0.17/0.39 (define @t112 () (or @t111 @t108)) % 0.17/0.39 (define @t113 () (lambda (@list @t29) @t105)) % 0.17/0.39 (define @t114 () (_ (lambda @t36 @t105) @t2)) % 0.17/0.39 (define @t115 () (=> (_ @t114 @t28) (_ @t114 @t30))) % 0.17/0.39 (define @t116 () (forall @t33 @t115)) % 0.17/0.39 (define @t117 () (=> (_ @t114 @t29) @t116)) % 0.17/0.39 (define @t118 () (forall @t36 @t117)) % 0.17/0.39 (define @t119 () (=> tptp.binunionEcases @t118)) % 0.17/0.39 (define @t120 () (=> tptp.subsetE @t119)) % 0.17/0.39 (define @t121 () (=> tptp.subsetI1 @t120)) % 0.17/0.39 (define @t122 () (lambda (@list @t43) (_ @t44 @t103))) % 0.17/0.39 (define @t123 () (lambda (@list @t1 @t43) @t45)) % 0.17/0.39 (define @t124 () (@quantifiers_skolemize @t56 0)) % 0.17/0.39 (define @t125 () (tptp.cartprod @t124 @t124)) % 0.17/0.39 (define @t126 () (@quantifiers_skolemize @t56 2)) % 0.17/0.39 (define @t127 () (@quantifiers_skolemize @t56 1)) % 0.17/0.39 (define @t128 () (tptp.binunion @t127 @t126)) % 0.17/0.39 (define @t129 () (forall @t9 (or (not (tptp.in @t4 @t128)) (tptp.in @t4 @t125)))) % 0.17/0.39 (define @t130 () (@quantifiers_skolemize @t129 0)) % 0.17/0.39 (define @t131 () (tptp.subset @t128 @t125)) % 0.17/0.39 (define @t132 () (tptp.subset @t126 @t125)) % 0.17/0.39 (define @t133 () (not @t132)) % 0.17/0.39 (define @t134 () (tptp.subset @t127 @t125)) % 0.17/0.39 (define @t135 () (not @t134)) % 0.17/0.39 (define @t136 () (or @t135 @t133 @t131)) % 0.17/0.39 (define @t137 () (@list true)) % 0.17/0.39 (define @t138 () (@list @t136)) % 0.17/0.39 (define @t139 () (not @t129)) % 0.17/0.39 (define @t140 () (or @t139 @t131)) % 0.17/0.39 (define @t141 () (@list true false)) % 0.17/0.39 (define @t142 () (tptp.in @t130 @t125)) % 0.17/0.39 (define @t143 () (tptp.in @t130 @t128)) % 0.17/0.39 (define @t144 () (not @t143)) % 0.17/0.39 (define @t145 () (or @t144 @t142)) % 0.17/0.39 (define @t146 () (@list @t145)) % 0.17/0.39 (define @t147 () (tptp.in @t130 @t127)) % 0.17/0.39 (define @t148 () (not @t147)) % 0.17/0.39 (define @t149 () (or @t135 @t148 @t142)) % 0.17/0.39 (define @t150 () (@list false true false)) % 0.17/0.39 (define @t151 () (tptp.in @t130 @t126)) % 0.17/0.39 (define @t152 () (or @t144 @t147 @t151)) % 0.17/0.39 (define @t153 () (not @t151)) % 0.17/0.39 (define @t154 () (or @t133 @t153 @t142)) % 0.17/0.39 (define @t155 () (not @t154)) % 0.17/0.39 (define @t156 () (forall @t15 (or (not @t82) @t87 @t57))) % 0.17/0.39 (assume @p1 @t14) % 0.17/0.39 (assume @p2 @t17) % 0.17/0.39 (assume @p3 @t27) % 0.17/0.39 (assume @p4 @t41) % 0.17/0.39 (assume @p5 true) % 0.17/0.39 (step @p6 (= tptp.breln @t46) :rule refl :args (@t46)) % 0.17/0.39 (step @p7 (= tptp.breln1 @t47) :rule refl :args (@t47)) % 0.17/0.39 (step @p8 :rule refl :args (@t56)) % 0.17/0.39 (step @p9 :rule aci_norm :args ((= (and @t57 true) @t57))) % 0.17/0.39 (step @p10 :rule evaluate :args (@t58)) % 0.17/0.39 (step @p11 :rule refl :args (@t57)) % 0.17/0.39 (step @p12 :rule nary_cong :premises (@p11 @p10) :args (@t59)) % 0.17/0.39 (step @p13 :rule trans :premises (@p12 @p9)) % 0.17/0.39 (step @p14 :rule aci_norm :args ((= (and @t60 true) @t60))) % 0.17/0.39 (step @p15 :rule refl :args (@t60)) % 0.17/0.39 (step @p16 :rule nary_cong :premises (@p15 @p10) :args (@t61)) % 0.17/0.39 (step @p17 :rule trans :premises (@p16 @p14)) % 0.17/0.39 (step @p18 :rule refl :args (@t64)) % 0.17/0.39 (step @p19 :rule nary_cong :premises (@p18 @p17 @p13) :args (@t65)) % 0.17/0.39 (step @p20 :rule aci_norm :args ((= @t66 @t65))) % 0.17/0.39 (step @p21 :rule trans :premises (@p20 @p19)) % 0.17/0.39 (step @p22 :rule cong :premises (@p21) :args ((forall @t15 @t66))) % 0.17/0.39 (step @p23 :rule quant-var-elim-eq :args ((= (forall @t70 (or (not (= @t18 false)) @t64 @t69 @t68 @t18)) @t66))) % 0.17/0.39 (step @p24 :rule refl :args (@t18)) % 0.17/0.39 (step @p25 :rule refl :args (@t68)) % 0.17/0.39 (step @p26 :rule refl :args (@t69)) % 0.17/0.39 (step @p27 :rule refl :args (@t64)) % 0.17/0.39 (step @p28 :rule bool-eq-false :args (@t18)) % 0.17/0.39 (step @p29 :rule symm :premises (@p28)) % 0.17/0.39 (step @p30 :rule cong :premises (@p29) :args ((not @t67))) % 0.17/0.39 (step @p31 :rule bool-double-not-elim :args (@t18)) % 0.17/0.39 (step @p32 :rule symm :premises (@p31)) % 0.17/0.39 (step @p33 :rule trans :premises (@p32 @p30)) % 0.17/0.39 (step @p34 :rule nary_cong :premises (@p33 @p27 @p26 @p25 @p24) :args (@t71)) % 0.17/0.39 (step @p35 :rule aci_norm :args ((= @t72 @t71))) % 0.17/0.39 (step @p36 :rule trans :premises (@p35 @p34)) % 0.17/0.39 (step @p37 :rule cong :premises (@p36) :args (@t73)) % 0.17/0.39 (step @p38 :rule trans :premises (@p37 @p23)) % 0.17/0.39 (step @p39 :rule cong :premises (@p38) :args (@t74)) % 0.17/0.39 (step @p40 :rule quant-merge-prenex :args ((= @t74 (forall @t25 @t72)))) % 0.17/0.39 (step @p41 :rule symm :premises (@p40)) % 0.17/0.39 (step @p42 :rule trans :premises (@p41 @p39)) % 0.17/0.39 (step @p43 :rule trans :premises (@p42 @p22)) % 0.17/0.39 (step @p44 :rule refl :args (@t67)) % 0.17/0.39 (step @p45 :rule refl :args (@t57)) % 0.17/0.39 (step @p46 :rule refl :args (@t6)) % 0.17/0.39 (step @p47 :rule cong :premises (@p46 @p45) :args ((= @t6 @t57))) % 0.17/0.39 (step @p48 :rule symm :premises (@p47)) % 0.17/0.39 (step @p49 :rule eq_resolve :premises (@p46 @p48)) % 0.17/0.39 (step @p50 :rule nary_cong :premises (@p49 @p44) :args (@t75)) % 0.17/0.39 (step @p51 :rule refl :args (@t60)) % 0.17/0.39 (step @p52 :rule refl :args (@t7)) % 0.17/0.39 (step @p53 :rule cong :premises (@p52 @p51) :args ((= @t7 @t60))) % 0.17/0.39 (step @p54 :rule symm :premises (@p53)) % 0.17/0.39 (step @p55 :rule eq_resolve :premises (@p52 @p54)) % 0.17/0.39 (step @p56 :rule nary_cong :premises (@p55 @p44) :args (@t76)) % 0.17/0.39 (step @p57 :rule refl :args ((tptp.in @t4 @t23))) % 0.17/0.39 (step @p58 :rule refl :args (@t62)) % 0.17/0.39 (step @p59 :rule refl :args (@t4)) % 0.17/0.39 (step @p60 :rule cong :premises (@p59 @p58) :args (@t63)) % 0.17/0.39 (step @p61 :rule trans :premises (@p60 @p57)) % 0.17/0.39 (step @p62 :rule refl :args (@t5)) % 0.17/0.39 (step @p63 :rule ho_cong :premises (@p62 @p58)) % 0.17/0.39 (step @p64 :rule cong :premises (@p63 @p61) :args ((= (_ @t5 @t62) @t63))) % 0.17/0.39 (step @p65 :rule symm :premises (@p64)) % 0.17/0.39 (step @p66 :rule refl :args (@t24)) % 0.17/0.39 (step @p67 :rule eq_resolve :premises (@p66 @p65)) % 0.17/0.39 (step @p68 :rule refl :args (@t23)) % 0.17/0.39 (step @p69 :rule cong :premises (@p68 @p58) :args ((= @t23 @t62))) % 0.17/0.39 (step @p70 :rule symm :premises (@p69)) % 0.17/0.39 (step @p71 :rule eq_resolve :premises (@p68 @p70)) % 0.17/0.39 (step @p72 :rule ho_cong :premises (@p62 @p71)) % 0.17/0.39 (step @p73 :rule trans :premises (@p72 @p67)) % 0.17/0.39 (step @p74 :rule cong :premises (@p73) :args (@t77)) % 0.17/0.39 (step @p75 :rule nary_cong :premises (@p74 @p56 @p50 @p24) :args (@t78)) % 0.17/0.39 (step @p76 :rule cong :premises (@p75) :args ((forall @t25 @t78))) % 0.17/0.39 (step @p77 :rule trans :premises (@p76 @p43)) % 0.17/0.39 (step @p78 :rule aci_norm :args ((= (or @t77 @t79) @t78))) % 0.17/0.39 (step @p79 :rule aci_norm :args ((= (or @t76 (or @t75 @t18)) @t79))) % 0.17/0.39 (step @p80 :rule bool-implies-de-morgan :args (@t6 @t18)) % 0.17/0.39 (step @p81 :rule nary_cong :premises (@p80 @p24) :args ((or (not @t19) @t18))) % 0.17/0.39 (step @p82 :rule bool-impl-elim :args (@t19 @t18)) % 0.17/0.39 (step @p83 :rule trans :premises (@p82 @p81)) % 0.17/0.39 (step @p84 :rule bool-implies-de-morgan :args (@t7 @t18)) % 0.17/0.39 (step @p85 :rule nary_cong :premises (@p84 @p83) :args ((or (not @t21) @t20))) % 0.17/0.39 (step @p86 :rule trans :premises (@p85 @p79)) % 0.17/0.39 (step @p87 :rule bool-impl-elim :args (@t21 @t20)) % 0.17/0.39 (step @p88 :rule trans :premises (@p87 @p86)) % 0.17/0.39 (step @p89 :rule refl :args (@t77)) % 0.17/0.39 (step @p90 :rule nary_cong :premises (@p89 @p88) :args ((or @t77 @t22))) % 0.17/0.39 (step @p91 :rule trans :premises (@p90 @p78)) % 0.17/0.39 (step @p92 :rule bool-impl-elim :args (@t24 @t22)) % 0.17/0.39 (step @p93 :rule trans :premises (@p92 @p91)) % 0.17/0.39 (step @p94 :rule cong :premises (@p93) :args (@t26)) % 0.17/0.39 (step @p95 :rule trans :premises (@p94 @p77)) % 0.17/0.39 (step @p96 :rule refl :args (tptp.binunionEcases)) % 0.17/0.39 (step @p97 :rule cong :premises (@p96 @p95) :args (@t27)) % 0.17/0.39 (step @p98 :rule eq_resolve :premises (@p3 @p97)) % 0.17/0.39 (step @p99 :rule cong :premises (@p98 @p8) :args (@t80)) % 0.17/0.39 (step @p100 :rule cong :premises (@p55) :args (@t81)) % 0.17/0.39 (step @p101 :rule refl :args (@t82)) % 0.17/0.39 (step @p102 :rule refl :args (@t3)) % 0.17/0.39 (step @p103 :rule cong :premises (@p102 @p101) :args ((= @t3 @t82))) % 0.17/0.39 (step @p104 :rule symm :premises (@p103)) % 0.17/0.39 (step @p105 :rule eq_resolve :premises (@p102 @p104)) % 0.17/0.39 (step @p106 :rule cong :premises (@p105) :args (@t83)) % 0.17/0.39 (step @p107 :rule nary_cong :premises (@p106 @p100 @p49) :args (@t84)) % 0.17/0.39 (step @p108 :rule cong :premises (@p107) :args ((forall @t15 @t84))) % 0.17/0.39 (step @p109 :rule aci_norm :args ((= (or @t83 @t85) @t84))) % 0.17/0.39 (step @p110 :rule bool-impl-elim :args (@t7 @t6)) % 0.17/0.39 (step @p111 :rule refl :args (@t83)) % 0.17/0.39 (step @p112 :rule nary_cong :premises (@p111 @p110) :args ((or @t83 @t8))) % 0.17/0.39 (step @p113 :rule trans :premises (@p112 @p109)) % 0.17/0.39 (step @p114 :rule bool-impl-elim :args (@t3 @t8)) % 0.17/0.39 (step @p115 :rule trans :premises (@p114 @p113)) % 0.17/0.39 (step @p116 :rule cong :premises (@p115) :args (@t16)) % 0.17/0.39 (step @p117 :rule trans :premises (@p116 @p108)) % 0.17/0.39 (step @p118 :rule refl :args (tptp.subsetE)) % 0.17/0.39 (step @p119 :rule cong :premises (@p118 @p117) :args (@t17)) % 0.17/0.39 (step @p120 :rule eq_resolve :premises (@p2 @p119)) % 0.17/0.39 (step @p121 :rule cong :premises (@p120 @p99) :args (@t86)) % 0.17/0.39 (step @p122 :rule refl :args (@t89)) % 0.17/0.39 (step @p123 :rule nary_cong :premises (@p122 @p105) :args (@t90)) % 0.17/0.39 (step @p124 :rule cong :premises (@p123) :args ((forall @t12 @t90))) % 0.17/0.39 (step @p125 :rule bool-impl-elim :args (@t88 @t3)) % 0.17/0.39 (step @p126 :rule cong :premises (@p125) :args ((forall @t12 (=> @t88 @t3)))) % 0.17/0.39 (step @p127 :rule trans :premises (@p126 @p124)) % 0.17/0.39 (step @p128 :rule refl :args (@t3)) % 0.17/0.39 (step @p129 :rule nary_cong :premises (@p100 @p49) :args (@t85)) % 0.17/0.39 (step @p130 :rule cong :premises (@p129) :args ((forall @t9 @t85))) % 0.17/0.39 (step @p131 :rule cong :premises (@p110) :args (@t10)) % 0.17/0.39 (step @p132 :rule trans :premises (@p131 @p130)) % 0.17/0.39 (step @p133 :rule cong :premises (@p132 @p128) :args (@t11)) % 0.17/0.39 (step @p134 :rule cong :premises (@p133) :args (@t13)) % 0.17/0.39 (step @p135 :rule trans :premises (@p134 @p127)) % 0.17/0.39 (step @p136 :rule refl :args (tptp.subsetI1)) % 0.17/0.39 (step @p137 :rule cong :premises (@p136 @p135) :args (@t14)) % 0.17/0.39 (step @p138 :rule eq_resolve :premises (@p1 @p137)) % 0.17/0.39 (step @p139 :rule cong :premises (@p138 @p121) :args (@t91)) % 0.17/0.39 (step @p140 :rule cong :premises (@p139) :args ((not @t91))) % 0.17/0.39 (step @p141 :rule aci_norm :args ((= @t93 @t54))) % 0.17/0.39 (step @p142 :rule cong :premises (@p141) :args (@t94)) % 0.17/0.39 (step @p143 :rule quant-merge-prenex :args ((= (forall @t36 @t96) @t94))) % 0.17/0.39 (step @p144 :rule alpha_equiv :args (@t97 (@list @t49) (@list @t28))) % 0.17/0.39 (step @p145 :rule refl :args (@t53)) % 0.17/0.39 (step @p146 :rule nary_cong :premises (@p145 @p144) :args (@t98)) % 0.17/0.39 (step @p147 :rule quant-miniscope-or :args ((= @t96 @t98))) % 0.17/0.39 (step @p148 :rule trans :premises (@p147 @p146)) % 0.17/0.39 (step @p149 :rule symm :premises (@p148)) % 0.17/0.39 (step @p150 :rule cong :premises (@p149) :args ((forall @t36 (or @t53 @t102)))) % 0.17/0.39 (step @p151 :rule trans :premises (@p150 @p143)) % 0.17/0.39 (step @p152 :rule trans :premises (@p151 @p142)) % 0.17/0.39 (step @p153 :rule refl :args (@t102)) % 0.17/0.39 (step @p154 :rule refl :args ((tptp.subset @t29 @t103))) % 0.17/0.39 (step @p155 :rule refl :args (@t48)) % 0.17/0.39 (step @p156 :rule refl :args (@t29)) % 0.17/0.39 (step @p157 :rule cong :premises (@p156 @p155) :args (@t52)) % 0.17/0.39 (step @p158 :rule trans :premises (@p157 @p154)) % 0.17/0.39 (step @p159 :rule refl :args (@t104)) % 0.17/0.39 (step @p160 :rule ho_cong :premises (@p159 @p155)) % 0.17/0.39 (step @p161 :rule cong :premises (@p160 @p158) :args ((= (_ @t104 @t48) @t52))) % 0.17/0.39 (step @p162 :rule symm :premises (@p161)) % 0.17/0.39 (step @p163 :rule refl :args (@t105)) % 0.17/0.39 (step @p164 :rule eq_resolve :premises (@p163 @p162)) % 0.17/0.39 (step @p165 :rule refl :args (@t103)) % 0.17/0.39 (step @p166 :rule cong :premises (@p165 @p155) :args ((= @t103 @t48))) % 0.17/0.39 (step @p167 :rule symm :premises (@p166)) % 0.17/0.39 (step @p168 :rule eq_resolve :premises (@p165 @p167)) % 0.17/0.39 (step @p169 :rule ho_cong :premises (@p159 @p168)) % 0.17/0.39 (step @p170 :rule trans :premises (@p169 @p164)) % 0.17/0.39 (step @p171 :rule cong :premises (@p170) :args (@t106)) % 0.17/0.39 (step @p172 :rule nary_cong :premises (@p171 @p153) :args (@t107)) % 0.17/0.39 (step @p173 :rule cong :premises (@p172) :args ((forall @t36 @t107))) % 0.17/0.39 (step @p174 :rule trans :premises (@p173 @p152)) % 0.17/0.39 (step @p175 :rule bool-impl-elim :args (@t105 @t102)) % 0.17/0.39 (step @p176 :rule cong :premises (@p175) :args ((forall @t36 (=> @t105 @t102)))) % 0.17/0.39 (step @p177 :rule trans :premises (@p176 @p174)) % 0.17/0.39 (step @p178 :rule refl :args ((tptp.subset @t30 @t103))) % 0.17/0.39 (step @p179 :rule refl :args (@t99)) % 0.17/0.39 (step @p180 :rule cong :premises (@p179 @p155) :args (@t100)) % 0.17/0.39 (step @p181 :rule trans :premises (@p180 @p178)) % 0.17/0.39 (step @p182 :rule refl :args (tptp.subset)) % 0.17/0.39 (step @p183 :rule ho_cong :premises (@p182 @p179)) % 0.17/0.39 (step @p184 :rule ho_cong :premises (@p183 @p155)) % 0.17/0.39 (step @p185 :rule cong :premises (@p184 @p181) :args ((= (_ (_ tptp.subset @t99) @t48) @t100))) % 0.17/0.39 (step @p186 :rule symm :premises (@p185)) % 0.17/0.39 (step @p187 :rule refl :args (@t108)) % 0.17/0.39 (step @p188 :rule eq_resolve :premises (@p187 @p186)) % 0.17/0.39 (step @p189 :rule refl :args (@t30)) % 0.17/0.39 (step @p190 :rule cong :premises (@p189 @p179) :args ((= @t30 @t99))) % 0.17/0.39 (step @p191 :rule symm :premises (@p190)) % 0.17/0.39 (step @p192 :rule eq_resolve :premises (@p189 @p191)) % 0.17/0.39 (step @p193 :rule ho_cong :premises (@p182 @p192)) % 0.17/0.39 (step @p194 :rule ho_cong :premises (@p193 @p168)) % 0.17/0.39 (step @p195 :rule trans :premises (@p194 @p188)) % 0.17/0.39 (step @p196 :rule refl :args ((tptp.subset @t28 @t103))) % 0.17/0.39 (step @p197 :rule refl :args (@t28)) % 0.17/0.39 (step @p198 :rule cong :premises (@p197 @p155) :args (@t101)) % 0.17/0.39 (step @p199 :rule trans :premises (@p198 @p196)) % 0.17/0.39 (step @p200 :rule refl :args (@t109)) % 0.17/0.39 (step @p201 :rule ho_cong :premises (@p200 @p155)) % 0.17/0.39 (step @p202 :rule cong :premises (@p201 @p199) :args ((= (_ @t109 @t48) @t101))) % 0.17/0.39 (step @p203 :rule symm :premises (@p202)) % 0.17/0.39 (step @p204 :rule refl :args (@t110)) % 0.17/0.39 (step @p205 :rule eq_resolve :premises (@p204 @p203)) % 0.17/0.39 (step @p206 :rule ho_cong :premises (@p200 @p168)) % 0.17/0.39 (step @p207 :rule trans :premises (@p206 @p205)) % 0.17/0.39 (step @p208 :rule cong :premises (@p207) :args (@t111)) % 0.17/0.39 (step @p209 :rule nary_cong :premises (@p208 @p195) :args (@t112)) % 0.17/0.39 (step @p210 :rule cong :premises (@p209) :args ((forall @t33 @t112))) % 0.17/0.39 (step @p211 :rule bool-impl-elim :args (@t110 @t108)) % 0.17/0.39 (step @p212 :rule cong :premises (@p211) :args ((forall @t33 (=> @t110 @t108)))) % 0.17/0.39 (step @p213 :rule trans :premises (@p212 @p210)) % 0.17/0.39 (step @p214 :rule beta-reduce :args ((= (_ @t113 @t30) @t108))) % 0.17/0.39 (step @p215 :rule refl :args (@t30)) % 0.17/0.39 (step @p216 :rule beta-reduce :args ((= @t114 @t113))) % 0.17/0.39 (step @p217 :rule ho_cong :premises (@p216 @p215)) % 0.17/0.39 (step @p218 :rule trans :premises (@p217 @p214)) % 0.17/0.39 (step @p219 :rule beta-reduce :args ((= (_ @t113 @t28) @t110))) % 0.17/0.39 (step @p220 :rule refl :args (@t28)) % 0.17/0.39 (step @p221 :rule ho_cong :premises (@p216 @p220)) % 0.17/0.39 (step @p222 :rule trans :premises (@p221 @p219)) % 0.17/0.39 (step @p223 :rule cong :premises (@p222 @p218) :args (@t115)) % 0.17/0.39 (step @p224 :rule cong :premises (@p223) :args (@t116)) % 0.17/0.39 (step @p225 :rule trans :premises (@p224 @p213)) % 0.17/0.39 (step @p226 :rule beta-reduce :args ((= (_ @t113 @t29) @t105))) % 0.17/0.39 (step @p227 :rule refl :args (@t29)) % 0.17/0.39 (step @p228 :rule ho_cong :premises (@p216 @p227)) % 0.17/0.39 (step @p229 :rule trans :premises (@p228 @p226)) % 0.17/0.39 (step @p230 :rule cong :premises (@p229 @p225) :args (@t117)) % 0.17/0.39 (step @p231 :rule cong :premises (@p230) :args (@t118)) % 0.17/0.39 (step @p232 :rule trans :premises (@p231 @p177)) % 0.17/0.39 (step @p233 :rule cong :premises (@p96 @p232) :args (@t119)) % 0.17/0.39 (step @p234 :rule cong :premises (@p118 @p233) :args (@t120)) % 0.17/0.39 (step @p235 :rule cong :premises (@p136 @p234) :args (@t121)) % 0.17/0.39 (step @p236 :rule cong :premises (@p235) :args ((not @t121))) % 0.17/0.39 (step @p237 :rule refl :args (@t2)) % 0.17/0.39 (step @p238 :rule beta-reduce :args ((= (_ @t122 @t29) @t105))) % 0.17/0.39 (step @p239 :rule beta-reduce :args ((= (_ @t123 @t2) @t122))) % 0.17/0.39 (step @p240 :rule beta-reduce :args ((= (_ @t46 @t2) @t123))) % 0.17/0.39 (step @p241 :rule ho_cong :premises (@p240 @p237)) % 0.17/0.39 (step @p242 :rule trans :premises (@p241 @p239)) % 0.17/0.39 (step @p243 :rule ho_cong :premises (@p242 @p227)) % 0.17/0.39 (step @p244 :rule trans :premises (@p243 @p238)) % 0.17/0.39 (step @p245 :rule ho_cong :premises (@p6 @p237)) % 0.17/0.39 (step @p246 :rule ho_cong :premises (@p245 @p237)) % 0.17/0.39 (step @p247 :rule ho_cong :premises (@p246 @p227)) % 0.17/0.39 (step @p248 :rule trans :premises (@p247 @p244)) % 0.17/0.39 (step @p249 :rule cong :premises (@p248) :args (@t47)) % 0.17/0.39 (step @p250 :rule trans :premises (@p7 @p249)) % 0.17/0.39 (step @p251 :rule ho_cong :premises (@p250 @p237)) % 0.17/0.39 (step @p252 :rule ho_cong :premises (@p251 @p215)) % 0.17/0.39 (step @p253 :rule ho_cong :premises (@p251 @p220)) % 0.17/0.39 (step @p254 :rule cong :premises (@p253 @p252) :args (@t32)) % 0.17/0.39 (step @p255 :rule cong :premises (@p254) :args (@t34)) % 0.17/0.39 (step @p256 :rule ho_cong :premises (@p251 @p227)) % 0.17/0.39 (step @p257 :rule cong :premises (@p256 @p255) :args (@t35)) % 0.17/0.39 (step @p258 :rule cong :premises (@p257) :args (@t37)) % 0.17/0.39 (step @p259 :rule cong :premises (@p96 @p258) :args (@t38)) % 0.17/0.39 (step @p260 :rule cong :premises (@p118 @p259) :args (@t39)) % 0.17/0.39 (step @p261 :rule cong :premises (@p136 @p260) :args (@t40)) % 0.17/0.39 (step @p262 :rule cong :premises (@p261) :args (@t41)) % 0.17/0.39 (step @p263 :rule trans :premises (@p262 @p236)) % 0.17/0.39 (step @p264 :rule trans :premises (@p263 @p140)) % 0.17/0.39 (step @p265 :rule eq_resolve :premises (@p4 @p264)) % 0.17/0.39 (step @p266 :rule not_implies_elim2 :premises (@p265)) % 0.17/0.39 (step @p267 :rule not_implies_elim1 :premises (@p266)) % 0.17/0.39 (step @p268 :rule not_implies_elim2 :premises (@p266)) % 0.17/0.39 (step @p269 :rule not_implies_elim1 :premises (@p268)) % 0.17/0.39 (step @p270 :rule instantiate :premises (@p269) :args ((@list @t127 @t126 @t130))) % 0.17/0.39 (step @p271 :rule instantiate :premises (@p267) :args ((@list @t127 @t125 @t130))) % 0.17/0.39 (step @p272 :rule not_implies_elim1 :premises (@p265)) % 0.17/0.39 (step @p273 :rule instantiate :premises (@p272) :args ((@list @t128 @t125))) % 0.17/0.39 (step @p274 :rule not_implies_elim2 :premises (@p268)) % 0.17/0.39 (step @p275 :rule skolemize :premises (@p274)) % 0.17/0.39 (step @p276 :rule cnf_or_neg :args (@t136 2)) % 0.17/0.39 (step @p277 :rule chain_m_resolution :premises (@p276 @p275) :args ((not @t131) @t137 @t138)) % 0.17/0.39 (step @p278 :rule cnf_or_pos :args (@t140)) % 0.17/0.39 (step @p279 :rule reordering :premises (@p278) :args ((or @t131 @t139 (not @t140)))) % 0.17/0.39 (step @p280 :rule chain_m_resolution :premises (@p279 @p277 @p273) :args (@t139 @t141 (@list @t131 @t140))) % 0.17/0.39 (step @p281 :rule skolemize :premises (@p280)) % 0.17/0.39 (step @p282 :rule cnf_or_neg :args (@t145 1)) % 0.17/0.39 (step @p283 :rule chain_m_resolution :premises (@p282 @p281) :args ((not @t142) @t137 @t146)) % 0.17/0.39 (step @p284 :rule bool-double-not-elim :args (@t134)) % 0.17/0.39 (step @p285 :rule refl :args (@t136)) % 0.17/0.39 (step @p286 :rule nary_cong :premises (@p285 @p284) :args ((or @t136 (not @t135)))) % 0.17/0.39 (step @p287 :rule cnf_or_neg :args (@t136 0)) % 0.17/0.39 (step @p288 :rule eq_resolve :premises (@p287 @p286)) % 0.17/0.39 (step @p289 :rule reordering :premises (@p288) :args ((or @t134 @t136))) % 0.17/0.39 (step @p290 :rule chain_m_resolution :premises (@p289 @p275) :args (@t134 @t137 @t138)) % 0.17/0.39 (step @p291 :rule cnf_or_pos :args (@t149)) % 0.17/0.39 (step @p292 :rule reordering :premises (@p291) :args ((or @t135 @t142 @t148 (not @t149)))) % 0.17/0.39 (step @p293 :rule chain_m_resolution :premises (@p292 @p290 @p283 @p271) :args (@t148 @t150 (@list @t134 @t142 @t149))) % 0.17/0.39 (step @p294 :rule bool-double-not-elim :args (@t143)) % 0.17/0.39 (step @p295 :rule refl :args (@t145)) % 0.17/0.39 (step @p296 :rule nary_cong :premises (@p295 @p294) :args ((or @t145 (not @t144)))) % 0.17/0.39 (step @p297 :rule cnf_or_neg :args (@t145 0)) % 0.17/0.39 (step @p298 :rule eq_resolve :premises (@p297 @p296)) % 0.17/0.39 (step @p299 :rule reordering :premises (@p298) :args ((or @t143 @t145))) % 0.17/0.39 (step @p300 :rule chain_m_resolution :premises (@p299 @p281) :args (@t143 @t137 @t146)) % 0.17/0.39 (step @p301 :rule cnf_or_pos :args (@t152)) % 0.17/0.39 (step @p302 :rule reordering :premises (@p301) :args ((or @t144 @t147 @t151 (not @t152)))) % 0.17/0.39 (step @p303 :rule chain_m_resolution :premises (@p302 @p300 @p293 @p270) :args (@t151 @t150 (@list @t143 @t147 @t152))) % 0.17/0.39 (step @p304 :rule bool-double-not-elim :args (@t132)) % 0.17/0.39 (step @p305 :rule nary_cong :premises (@p285 @p304) :args ((or @t136 (not @t133)))) % 0.17/0.39 (step @p306 :rule cnf_or_neg :args (@t136 1)) % 0.17/0.39 (step @p307 :rule eq_resolve :premises (@p306 @p305)) % 0.17/0.39 (step @p308 :rule reordering :premises (@p307) :args ((or @t132 @t136))) % 0.17/0.39 (step @p309 :rule chain_m_resolution :premises (@p308 @p275) :args (@t132 @t137 @t138)) % 0.17/0.39 (step @p310 :rule cnf_or_pos :args (@t154)) % 0.17/0.39 (step @p311 :rule reordering :premises (@p310) :args ((or @t133 @t142 @t153 @t155))) % 0.17/0.39 (step @p312 :rule chain_m_resolution :premises (@p311 @p309 @p283 @p303) :args (@t155 @t150 (@list @t132 @t142 @t151))) % 0.17/0.39 (assume-push @p319 @t156) % 0.17/0.39 (step @p314 :rule instantiate :premises (@p267) :args ((@list @t126 @t125 @t130))) % 0.17/0.39 (step-pop @p320 :rule scope :premises (@p314)) % 0.17/0.39 (step @p315 :rule process_scope :premises (@p320) :args (@t154)) % 0.17/0.39 (step @p317 :rule implies_elim :premises (@p315)) % 0.17/0.39 (step @p318 false :rule chain_m_resolution :premises (@p317 @p312 @p267) :args (false @t141 (@list @t154 @t156))) % 0.17/0.39 ) % 0.17/0.39 % SZS output end Proof % 0.17/0.39 % cvc5 exiting %------------------------------------------------------------------------------