%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU787^2 : 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 : n007.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 08:53:12 AM UTC 2026 % Result : Theorem 0.41s 0.59s % Output : Proof 0.41s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU787^2 : TPTP v9.2.1. Released v3.7.0. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.18/0.35 % Computer : n007.cluster.edu % 0.18/0.35 % Model : x86_64 x86_64 % 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.35 % Memory : 8042.1875MB % 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.35 % CPULimit : 300 % 0.18/0.35 % WCLimit : 300 % 0.18/0.35 % DateTime : Tue Jun 2 17:50:56 EDT 2026 % 0.18/0.35 % CPUTime : % 0.33/0.50 %----Proving TH0 % 0.41/0.59 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.41/0.59 % SZS status Theorem % 0.41/0.59 % SZS output start Proof % 0.41/0.59 ( % 0.41/0.59 (declare-sort $$unsorted 0) % 0.41/0.59 (declare-const tptp.breln1unionE Bool) % 0.41/0.59 (declare-const tptp.breln1 (-> $$unsorted $$unsorted Bool)) % 0.41/0.59 (declare-const tptp.binunion (-> $$unsorted $$unsorted $$unsorted)) % 0.41/0.59 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.41/0.59 (declare-const tptp.kpair (-> $$unsorted $$unsorted $$unsorted)) % 0.41/0.59 (define @t1 () (@var "S" $$unsorted)) % 0.41/0.59 (define @t2 () (@var "Xy" $$unsorted)) % 0.41/0.59 (define @t3 () (@var "Xx" $$unsorted)) % 0.41/0.59 (define @t4 () (_ (_ tptp.kpair @t3) @t2)) % 0.41/0.59 (define @t5 () (_ tptp.in @t4)) % 0.41/0.59 (define @t6 () (_ @t5 @t1)) % 0.41/0.59 (define @t7 () (@var "R" $$unsorted)) % 0.41/0.59 (define @t8 () (_ @t5 @t7)) % 0.41/0.59 (define @t9 () (or @t8 @t6)) % 0.41/0.59 (define @t10 () (_ (_ tptp.binunion @t7) @t1)) % 0.41/0.59 (define @t11 () (_ @t5 @t10)) % 0.41/0.59 (define @t12 () (=> @t11 @t9)) % 0.41/0.59 (define @t13 () (@var "A" $$unsorted)) % 0.41/0.59 (define @t14 () (_ (_ tptp.in @t2) @t13)) % 0.41/0.59 (define @t15 () (@list @t2)) % 0.41/0.59 (define @t16 () (forall @t15 (=> @t14 @t12))) % 0.41/0.59 (define @t17 () (_ (_ tptp.in @t3) @t13)) % 0.41/0.59 (define @t18 () (=> @t17 @t16)) % 0.41/0.59 (define @t19 () (@list @t3)) % 0.41/0.59 (define @t20 () (forall @t19 @t18)) % 0.41/0.59 (define @t21 () (_ tptp.breln1 @t13)) % 0.41/0.59 (define @t22 () (_ @t21 @t1)) % 0.41/0.59 (define @t23 () (=> @t22 @t20)) % 0.41/0.59 (define @t24 () (@list @t1)) % 0.41/0.59 (define @t25 () (forall @t24 @t23)) % 0.41/0.59 (define @t26 () (_ @t21 @t7)) % 0.41/0.59 (define @t27 () (=> @t26 @t25)) % 0.41/0.59 (define @t28 () (@list @t13 @t7)) % 0.41/0.59 (define @t29 () (forall @t28 @t27)) % 0.41/0.59 (define @t30 () (= tptp.breln1unionE @t29)) % 0.41/0.59 (define @t31 () (@var "Xphi" Bool)) % 0.41/0.59 (define @t32 () (=> @t6 @t31)) % 0.41/0.59 (define @t33 () (=> @t32 @t31)) % 0.41/0.59 (define @t34 () (=> @t8 @t31)) % 0.41/0.59 (define @t35 () (@list @t31)) % 0.41/0.59 (define @t36 () (forall @t35 (=> @t34 @t33))) % 0.41/0.59 (define @t37 () (=> @t11 @t36)) % 0.41/0.59 (define @t38 () (=> @t14 @t37)) % 0.41/0.59 (define @t39 () (forall @t15 @t38)) % 0.41/0.59 (define @t40 () (=> @t17 @t39)) % 0.41/0.59 (define @t41 () (forall @t19 @t40)) % 0.41/0.59 (define @t42 () (=> @t22 @t41)) % 0.41/0.59 (define @t43 () (forall @t24 @t42)) % 0.41/0.59 (define @t44 () (=> @t26 @t43)) % 0.41/0.59 (define @t45 () (forall @t28 @t44)) % 0.41/0.59 (define @t46 () (=> tptp.breln1unionE @t45)) % 0.41/0.59 (define @t47 () (not @t46)) % 0.41/0.59 (define @t48 () (@var "BOUND_VARIABLE_7548" $$unsorted)) % 0.41/0.59 (define @t49 () (@var "BOUND_VARIABLE_7552" $$unsorted)) % 0.41/0.59 (define @t50 () (@var "BOUND_VARIABLE_7550" $$unsorted)) % 0.41/0.59 (define @t51 () (tptp.kpair @t50 @t49)) % 0.41/0.59 (define @t52 () (tptp.in @t51 @t48)) % 0.41/0.59 (define @t53 () (tptp.in @t51 @t7)) % 0.41/0.59 (define @t54 () (not (tptp.in @t51 (tptp.binunion @t7 @t48)))) % 0.41/0.59 (define @t55 () (not (tptp.in @t49 @t13))) % 0.41/0.59 (define @t56 () (not (tptp.in @t50 @t13))) % 0.41/0.59 (define @t57 () (not (tptp.breln1 @t13 @t48))) % 0.41/0.59 (define @t58 () (tptp.breln1 @t13 @t7)) % 0.41/0.59 (define @t59 () (not @t58)) % 0.41/0.59 (define @t60 () (or @t59 @t57 @t56 @t55 @t54 @t53 @t52)) % 0.41/0.59 (define @t61 () (or @t57 @t56 @t55 @t54 @t53 @t52)) % 0.41/0.59 (define @t62 () (or @t59 @t61)) % 0.41/0.59 (define @t63 () (@list @t13 @t7 @t48 @t50 @t49)) % 0.41/0.59 (define @t64 () (forall @t63 @t62)) % 0.41/0.59 (define @t65 () (@list @t48 @t50 @t49)) % 0.41/0.59 (define @t66 () (forall @t65 @t62)) % 0.41/0.59 (define @t67 () (forall @t65 @t61)) % 0.41/0.59 (define @t68 () (@var "BOUND_VARIABLE_7522" $$unsorted)) % 0.41/0.59 (define @t69 () (@var "BOUND_VARIABLE_7520" $$unsorted)) % 0.41/0.59 (define @t70 () (or @t59 @t67)) % 0.41/0.59 (define @t71 () (tptp.kpair @t69 @t68)) % 0.41/0.59 (define @t72 () (tptp.in @t71 @t1)) % 0.41/0.59 (define @t73 () (tptp.in @t71 @t7)) % 0.41/0.59 (define @t74 () (tptp.binunion @t7 @t1)) % 0.41/0.59 (define @t75 () (not (tptp.in @t71 @t74))) % 0.41/0.59 (define @t76 () (not (tptp.in @t68 @t13))) % 0.41/0.59 (define @t77 () (not (tptp.in @t69 @t13))) % 0.41/0.59 (define @t78 () (tptp.breln1 @t13 @t1)) % 0.41/0.59 (define @t79 () (not @t78)) % 0.41/0.59 (define @t80 () (or @t79 @t77 @t76 @t75 @t73 @t72)) % 0.41/0.59 (define @t81 () (@list @t1 @t69 @t68)) % 0.41/0.59 (define @t82 () (forall @t81 @t80)) % 0.41/0.59 (define @t83 () (not @t26)) % 0.41/0.59 (define @t84 () (or @t83 @t82)) % 0.41/0.59 (define @t85 () (or @t77 @t76 @t75 @t73 @t72)) % 0.41/0.59 (define @t86 () (or @t79 @t85)) % 0.41/0.59 (define @t87 () (forall @t81 @t86)) % 0.41/0.59 (define @t88 () (@list @t69 @t68)) % 0.41/0.59 (define @t89 () (forall @t88 @t86)) % 0.41/0.59 (define @t90 () (forall @t88 @t85)) % 0.41/0.59 (define @t91 () (@var "BOUND_VARIABLE_7496" $$unsorted)) % 0.41/0.59 (define @t92 () (or @t79 @t90)) % 0.41/0.59 (define @t93 () (tptp.kpair @t3 @t91)) % 0.41/0.59 (define @t94 () (tptp.in @t93 @t1)) % 0.41/0.59 (define @t95 () (tptp.in @t93 @t7)) % 0.41/0.59 (define @t96 () (not (tptp.in @t93 @t74))) % 0.41/0.59 (define @t97 () (not (tptp.in @t91 @t13))) % 0.41/0.59 (define @t98 () (tptp.in @t3 @t13)) % 0.41/0.59 (define @t99 () (not @t98)) % 0.41/0.59 (define @t100 () (or @t99 @t97 @t96 @t95 @t94)) % 0.41/0.59 (define @t101 () (@list @t3 @t91)) % 0.41/0.59 (define @t102 () (forall @t101 @t100)) % 0.41/0.59 (define @t103 () (not @t22)) % 0.41/0.59 (define @t104 () (or @t103 @t102)) % 0.41/0.59 (define @t105 () (or @t97 @t96 @t95 @t94)) % 0.41/0.59 (define @t106 () (or @t99 @t105)) % 0.41/0.59 (define @t107 () (forall @t101 @t106)) % 0.41/0.59 (define @t108 () (@list @t91)) % 0.41/0.59 (define @t109 () (forall @t108 @t106)) % 0.41/0.59 (define @t110 () (forall @t108 @t105)) % 0.41/0.59 (define @t111 () (or @t99 @t110)) % 0.41/0.59 (define @t112 () (tptp.kpair @t3 @t2)) % 0.41/0.59 (define @t113 () (tptp.in @t112 @t1)) % 0.41/0.59 (define @t114 () (tptp.in @t112 @t7)) % 0.41/0.59 (define @t115 () (tptp.in @t112 @t74)) % 0.41/0.59 (define @t116 () (tptp.in @t2 @t13)) % 0.41/0.59 (define @t117 () (forall @t15 (or (not @t116) (not @t115) @t114 @t113))) % 0.41/0.59 (define @t118 () (not @t17)) % 0.41/0.59 (define @t119 () (or @t118 @t117)) % 0.41/0.59 (define @t120 () (_ tptp.in @t112)) % 0.41/0.59 (define @t121 () (not @t11)) % 0.41/0.59 (define @t122 () (not @t14)) % 0.41/0.59 (define @t123 () (or @t122 @t121 @t114 @t113)) % 0.41/0.59 (define @t124 () (or @t121 @t114 @t113)) % 0.41/0.59 (define @t125 () (or @t114 @t113)) % 0.41/0.59 (define @t126 () (=> @t11 @t125)) % 0.41/0.59 (define @t127 () (not false)) % 0.41/0.59 (define @t128 () (and @t113 @t127)) % 0.41/0.59 (define @t129 () (and @t114 @t127)) % 0.41/0.59 (define @t130 () (or @t129 @t128)) % 0.41/0.59 (define @t131 () (or @t129 @t128 false)) % 0.41/0.59 (define @t132 () (not @t31)) % 0.41/0.59 (define @t133 () (and @t113 @t132)) % 0.41/0.59 (define @t134 () (and @t114 @t132)) % 0.41/0.59 (define @t135 () (or @t31 @t134 @t133 @t31)) % 0.41/0.59 (define @t136 () (or @t134 @t133 @t31)) % 0.41/0.59 (define @t137 () (and @t6 @t132)) % 0.41/0.59 (define @t138 () (and @t8 @t132)) % 0.41/0.59 (define @t139 () (or @t138 @t137 @t31)) % 0.41/0.59 (define @t140 () (forall @t63 @t60)) % 0.41/0.59 (define @t141 () (or @t122 @t121 @t8 @t6)) % 0.41/0.59 (define @t142 () (or @t121 @t8 @t6)) % 0.41/0.59 (assume @p1 @t30) % 0.41/0.59 (assume @p2 @t47) % 0.41/0.59 (assume @p3 true) % 0.41/0.59 (step @p4 :rule aci_norm :args ((= @t62 @t60))) % 0.41/0.59 (step @p5 :rule cong :premises (@p4) :args (@t64)) % 0.41/0.59 (step @p6 :rule quant-merge-prenex :args ((= (forall @t28 @t66) @t64))) % 0.41/0.59 (step @p7 :rule alpha_equiv :args (@t67 (@list @t48 @t50 @t49) (@list @t1 @t69 @t68))) % 0.41/0.59 (step @p8 :rule refl :args (@t59)) % 0.41/0.59 (step @p9 :rule nary_cong :premises (@p8 @p7) :args (@t70)) % 0.41/0.59 (step @p10 :rule quant-miniscope-or :args ((= @t66 @t70))) % 0.41/0.59 (step @p11 :rule trans :premises (@p10 @p9)) % 0.41/0.59 (step @p12 :rule symm :premises (@p11)) % 0.41/0.59 (step @p13 :rule cong :premises (@p12) :args ((forall @t28 (or @t59 @t82)))) % 0.41/0.59 (step @p14 :rule trans :premises (@p13 @p6)) % 0.41/0.59 (step @p15 :rule trans :premises (@p14 @p5)) % 0.41/0.59 (step @p16 :rule refl :args (@t82)) % 0.41/0.59 (step @p17 :rule refl :args (@t58)) % 0.41/0.59 (step @p18 :rule refl :args (@t26)) % 0.41/0.59 (step @p19 :rule cong :premises (@p18 @p17) :args ((= @t26 @t58))) % 0.41/0.59 (step @p20 :rule symm :premises (@p19)) % 0.41/0.59 (step @p21 :rule eq_resolve :premises (@p18 @p20)) % 0.41/0.59 (step @p22 :rule cong :premises (@p21) :args (@t83)) % 0.41/0.59 (step @p23 :rule nary_cong :premises (@p22 @p16) :args (@t84)) % 0.41/0.59 (step @p24 :rule cong :premises (@p23) :args ((forall @t28 @t84))) % 0.41/0.59 (step @p25 :rule trans :premises (@p24 @p15)) % 0.41/0.59 (step @p26 :rule bool-impl-elim :args (@t26 @t82)) % 0.41/0.59 (step @p27 :rule cong :premises (@p26) :args ((forall @t28 (=> @t26 @t82)))) % 0.41/0.59 (step @p28 :rule trans :premises (@p27 @p25)) % 0.41/0.59 (step @p29 :rule aci_norm :args ((= @t86 @t80))) % 0.41/0.59 (step @p30 :rule cong :premises (@p29) :args (@t87)) % 0.41/0.59 (step @p31 :rule quant-merge-prenex :args ((= (forall @t24 @t89) @t87))) % 0.41/0.59 (step @p32 :rule alpha_equiv :args (@t90 (@list @t69 @t68) (@list @t3 @t91))) % 0.41/0.59 (step @p33 :rule refl :args (@t79)) % 0.41/0.59 (step @p34 :rule nary_cong :premises (@p33 @p32) :args (@t92)) % 0.41/0.59 (step @p35 :rule quant-miniscope-or :args ((= @t89 @t92))) % 0.41/0.59 (step @p36 :rule trans :premises (@p35 @p34)) % 0.41/0.59 (step @p37 :rule symm :premises (@p36)) % 0.41/0.59 (step @p38 :rule cong :premises (@p37) :args ((forall @t24 (or @t79 @t102)))) % 0.41/0.59 (step @p39 :rule trans :premises (@p38 @p31)) % 0.41/0.59 (step @p40 :rule trans :premises (@p39 @p30)) % 0.41/0.59 (step @p41 :rule refl :args (@t102)) % 0.41/0.59 (step @p42 :rule refl :args (@t78)) % 0.41/0.59 (step @p43 :rule refl :args (@t22)) % 0.41/0.59 (step @p44 :rule cong :premises (@p43 @p42) :args ((= @t22 @t78))) % 0.41/0.59 (step @p45 :rule symm :premises (@p44)) % 0.41/0.59 (step @p46 :rule eq_resolve :premises (@p43 @p45)) % 0.41/0.59 (step @p47 :rule cong :premises (@p46) :args (@t103)) % 0.41/0.59 (step @p48 :rule nary_cong :premises (@p47 @p41) :args (@t104)) % 0.41/0.59 (step @p49 :rule cong :premises (@p48) :args ((forall @t24 @t104))) % 0.41/0.59 (step @p50 :rule trans :premises (@p49 @p40)) % 0.41/0.59 (step @p51 :rule bool-impl-elim :args (@t22 @t102)) % 0.41/0.59 (step @p52 :rule cong :premises (@p51) :args ((forall @t24 (=> @t22 @t102)))) % 0.41/0.59 (step @p53 :rule trans :premises (@p52 @p50)) % 0.41/0.59 (step @p54 :rule aci_norm :args ((= @t106 @t100))) % 0.41/0.59 (step @p55 :rule cong :premises (@p54) :args (@t107)) % 0.41/0.59 (step @p56 :rule quant-merge-prenex :args ((= (forall @t19 @t109) @t107))) % 0.41/0.59 (step @p57 :rule alpha_equiv :args (@t110 (@list @t91) (@list @t2))) % 0.41/0.59 (step @p58 :rule refl :args (@t99)) % 0.41/0.59 (step @p59 :rule nary_cong :premises (@p58 @p57) :args (@t111)) % 0.41/0.59 (step @p60 :rule quant-miniscope-or :args ((= @t109 @t111))) % 0.41/0.59 (step @p61 :rule trans :premises (@p60 @p59)) % 0.41/0.59 (step @p62 :rule symm :premises (@p61)) % 0.41/0.59 (step @p63 :rule cong :premises (@p62) :args ((forall @t19 (or @t99 @t117)))) % 0.41/0.59 (step @p64 :rule trans :premises (@p63 @p56)) % 0.41/0.59 (step @p65 :rule trans :premises (@p64 @p55)) % 0.41/0.59 (step @p66 :rule refl :args (@t117)) % 0.41/0.59 (step @p67 :rule refl :args (@t98)) % 0.41/0.59 (step @p68 :rule refl :args (@t17)) % 0.41/0.59 (step @p69 :rule cong :premises (@p68 @p67) :args ((= @t17 @t98))) % 0.41/0.59 (step @p70 :rule symm :premises (@p69)) % 0.41/0.59 (step @p71 :rule eq_resolve :premises (@p68 @p70)) % 0.41/0.59 (step @p72 :rule cong :premises (@p71) :args (@t118)) % 0.41/0.59 (step @p73 :rule nary_cong :premises (@p72 @p66) :args (@t119)) % 0.41/0.59 (step @p74 :rule cong :premises (@p73) :args ((forall @t19 @t119))) % 0.41/0.59 (step @p75 :rule trans :premises (@p74 @p65)) % 0.41/0.59 (step @p76 :rule bool-impl-elim :args (@t17 @t117)) % 0.41/0.59 (step @p77 :rule cong :premises (@p76) :args ((forall @t19 (=> @t17 @t117)))) % 0.41/0.59 (step @p78 :rule trans :premises (@p77 @p75)) % 0.41/0.59 (step @p79 :rule refl :args (@t113)) % 0.41/0.59 (step @p80 :rule refl :args (@t114)) % 0.41/0.59 (step @p81 :rule refl :args ((tptp.in @t4 @t10))) % 0.41/0.59 (step @p82 :rule refl :args (@t74)) % 0.41/0.59 (step @p83 :rule refl :args (@t112)) % 0.41/0.59 (step @p84 :rule cong :premises (@p83 @p82) :args (@t115)) % 0.41/0.59 (step @p85 :rule trans :premises (@p84 @p81)) % 0.41/0.59 (step @p86 :rule refl :args (tptp.in)) % 0.41/0.59 (step @p87 :rule ho_cong :premises (@p86 @p83)) % 0.41/0.59 (step @p88 :rule ho_cong :premises (@p87 @p82)) % 0.41/0.59 (step @p89 :rule cong :premises (@p88 @p85) :args ((= (_ @t120 @t74) @t115))) % 0.41/0.59 (step @p90 :rule symm :premises (@p89)) % 0.41/0.59 (step @p91 :rule refl :args (@t11)) % 0.41/0.59 (step @p92 :rule eq_resolve :premises (@p91 @p90)) % 0.41/0.59 (step @p93 :rule refl :args (@t10)) % 0.41/0.59 (step @p94 :rule cong :premises (@p93 @p82) :args ((= @t10 @t74))) % 0.41/0.59 (step @p95 :rule symm :premises (@p94)) % 0.41/0.59 (step @p96 :rule eq_resolve :premises (@p93 @p95)) % 0.41/0.59 (step @p97 :rule refl :args (@t4)) % 0.41/0.59 (step @p98 :rule cong :premises (@p97 @p83) :args ((= @t4 @t112))) % 0.41/0.59 (step @p99 :rule symm :premises (@p98)) % 0.41/0.59 (step @p100 :rule eq_resolve :premises (@p97 @p99)) % 0.41/0.59 (step @p101 :rule ho_cong :premises (@p86 @p100)) % 0.41/0.59 (step @p102 :rule ho_cong :premises (@p101 @p96)) % 0.41/0.59 (step @p103 :rule trans :premises (@p102 @p92)) % 0.41/0.59 (step @p104 :rule cong :premises (@p103) :args (@t121)) % 0.41/0.59 (step @p105 :rule refl :args (@t116)) % 0.41/0.59 (step @p106 :rule refl :args (@t14)) % 0.41/0.59 (step @p107 :rule cong :premises (@p106 @p105) :args ((= @t14 @t116))) % 0.41/0.59 (step @p108 :rule symm :premises (@p107)) % 0.41/0.59 (step @p109 :rule eq_resolve :premises (@p106 @p108)) % 0.41/0.59 (step @p110 :rule cong :premises (@p109) :args (@t122)) % 0.41/0.59 (step @p111 :rule nary_cong :premises (@p110 @p104 @p80 @p79) :args (@t123)) % 0.41/0.59 (step @p112 :rule cong :premises (@p111) :args ((forall @t15 @t123))) % 0.41/0.59 (step @p113 :rule aci_norm :args ((= (or @t122 @t124) @t123))) % 0.41/0.59 (step @p114 :rule aci_norm :args ((= (or @t121 @t125) @t124))) % 0.41/0.59 (step @p115 :rule bool-impl-elim :args (@t11 @t125)) % 0.41/0.59 (step @p116 :rule trans :premises (@p115 @p114)) % 0.41/0.59 (step @p117 :rule refl :args (@t122)) % 0.41/0.59 (step @p118 :rule nary_cong :premises (@p117 @p116) :args ((or @t122 @t126))) % 0.41/0.59 (step @p119 :rule trans :premises (@p118 @p113)) % 0.41/0.59 (step @p120 :rule bool-impl-elim :args (@t14 @t126)) % 0.41/0.59 (step @p121 :rule trans :premises (@p120 @p119)) % 0.41/0.59 (step @p122 :rule cong :premises (@p121) :args ((forall @t15 (=> @t14 @t126)))) % 0.41/0.59 (step @p123 :rule trans :premises (@p122 @p112)) % 0.41/0.59 (step @p124 :rule aci_norm :args ((= (and @t113 true) @t113))) % 0.41/0.59 (step @p125 :rule evaluate :args (@t127)) % 0.41/0.59 (step @p126 :rule refl :args (@t113)) % 0.41/0.59 (step @p127 :rule nary_cong :premises (@p126 @p125) :args (@t128)) % 0.41/0.59 (step @p128 :rule trans :premises (@p127 @p124)) % 0.41/0.59 (step @p129 :rule aci_norm :args ((= (and @t114 true) @t114))) % 0.41/0.59 (step @p130 :rule refl :args (@t114)) % 0.41/0.59 (step @p131 :rule nary_cong :premises (@p130 @p125) :args (@t129)) % 0.41/0.59 (step @p132 :rule trans :premises (@p131 @p129)) % 0.41/0.59 (step @p133 :rule nary_cong :premises (@p132 @p128) :args (@t130)) % 0.41/0.59 (step @p134 :rule aci_norm :args ((= @t131 @t130))) % 0.41/0.59 (step @p135 :rule trans :premises (@p134 @p133)) % 0.41/0.59 (step @p136 :rule quant-var-elim-eq :args ((= (forall @t35 (or (not (= @t31 false)) @t134 @t133 @t31)) @t131))) % 0.41/0.59 (step @p137 :rule refl :args (@t31)) % 0.41/0.59 (step @p138 :rule refl :args (@t133)) % 0.41/0.59 (step @p139 :rule refl :args (@t134)) % 0.41/0.59 (step @p140 :rule bool-eq-false :args (@t31)) % 0.41/0.59 (step @p141 :rule symm :premises (@p140)) % 0.41/0.59 (step @p142 :rule cong :premises (@p141) :args ((not @t132))) % 0.41/0.59 (step @p143 :rule bool-double-not-elim :args (@t31)) % 0.41/0.59 (step @p144 :rule symm :premises (@p143)) % 0.41/0.59 (step @p145 :rule trans :premises (@p144 @p142)) % 0.41/0.59 (step @p146 :rule nary_cong :premises (@p145 @p139 @p138 @p137) :args (@t135)) % 0.41/0.59 (step @p147 :rule aci_norm :args ((= @t136 @t135))) % 0.41/0.59 (step @p148 :rule trans :premises (@p147 @p146)) % 0.41/0.59 (step @p149 :rule cong :premises (@p148) :args ((forall @t35 @t136))) % 0.41/0.59 (step @p150 :rule trans :premises (@p149 @p136)) % 0.41/0.59 (step @p151 :rule trans :premises (@p150 @p135)) % 0.41/0.59 (step @p152 :rule refl :args (@t132)) % 0.41/0.59 (step @p153 :rule refl :args ((tptp.in @t4 @t1))) % 0.41/0.59 (step @p154 :rule refl :args (@t1)) % 0.41/0.59 (step @p155 :rule cong :premises (@p83 @p154) :args (@t113)) % 0.41/0.59 (step @p156 :rule trans :premises (@p155 @p153)) % 0.41/0.59 (step @p157 :rule ho_cong :premises (@p87 @p154)) % 0.41/0.59 (step @p158 :rule cong :premises (@p157 @p156) :args ((= (_ @t120 @t1) @t113))) % 0.41/0.59 (step @p159 :rule symm :premises (@p158)) % 0.41/0.59 (step @p160 :rule refl :args (@t6)) % 0.41/0.59 (step @p161 :rule eq_resolve :premises (@p160 @p159)) % 0.41/0.59 (step @p162 :rule ho_cong :premises (@p101 @p154)) % 0.41/0.59 (step @p163 :rule trans :premises (@p162 @p161)) % 0.41/0.59 (step @p164 :rule nary_cong :premises (@p163 @p152) :args (@t137)) % 0.41/0.59 (step @p165 :rule refl :args ((tptp.in @t4 @t7))) % 0.41/0.59 (step @p166 :rule refl :args (@t7)) % 0.41/0.59 (step @p167 :rule cong :premises (@p83 @p166) :args (@t114)) % 0.41/0.59 (step @p168 :rule trans :premises (@p167 @p165)) % 0.41/0.59 (step @p169 :rule ho_cong :premises (@p87 @p166)) % 0.41/0.59 (step @p170 :rule cong :premises (@p169 @p168) :args ((= (_ @t120 @t7) @t114))) % 0.41/0.59 (step @p171 :rule symm :premises (@p170)) % 0.41/0.59 (step @p172 :rule refl :args (@t8)) % 0.41/0.59 (step @p173 :rule eq_resolve :premises (@p172 @p171)) % 0.41/0.59 (step @p174 :rule ho_cong :premises (@p101 @p166)) % 0.41/0.59 (step @p175 :rule trans :premises (@p174 @p173)) % 0.41/0.59 (step @p176 :rule nary_cong :premises (@p175 @p152) :args (@t138)) % 0.41/0.59 (step @p177 :rule nary_cong :premises (@p176 @p164 @p137) :args (@t139)) % 0.41/0.59 (step @p178 :rule cong :premises (@p177) :args ((forall @t35 @t139))) % 0.41/0.59 (step @p179 :rule trans :premises (@p178 @p151)) % 0.41/0.59 (step @p180 :rule aci_norm :args ((= (or @t138 (or @t137 @t31)) @t139))) % 0.41/0.59 (step @p181 :rule bool-implies-de-morgan :args (@t6 @t31)) % 0.41/0.59 (step @p182 :rule nary_cong :premises (@p181 @p137) :args ((or (not @t32) @t31))) % 0.41/0.59 (step @p183 :rule bool-impl-elim :args (@t32 @t31)) % 0.41/0.59 (step @p184 :rule trans :premises (@p183 @p182)) % 0.41/0.59 (step @p185 :rule bool-implies-de-morgan :args (@t8 @t31)) % 0.41/0.59 (step @p186 :rule nary_cong :premises (@p185 @p184) :args ((or (not @t34) @t33))) % 0.41/0.59 (step @p187 :rule trans :premises (@p186 @p180)) % 0.41/0.59 (step @p188 :rule bool-impl-elim :args (@t34 @t33)) % 0.41/0.59 (step @p189 :rule trans :premises (@p188 @p187)) % 0.41/0.59 (step @p190 :rule cong :premises (@p189) :args (@t36)) % 0.41/0.59 (step @p191 :rule trans :premises (@p190 @p179)) % 0.41/0.59 (step @p192 :rule refl :args (@t11)) % 0.41/0.59 (step @p193 :rule cong :premises (@p192 @p191) :args (@t37)) % 0.41/0.59 (step @p194 :rule refl :args (@t14)) % 0.41/0.59 (step @p195 :rule cong :premises (@p194 @p193) :args (@t38)) % 0.41/0.59 (step @p196 :rule cong :premises (@p195) :args (@t39)) % 0.41/0.59 (step @p197 :rule trans :premises (@p196 @p123)) % 0.41/0.59 (step @p198 :rule refl :args (@t17)) % 0.41/0.59 (step @p199 :rule cong :premises (@p198 @p197) :args (@t40)) % 0.41/0.59 (step @p200 :rule cong :premises (@p199) :args (@t41)) % 0.41/0.59 (step @p201 :rule trans :premises (@p200 @p78)) % 0.41/0.59 (step @p202 :rule refl :args (@t22)) % 0.41/0.59 (step @p203 :rule cong :premises (@p202 @p201) :args (@t42)) % 0.41/0.59 (step @p204 :rule cong :premises (@p203) :args (@t43)) % 0.41/0.59 (step @p205 :rule trans :premises (@p204 @p53)) % 0.41/0.59 (step @p206 :rule refl :args (@t26)) % 0.41/0.59 (step @p207 :rule cong :premises (@p206 @p205) :args (@t44)) % 0.41/0.59 (step @p208 :rule cong :premises (@p207) :args (@t45)) % 0.41/0.59 (step @p209 :rule trans :premises (@p208 @p28)) % 0.41/0.59 (step @p210 :rule refl :args (tptp.breln1unionE)) % 0.41/0.59 (step @p211 :rule cong :premises (@p210 @p209) :args (@t46)) % 0.41/0.59 (step @p212 :rule cong :premises (@p211) :args (@t47)) % 0.41/0.59 (step @p213 :rule eq_resolve :premises (@p2 @p212)) % 0.41/0.59 (step @p214 :rule not_implies_elim2 :premises (@p213)) % 0.41/0.59 (step @p215 :rule not_implies_elim1 :premises (@p213)) % 0.41/0.59 (step @p216 :rule cnf_equiv_pos1 :args ((= tptp.breln1unionE @t140))) % 0.41/0.59 (step @p217 :rule chain_resolution :premises (@p216 @p215 @p214) :args ((@list false true) (@list tptp.breln1unionE @t140))) % 0.41/0.59 (step @p218 :rule nary_cong :premises (@p110 @p104 @p175 @p163) :args (@t141)) % 0.41/0.59 (step @p219 :rule cong :premises (@p218) :args ((forall @t15 @t141))) % 0.41/0.59 (step @p220 :rule aci_norm :args ((= (or @t122 @t142) @t141))) % 0.41/0.59 (step @p221 :rule aci_norm :args ((= (or @t121 @t9) @t142))) % 0.41/0.59 (step @p222 :rule bool-impl-elim :args (@t11 @t9)) % 0.41/0.59 (step @p223 :rule trans :premises (@p222 @p221)) % 0.41/0.59 (step @p224 :rule nary_cong :premises (@p117 @p223) :args ((or @t122 @t12))) % 0.41/0.59 (step @p225 :rule trans :premises (@p224 @p220)) % 0.41/0.59 (step @p226 :rule bool-impl-elim :args (@t14 @t12)) % 0.41/0.59 (step @p227 :rule trans :premises (@p226 @p225)) % 0.41/0.59 (step @p228 :rule cong :premises (@p227) :args (@t16)) % 0.41/0.59 (step @p229 :rule trans :premises (@p228 @p219)) % 0.41/0.59 (step @p230 :rule cong :premises (@p198 @p229) :args (@t18)) % 0.41/0.59 (step @p231 :rule cong :premises (@p230) :args (@t20)) % 0.41/0.59 (step @p232 :rule trans :premises (@p231 @p78)) % 0.41/0.59 (step @p233 :rule cong :premises (@p202 @p232) :args (@t23)) % 0.41/0.59 (step @p234 :rule cong :premises (@p233) :args (@t25)) % 0.41/0.59 (step @p235 :rule trans :premises (@p234 @p53)) % 0.41/0.59 (step @p236 :rule cong :premises (@p206 @p235) :args (@t27)) % 0.41/0.59 (step @p237 :rule cong :premises (@p236) :args (@t29)) % 0.41/0.59 (step @p238 :rule trans :premises (@p237 @p28)) % 0.41/0.59 (step @p239 :rule cong :premises (@p210 @p238) :args (@t30)) % 0.41/0.59 (step @p240 :rule eq_resolve :premises (@p1 @p239)) % 0.41/0.59 (step @p241 false :rule contra :premises (@p240 @p217)) % 0.41/0.59 ) % 0.41/0.59 % SZS output end Proof % 0.41/0.59 % cvc5 exiting %------------------------------------------------------------------------------