%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM824^5 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n018.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 08:40:45 AM UTC 2026 % Result : Theorem 0.39s 0.59s % Output : Proof 0.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM824^5 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.18/0.35 % Computer : n018.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 12:27:05 EDT 2026 % 0.18/0.35 % CPUTime : % 0.28/0.50 %----Proving TH0 % 0.39/0.59 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.39/0.59 % SZS status Theorem % 0.39/0.59 % SZS output start Proof % 0.39/0.59 ( % 0.39/0.59 (declare-sort $$unsorted 0) % 0.39/0.59 (declare-const tptp.c0 $$unsorted) % 0.39/0.59 (declare-const tptp.cS (-> $$unsorted $$unsorted)) % 0.39/0.59 (declare-const tptp.cEVEN (-> $$unsorted Bool)) % 0.39/0.59 (declare-const tptp.cODD (-> $$unsorted Bool)) % 0.39/0.59 (declare-const tptp.cN (-> $$unsorted Bool)) % 0.39/0.59 (define @t1 () (@var "Xm" $$unsorted)) % 0.39/0.59 (define @t2 () (_ tptp.cN @t1)) % 0.39/0.59 (define @t3 () (_ tptp.cODD @t1)) % 0.39/0.59 (define @t4 () (_ tptp.cEVEN @t1)) % 0.39/0.59 (define @t5 () (or @t4 @t3)) % 0.39/0.59 (define @t6 () (@list @t1)) % 0.39/0.59 (define @t7 () (forall @t6 (=> @t5 @t2))) % 0.39/0.59 (define @t8 () (@var "Xn" $$unsorted)) % 0.39/0.59 (define @t9 () (_ tptp.cS @t8)) % 0.39/0.59 (define @t10 () (_ tptp.cN @t9)) % 0.39/0.59 (define @t11 () (_ tptp.cN @t8)) % 0.39/0.59 (define @t12 () (@list @t8)) % 0.39/0.59 (define @t13 () (forall @t12 (=> @t11 @t10))) % 0.39/0.59 (define @t14 () (_ tptp.cN tptp.c0)) % 0.39/0.59 (define @t15 () (@var "Xx" $$unsorted)) % 0.39/0.59 (define @t16 () (@var "Xq" (-> $$unsorted Bool))) % 0.39/0.59 (define @t17 () (_ @t16 @t15)) % 0.39/0.59 (define @t18 () (_ tptp.cODD @t15)) % 0.39/0.59 (define @t19 () (@list @t15)) % 0.39/0.59 (define @t20 () (forall @t19 (=> @t18 @t17))) % 0.39/0.59 (define @t21 () (@var "Xp" (-> $$unsorted Bool))) % 0.39/0.59 (define @t22 () (_ @t21 @t15)) % 0.39/0.59 (define @t23 () (_ tptp.cEVEN @t15)) % 0.39/0.59 (define @t24 () (forall @t19 (=> @t23 @t22))) % 0.39/0.59 (define @t25 () (and @t24 @t20)) % 0.39/0.59 (define @t26 () (@var "Xv" $$unsorted)) % 0.39/0.59 (define @t27 () (_ tptp.cS @t26)) % 0.39/0.59 (define @t28 () (_ @t21 @t27)) % 0.39/0.59 (define @t29 () (_ @t16 @t26)) % 0.39/0.59 (define @t30 () (@list @t26)) % 0.39/0.59 (define @t31 () (forall @t30 (=> @t29 @t28))) % 0.39/0.59 (define @t32 () (@var "Xu" $$unsorted)) % 0.39/0.59 (define @t33 () (_ tptp.cS @t32)) % 0.39/0.59 (define @t34 () (_ @t16 @t33)) % 0.39/0.59 (define @t35 () (_ @t21 @t32)) % 0.39/0.59 (define @t36 () (@list @t32)) % 0.39/0.59 (define @t37 () (forall @t36 (=> @t35 @t34))) % 0.39/0.59 (define @t38 () (_ @t21 tptp.c0)) % 0.39/0.59 (define @t39 () (and @t38 @t37 @t31)) % 0.39/0.59 (define @t40 () (=> @t39 @t25)) % 0.39/0.59 (define @t41 () (@list @t21 @t16)) % 0.39/0.59 (define @t42 () (forall @t41 @t40)) % 0.39/0.59 (define @t43 () (and @t42 @t14 @t13)) % 0.39/0.59 (define @t44 () (=> @t43 @t7)) % 0.39/0.59 (define @t45 () (not @t44)) % 0.39/0.59 (define @t46 () (tptp.cN @t1)) % 0.39/0.59 (define @t47 () (tptp.cODD @t1)) % 0.39/0.59 (define @t48 () (tptp.cEVEN @t1)) % 0.39/0.59 (define @t49 () (forall @t6 (or (and (not @t48) (not @t47)) @t46))) % 0.39/0.59 (define @t50 () (tptp.cS @t8)) % 0.39/0.59 (define @t51 () (tptp.cN @t50)) % 0.39/0.59 (define @t52 () (tptp.cN @t8)) % 0.39/0.59 (define @t53 () (forall @t12 (or (not @t52) @t51))) % 0.39/0.59 (define @t54 () (tptp.cN tptp.c0)) % 0.39/0.59 (define @t55 () (@var "BOUND_VARIABLE_7521" $$unsorted)) % 0.39/0.59 (define @t56 () (or (not (tptp.cODD @t55)) (_ @t16 @t55))) % 0.39/0.59 (define @t57 () (@var "BOUND_VARIABLE_7515" $$unsorted)) % 0.39/0.59 (define @t58 () (or (not (tptp.cEVEN @t57)) (_ @t21 @t57))) % 0.39/0.59 (define @t59 () (and @t58 @t56)) % 0.39/0.59 (define @t60 () (tptp.cS @t26)) % 0.39/0.59 (define @t61 () (_ @t21 @t60)) % 0.39/0.59 (define @t62 () (_ @t16 @t26)) % 0.39/0.59 (define @t63 () (forall @t30 (or (not @t62) @t61))) % 0.39/0.59 (define @t64 () (not @t63)) % 0.39/0.59 (define @t65 () (tptp.cS @t32)) % 0.39/0.59 (define @t66 () (_ @t16 @t65)) % 0.39/0.59 (define @t67 () (_ @t21 @t32)) % 0.39/0.59 (define @t68 () (forall @t36 (or (not @t67) @t66))) % 0.39/0.59 (define @t69 () (not @t68)) % 0.39/0.59 (define @t70 () (_ @t21 tptp.c0)) % 0.39/0.59 (define @t71 () (not @t70)) % 0.39/0.59 (define @t72 () (or @t71 @t69 @t64 @t59)) % 0.39/0.59 (define @t73 () (forall (@list @t21 @t16 @t57 @t55) @t72)) % 0.39/0.59 (define @t74 () (and @t73 @t14 @t53)) % 0.39/0.59 (define @t75 () (=> @t74 @t49)) % 0.39/0.59 (define @t76 () (not @t3)) % 0.39/0.59 (define @t77 () (not @t4)) % 0.39/0.59 (define @t78 () (and @t77 @t76)) % 0.39/0.59 (define @t79 () (or @t78 @t2)) % 0.39/0.59 (define @t80 () (not @t11)) % 0.39/0.59 (define @t81 () (or @t80 @t10)) % 0.39/0.59 (define @t82 () (@list @t57 @t55)) % 0.39/0.59 (define @t83 () (forall @t82 @t72)) % 0.39/0.59 (define @t84 () (forall (@list @t55) @t56)) % 0.39/0.59 (define @t85 () (@list @t15)) % 0.39/0.59 (define @t86 () (forall @t82 @t56)) % 0.39/0.59 (define @t87 () (forall (@list @t57) @t58)) % 0.39/0.59 (define @t88 () (forall @t82 @t58)) % 0.39/0.59 (define @t89 () (and @t88 @t86)) % 0.39/0.59 (define @t90 () (forall @t82 @t59)) % 0.39/0.59 (define @t91 () (or @t71 @t69 @t64 @t90)) % 0.39/0.59 (define @t92 () (_ @t16 @t15)) % 0.39/0.59 (define @t93 () (tptp.cODD @t15)) % 0.39/0.59 (define @t94 () (_ @t21 @t15)) % 0.39/0.59 (define @t95 () (tptp.cEVEN @t15)) % 0.39/0.59 (define @t96 () (and (forall @t19 (or (not @t95) @t94)) (forall @t19 (or (not @t93) @t92)))) % 0.39/0.59 (define @t97 () (not @t38)) % 0.39/0.59 (define @t98 () (or @t97 @t69 @t64 @t96)) % 0.39/0.59 (define @t99 () (or @t97 @t69 @t64)) % 0.39/0.59 (define @t100 () (and @t38 @t68 @t63)) % 0.39/0.59 (define @t101 () (not @t18)) % 0.39/0.59 (define @t102 () (or @t101 @t17)) % 0.39/0.59 (define @t103 () (not @t23)) % 0.39/0.59 (define @t104 () (or @t103 @t22)) % 0.39/0.59 (define @t105 () (not @t29)) % 0.39/0.59 (define @t106 () (or @t105 @t28)) % 0.39/0.59 (define @t107 () (not @t35)) % 0.39/0.59 (define @t108 () (or @t107 @t34)) % 0.39/0.59 (define @t109 () (@quantifiers_skolemize @t49 0)) % 0.39/0.59 (define @t110 () (tptp.cN @t109)) % 0.39/0.59 (define @t111 () (tptp.cODD @t109)) % 0.39/0.59 (define @t112 () (not @t111)) % 0.39/0.59 (define @t113 () (tptp.cEVEN @t109)) % 0.39/0.59 (define @t114 () (not @t113)) % 0.39/0.59 (define @t115 () (and @t114 @t112)) % 0.39/0.59 (define @t116 () (or @t115 @t110)) % 0.39/0.59 (define @t117 () (@list true)) % 0.39/0.59 (define @t118 () (@list @t116)) % 0.39/0.59 (define @t119 () (@const 0 $$unsorted)) % 0.39/0.59 (define @t120 () (@list @t8)) % 0.39/0.59 (define @t121 () (forall @t30 (or (not (tptp.cN @t26)) (tptp.cN @t60)))) % 0.39/0.59 (define @t122 () (@list false)) % 0.39/0.59 (define @t123 () (@list @t53)) % 0.39/0.59 (define @t124 () (forall @t36 (or (not (tptp.cN @t32)) (tptp.cN @t65)))) % 0.39/0.59 (define @t125 () (or @t112 @t110)) % 0.39/0.59 (define @t126 () (tptp.cN @t119)) % 0.39/0.59 (define @t127 () (and (or (not (tptp.cEVEN @t119)) @t126) @t125)) % 0.39/0.59 (define @t128 () (not @t121)) % 0.39/0.59 (define @t129 () (not @t124)) % 0.39/0.59 (define @t130 () (not @t54)) % 0.39/0.59 (define @t131 () (or @t130 @t129 @t128 @t127)) % 0.39/0.59 (define @t132 () (@list false false false false)) % 0.39/0.59 (define @t133 () (@list true false)) % 0.39/0.59 (define @t134 () (or @t114 @t110)) % 0.39/0.59 (define @t135 () (and @t134 (or (not (tptp.cODD @t119)) @t126))) % 0.39/0.59 (define @t136 () (or @t130 @t129 @t128 @t135)) % 0.39/0.59 (assume @p1 @t45) % 0.39/0.59 (assume @p2 true) % 0.39/0.59 (step @p3 :rule refl :args (@t49)) % 0.39/0.59 (step @p4 :rule refl :args (@t53)) % 0.39/0.59 (step @p5 :rule refl :args (@t54)) % 0.39/0.59 (step @p6 :rule refl :args (@t14)) % 0.39/0.59 (step @p7 :rule cong :premises (@p6 @p5) :args ((= @t14 @t54))) % 0.39/0.59 (step @p8 :rule symm :premises (@p7)) % 0.39/0.59 (step @p9 :rule eq_resolve :premises (@p6 @p8)) % 0.39/0.59 (step @p10 :rule refl :args (@t73)) % 0.39/0.59 (step @p11 :rule nary_cong :premises (@p10 @p9 @p4) :args (@t74)) % 0.39/0.59 (step @p12 :rule cong :premises (@p11 @p3) :args (@t75)) % 0.39/0.59 (step @p13 :rule cong :premises (@p12) :args ((not @t75))) % 0.39/0.59 (step @p14 :rule refl :args (@t46)) % 0.39/0.59 (step @p15 :rule refl :args (@t2)) % 0.39/0.59 (step @p16 :rule cong :premises (@p15 @p14) :args ((= @t2 @t46))) % 0.39/0.59 (step @p17 :rule symm :premises (@p16)) % 0.39/0.59 (step @p18 :rule eq_resolve :premises (@p15 @p17)) % 0.39/0.59 (step @p19 :rule refl :args (@t47)) % 0.39/0.59 (step @p20 :rule refl :args (@t3)) % 0.39/0.59 (step @p21 :rule cong :premises (@p20 @p19) :args ((= @t3 @t47))) % 0.39/0.59 (step @p22 :rule symm :premises (@p21)) % 0.39/0.59 (step @p23 :rule eq_resolve :premises (@p20 @p22)) % 0.39/0.59 (step @p24 :rule cong :premises (@p23) :args (@t76)) % 0.39/0.59 (step @p25 :rule refl :args (@t48)) % 0.39/0.59 (step @p26 :rule refl :args (@t4)) % 0.39/0.59 (step @p27 :rule cong :premises (@p26 @p25) :args ((= @t4 @t48))) % 0.39/0.59 (step @p28 :rule symm :premises (@p27)) % 0.39/0.59 (step @p29 :rule eq_resolve :premises (@p26 @p28)) % 0.39/0.59 (step @p30 :rule cong :premises (@p29) :args (@t77)) % 0.39/0.59 (step @p31 :rule nary_cong :premises (@p30 @p24) :args (@t78)) % 0.39/0.59 (step @p32 :rule nary_cong :premises (@p31 @p18) :args (@t79)) % 0.39/0.59 (step @p33 :rule cong :premises (@p32) :args ((forall @t6 @t79))) % 0.39/0.59 (step @p34 :rule bool-or-de-morgan :args (@t4 @t3 false)) % 0.39/0.59 (step @p35 :rule nary_cong :premises (@p34 @p15) :args ((or (not @t5) @t2))) % 0.39/0.59 (step @p36 :rule bool-impl-elim :args (@t5 @t2)) % 0.39/0.59 (step @p37 :rule trans :premises (@p36 @p35)) % 0.39/0.59 (step @p38 :rule cong :premises (@p37) :args (@t7)) % 0.39/0.59 (step @p39 :rule trans :premises (@p38 @p33)) % 0.39/0.59 (step @p40 :rule refl :args ((tptp.cN @t9))) % 0.39/0.59 (step @p41 :rule refl :args (@t50)) % 0.39/0.59 (step @p42 :rule cong :premises (@p41) :args (@t51)) % 0.39/0.59 (step @p43 :rule trans :premises (@p42 @p40)) % 0.39/0.59 (step @p44 :rule refl :args (tptp.cN)) % 0.39/0.59 (step @p45 :rule ho_cong :premises (@p44 @p41)) % 0.39/0.59 (step @p46 :rule cong :premises (@p45 @p43) :args ((= (_ tptp.cN @t50) @t51))) % 0.39/0.59 (step @p47 :rule symm :premises (@p46)) % 0.39/0.59 (step @p48 :rule refl :args (@t10)) % 0.39/0.59 (step @p49 :rule eq_resolve :premises (@p48 @p47)) % 0.39/0.59 (step @p50 :rule refl :args (@t9)) % 0.39/0.59 (step @p51 :rule cong :premises (@p50 @p41) :args ((= @t9 @t50))) % 0.39/0.59 (step @p52 :rule symm :premises (@p51)) % 0.39/0.59 (step @p53 :rule eq_resolve :premises (@p50 @p52)) % 0.39/0.59 (step @p54 :rule ho_cong :premises (@p44 @p53)) % 0.39/0.59 (step @p55 :rule trans :premises (@p54 @p49)) % 0.39/0.59 (step @p56 :rule refl :args (@t52)) % 0.39/0.59 (step @p57 :rule refl :args (@t11)) % 0.39/0.59 (step @p58 :rule cong :premises (@p57 @p56) :args ((= @t11 @t52))) % 0.39/0.59 (step @p59 :rule symm :premises (@p58)) % 0.39/0.59 (step @p60 :rule eq_resolve :premises (@p57 @p59)) % 0.39/0.59 (step @p61 :rule cong :premises (@p60) :args (@t80)) % 0.39/0.59 (step @p62 :rule nary_cong :premises (@p61 @p55) :args (@t81)) % 0.39/0.59 (step @p63 :rule cong :premises (@p62) :args ((forall @t12 @t81))) % 0.39/0.59 (step @p64 :rule bool-impl-elim :args (@t11 @t10)) % 0.39/0.59 (step @p65 :rule cong :premises (@p64) :args (@t13)) % 0.39/0.59 (step @p66 :rule trans :premises (@p65 @p63)) % 0.39/0.59 (step @p67 :rule refl :args (@t14)) % 0.39/0.59 (step @p68 :rule quant-merge-prenex :args ((= (forall @t41 @t83) @t73))) % 0.39/0.59 (step @p69 :rule alpha_equiv :args (@t84 (@list @t55) @t85)) % 0.39/0.59 (step @p70 :rule quant-unused-vars :args ((= @t86 @t84))) % 0.39/0.59 (step @p71 :rule trans :premises (@p70 @p69)) % 0.39/0.59 (step @p72 :rule alpha_equiv :args (@t87 (@list @t57) @t85)) % 0.39/0.59 (step @p73 :rule quant-unused-vars :args ((= @t88 @t87))) % 0.39/0.59 (step @p74 :rule trans :premises (@p73 @p72)) % 0.39/0.59 (step @p75 :rule nary_cong :premises (@p74 @p71) :args (@t89)) % 0.39/0.59 (step @p76 :rule quant-miniscope-and :args ((= @t90 @t89))) % 0.39/0.59 (step @p77 :rule trans :premises (@p76 @p75)) % 0.39/0.59 (step @p78 :rule refl :args (@t64)) % 0.39/0.59 (step @p79 :rule refl :args (@t69)) % 0.39/0.59 (step @p80 :rule refl :args (@t71)) % 0.39/0.59 (step @p81 :rule nary_cong :premises (@p80 @p79 @p78 @p77) :args (@t91)) % 0.39/0.59 (step @p82 :rule quant-miniscope-or :args ((= @t83 @t91))) % 0.39/0.59 (step @p83 :rule trans :premises (@p82 @p81)) % 0.39/0.59 (step @p84 :rule symm :premises (@p83)) % 0.39/0.59 (step @p85 :rule cong :premises (@p84) :args ((forall @t41 (or @t71 @t69 @t64 @t96)))) % 0.39/0.59 (step @p86 :rule trans :premises (@p85 @p68)) % 0.39/0.59 (step @p87 :rule refl :args (@t96)) % 0.39/0.59 (step @p88 :rule refl :args (@t70)) % 0.39/0.59 (step @p89 :rule refl :args (@t38)) % 0.39/0.59 (step @p90 :rule cong :premises (@p89 @p88) :args ((= @t38 @t70))) % 0.39/0.59 (step @p91 :rule symm :premises (@p90)) % 0.39/0.59 (step @p92 :rule eq_resolve :premises (@p89 @p91)) % 0.39/0.59 (step @p93 :rule cong :premises (@p92) :args (@t97)) % 0.39/0.59 (step @p94 :rule nary_cong :premises (@p93 @p79 @p78 @p87) :args (@t98)) % 0.39/0.59 (step @p95 :rule cong :premises (@p94) :args ((forall @t41 @t98))) % 0.39/0.59 (step @p96 :rule trans :premises (@p95 @p86)) % 0.39/0.59 (step @p97 :rule aci_norm :args ((= (or @t99 @t96) @t98))) % 0.39/0.59 (step @p98 :rule aci_norm :args ((= (or @t97 (or @t69 @t64)) @t99))) % 0.39/0.59 (step @p99 :rule bool-and-de-morgan :args (@t68 @t63 true)) % 0.39/0.59 (step @p100 :rule refl :args (@t97)) % 0.39/0.59 (step @p101 :rule nary_cong :premises (@p100 @p99) :args ((or @t97 (not (and @t68 @t63))))) % 0.39/0.59 (step @p102 :rule bool-and-de-morgan :args (@t38 @t68 (and @t63))) % 0.39/0.59 (step @p103 :rule trans :premises (@p102 @p101)) % 0.39/0.59 (step @p104 :rule trans :premises (@p103 @p98)) % 0.39/0.59 (step @p105 :rule nary_cong :premises (@p104 @p87) :args ((or (not @t100) @t96))) % 0.39/0.59 (step @p106 :rule trans :premises (@p105 @p97)) % 0.39/0.59 (step @p107 :rule bool-impl-elim :args (@t100 @t96)) % 0.39/0.59 (step @p108 :rule trans :premises (@p107 @p106)) % 0.39/0.59 (step @p109 :rule cong :premises (@p108) :args ((forall @t41 (=> @t100 @t96)))) % 0.39/0.59 (step @p110 :rule trans :premises (@p109 @p96)) % 0.39/0.59 (step @p111 :rule refl :args (@t92)) % 0.39/0.59 (step @p112 :rule refl :args (@t17)) % 0.39/0.59 (step @p113 :rule cong :premises (@p112 @p111) :args ((= @t17 @t92))) % 0.39/0.59 (step @p114 :rule symm :premises (@p113)) % 0.39/0.59 (step @p115 :rule eq_resolve :premises (@p112 @p114)) % 0.39/0.59 (step @p116 :rule refl :args (@t93)) % 0.39/0.59 (step @p117 :rule refl :args (@t18)) % 0.39/0.59 (step @p118 :rule cong :premises (@p117 @p116) :args ((= @t18 @t93))) % 0.39/0.59 (step @p119 :rule symm :premises (@p118)) % 0.39/0.59 (step @p120 :rule eq_resolve :premises (@p117 @p119)) % 0.39/0.59 (step @p121 :rule cong :premises (@p120) :args (@t101)) % 0.39/0.59 (step @p122 :rule nary_cong :premises (@p121 @p115) :args (@t102)) % 0.39/0.59 (step @p123 :rule cong :premises (@p122) :args ((forall @t19 @t102))) % 0.39/0.59 (step @p124 :rule bool-impl-elim :args (@t18 @t17)) % 0.39/0.59 (step @p125 :rule cong :premises (@p124) :args (@t20)) % 0.39/0.59 (step @p126 :rule trans :premises (@p125 @p123)) % 0.39/0.59 (step @p127 :rule refl :args (@t94)) % 0.39/0.59 (step @p128 :rule refl :args (@t22)) % 0.39/0.59 (step @p129 :rule cong :premises (@p128 @p127) :args ((= @t22 @t94))) % 0.39/0.59 (step @p130 :rule symm :premises (@p129)) % 0.39/0.59 (step @p131 :rule eq_resolve :premises (@p128 @p130)) % 0.39/0.59 (step @p132 :rule refl :args (@t95)) % 0.39/0.59 (step @p133 :rule refl :args (@t23)) % 0.39/0.59 (step @p134 :rule cong :premises (@p133 @p132) :args ((= @t23 @t95))) % 0.39/0.59 (step @p135 :rule symm :premises (@p134)) % 0.39/0.59 (step @p136 :rule eq_resolve :premises (@p133 @p135)) % 0.39/0.59 (step @p137 :rule cong :premises (@p136) :args (@t103)) % 0.39/0.59 (step @p138 :rule nary_cong :premises (@p137 @p131) :args (@t104)) % 0.39/0.59 (step @p139 :rule cong :premises (@p138) :args ((forall @t19 @t104))) % 0.39/0.59 (step @p140 :rule bool-impl-elim :args (@t23 @t22)) % 0.39/0.59 (step @p141 :rule cong :premises (@p140) :args (@t24)) % 0.39/0.59 (step @p142 :rule trans :premises (@p141 @p139)) % 0.39/0.59 (step @p143 :rule nary_cong :premises (@p142 @p126) :args (@t25)) % 0.39/0.59 (step @p144 :rule refl :args ((_ @t21 @t27))) % 0.39/0.59 (step @p145 :rule refl :args (@t60)) % 0.39/0.59 (step @p146 :rule cong :premises (@p145) :args (@t61)) % 0.39/0.59 (step @p147 :rule trans :premises (@p146 @p144)) % 0.39/0.59 (step @p148 :rule refl :args (@t21)) % 0.39/0.59 (step @p149 :rule ho_cong :premises (@p148 @p145)) % 0.39/0.59 (step @p150 :rule cong :premises (@p149 @p147) :args ((= (_ @t21 @t60) @t61))) % 0.39/0.59 (step @p151 :rule symm :premises (@p150)) % 0.39/0.59 (step @p152 :rule refl :args (@t28)) % 0.39/0.59 (step @p153 :rule eq_resolve :premises (@p152 @p151)) % 0.39/0.59 (step @p154 :rule refl :args (@t27)) % 0.39/0.59 (step @p155 :rule cong :premises (@p154 @p145) :args ((= @t27 @t60))) % 0.39/0.59 (step @p156 :rule symm :premises (@p155)) % 0.39/0.59 (step @p157 :rule eq_resolve :premises (@p154 @p156)) % 0.39/0.59 (step @p158 :rule ho_cong :premises (@p148 @p157)) % 0.39/0.59 (step @p159 :rule trans :premises (@p158 @p153)) % 0.39/0.59 (step @p160 :rule refl :args (@t62)) % 0.39/0.59 (step @p161 :rule refl :args (@t29)) % 0.39/0.59 (step @p162 :rule cong :premises (@p161 @p160) :args ((= @t29 @t62))) % 0.39/0.59 (step @p163 :rule symm :premises (@p162)) % 0.39/0.59 (step @p164 :rule eq_resolve :premises (@p161 @p163)) % 0.39/0.59 (step @p165 :rule cong :premises (@p164) :args (@t105)) % 0.39/0.59 (step @p166 :rule nary_cong :premises (@p165 @p159) :args (@t106)) % 0.39/0.59 (step @p167 :rule cong :premises (@p166) :args ((forall @t30 @t106))) % 0.39/0.59 (step @p168 :rule bool-impl-elim :args (@t29 @t28)) % 0.39/0.59 (step @p169 :rule cong :premises (@p168) :args (@t31)) % 0.39/0.59 (step @p170 :rule trans :premises (@p169 @p167)) % 0.39/0.59 (step @p171 :rule refl :args ((_ @t16 @t33))) % 0.39/0.59 (step @p172 :rule refl :args (@t65)) % 0.39/0.59 (step @p173 :rule cong :premises (@p172) :args (@t66)) % 0.39/0.59 (step @p174 :rule trans :premises (@p173 @p171)) % 0.39/0.59 (step @p175 :rule refl :args (@t16)) % 0.39/0.59 (step @p176 :rule ho_cong :premises (@p175 @p172)) % 0.39/0.59 (step @p177 :rule cong :premises (@p176 @p174) :args ((= (_ @t16 @t65) @t66))) % 0.39/0.59 (step @p178 :rule symm :premises (@p177)) % 0.39/0.59 (step @p179 :rule refl :args (@t34)) % 0.39/0.59 (step @p180 :rule eq_resolve :premises (@p179 @p178)) % 0.39/0.59 (step @p181 :rule refl :args (@t33)) % 0.39/0.59 (step @p182 :rule cong :premises (@p181 @p172) :args ((= @t33 @t65))) % 0.39/0.59 (step @p183 :rule symm :premises (@p182)) % 0.39/0.59 (step @p184 :rule eq_resolve :premises (@p181 @p183)) % 0.39/0.59 (step @p185 :rule ho_cong :premises (@p175 @p184)) % 0.39/0.59 (step @p186 :rule trans :premises (@p185 @p180)) % 0.39/0.59 (step @p187 :rule refl :args (@t67)) % 0.39/0.59 (step @p188 :rule refl :args (@t35)) % 0.39/0.59 (step @p189 :rule cong :premises (@p188 @p187) :args ((= @t35 @t67))) % 0.39/0.59 (step @p190 :rule symm :premises (@p189)) % 0.39/0.59 (step @p191 :rule eq_resolve :premises (@p188 @p190)) % 0.39/0.59 (step @p192 :rule cong :premises (@p191) :args (@t107)) % 0.39/0.59 (step @p193 :rule nary_cong :premises (@p192 @p186) :args (@t108)) % 0.39/0.59 (step @p194 :rule cong :premises (@p193) :args ((forall @t36 @t108))) % 0.39/0.59 (step @p195 :rule bool-impl-elim :args (@t35 @t34)) % 0.39/0.59 (step @p196 :rule cong :premises (@p195) :args (@t37)) % 0.39/0.59 (step @p197 :rule trans :premises (@p196 @p194)) % 0.39/0.59 (step @p198 :rule refl :args (@t38)) % 0.39/0.59 (step @p199 :rule nary_cong :premises (@p198 @p197 @p170) :args (@t39)) % 0.39/0.59 (step @p200 :rule cong :premises (@p199 @p143) :args (@t40)) % 0.39/0.59 (step @p201 :rule cong :premises (@p200) :args (@t42)) % 0.39/0.59 (step @p202 :rule trans :premises (@p201 @p110)) % 0.39/0.59 (step @p203 :rule nary_cong :premises (@p202 @p67 @p66) :args (@t43)) % 0.39/0.59 (step @p204 :rule cong :premises (@p203 @p39) :args (@t44)) % 0.39/0.59 (step @p205 :rule cong :premises (@p204) :args (@t45)) % 0.39/0.59 (step @p206 :rule trans :premises (@p205 @p13)) % 0.39/0.59 (step @p207 :rule eq_resolve :premises (@p1 @p206)) % 0.39/0.59 (step @p208 :rule not_implies_elim2 :premises (@p207)) % 0.39/0.59 (step @p209 :rule skolemize :premises (@p208)) % 0.39/0.59 (step @p210 :rule cnf_or_neg :args (@t116 0)) % 0.39/0.59 (step @p211 :rule chain_m_resolution :premises (@p210 @p209) :args ((not @t115) @t117 @t118)) % 0.39/0.60 (step @p212 :rule not_implies_elim1 :premises (@p207)) % 0.39/0.60 (step @p213 :rule and_elim :premises (@p212) :args (0)) % 0.39/0.60 (step @p214 :rule instantiate :premises (@p213) :args ((@list tptp.cN tptp.cN @t119 @t109))) % 0.39/0.60 (step @p215 :rule and_elim :premises (@p212) :args (2)) % 0.39/0.60 (step @p216 :rule alpha_equiv :args (@t53 @t120 (@list @t26))) % 0.39/0.60 (step @p217 :rule equiv_elim1 :premises (@p216)) % 0.39/0.60 (step @p218 :rule chain_m_resolution :premises (@p217 @p215) :args (@t121 @t122 @t123)) % 0.39/0.60 (step @p219 :rule alpha_equiv :args (@t53 @t120 (@list @t32))) % 0.39/0.60 (step @p220 :rule equiv_elim1 :premises (@p219)) % 0.39/0.60 (step @p221 :rule chain_m_resolution :premises (@p220 @p215) :args (@t124 @t122 @t123)) % 0.39/0.60 (step @p222 :rule and_elim :premises (@p212) :args (1)) % 0.39/0.60 (step @p223 :rule cnf_or_pos :args (@t131)) % 0.39/0.60 (step @p224 :rule reordering :premises (@p223) :args ((or @t130 @t129 @t128 @t127 (not @t131)))) % 0.39/0.60 (step @p225 :rule chain_m_resolution :premises (@p224 @p222 @p221 @p218 @p214) :args (@t127 @t132 (@list @t54 @t124 @t121 @t131))) % 0.39/0.60 (step @p226 :rule cnf_and_pos :args (@t127 1)) % 0.39/0.60 (step @p227 :rule reordering :premises (@p226) :args ((or @t125 (not @t127)))) % 0.39/0.60 (step @p228 :rule chain_m_resolution :premises (@p227 @p225) :args (@t125 @t122 (@list @t127))) % 0.39/0.60 (step @p229 :rule cnf_or_neg :args (@t116 1)) % 0.39/0.60 (step @p230 :rule chain_m_resolution :premises (@p229 @p209) :args ((not @t110) @t117 @t118)) % 0.39/0.60 (step @p231 :rule cnf_or_pos :args (@t125)) % 0.39/0.60 (step @p232 :rule reordering :premises (@p231) :args ((or @t112 @t110 (not @t125)))) % 0.39/0.60 (step @p233 :rule chain_m_resolution :premises (@p232 @p230 @p228) :args (@t112 @t133 (@list @t110 @t125))) % 0.39/0.60 (step @p234 :rule instantiate :premises (@p213) :args ((@list tptp.cN tptp.cN @t109 @t119))) % 0.39/0.60 (step @p235 :rule cnf_or_pos :args (@t136)) % 0.39/0.60 (step @p236 :rule reordering :premises (@p235) :args ((or @t130 @t129 @t128 @t135 (not @t136)))) % 0.39/0.60 (step @p237 :rule chain_m_resolution :premises (@p236 @p222 @p221 @p218 @p234) :args (@t135 @t132 (@list @t54 @t124 @t121 @t136))) % 0.39/0.60 (step @p238 :rule cnf_and_pos :args (@t135 0)) % 0.39/0.60 (step @p239 :rule reordering :premises (@p238) :args ((or @t134 (not @t135)))) % 0.39/0.60 (step @p240 :rule chain_m_resolution :premises (@p239 @p237) :args (@t134 @t122 (@list @t135))) % 0.39/0.60 (step @p241 :rule cnf_or_pos :args (@t134)) % 0.39/0.60 (step @p242 :rule reordering :premises (@p241) :args ((or @t114 @t110 (not @t134)))) % 0.39/0.60 (step @p243 :rule chain_m_resolution :premises (@p242 @p230 @p240) :args (@t114 @t133 (@list @t110 @t134))) % 0.39/0.60 (step @p244 :rule bool-double-not-elim :args (@t111)) % 0.39/0.60 (step @p245 :rule bool-double-not-elim :args (@t113)) % 0.39/0.60 (step @p246 :rule refl :args (@t115)) % 0.39/0.60 (step @p247 :rule nary_cong :premises (@p246 @p245 @p244) :args ((or @t115 (not @t114) (not @t112)))) % 0.39/0.60 (step @p248 :rule cnf_and_neg :args (@t115)) % 0.39/0.60 (step @p249 :rule eq_resolve :premises (@p248 @p247)) % 0.39/0.60 (step @p250 :rule reordering :premises (@p249) :args ((or @t113 @t111 @t115))) % 0.39/0.60 (step @p251 false :rule chain_m_resolution :premises (@p250 @p243 @p233 @p211) :args (false (@list true true true) (@list @t113 @t111 @t115))) % 0.39/0.60 ) % 0.39/0.60 % SZS output end Proof % 0.39/0.60 % cvc5 exiting %------------------------------------------------------------------------------