%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO539^1 : TPTP v9.2.1. Released v5.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n016.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 09:13:05 AM UTC 2026 % Result : Theorem 0.53s 0.71s % Output : Proof 0.53s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SYO539^1 : TPTP v9.2.1. Released v5.2.0. % 0.12/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n016.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Wed Jun 3 00:20:24 EDT 2026 % 0.17/0.35 % CPUTime : % 0.28/0.50 %----Proving TH0 % 0.53/0.71 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.53/0.71 % SZS status Theorem % 0.53/0.71 % SZS output start Proof % 0.53/0.71 ( % 0.53/0.71 (declare-sort $$unsorted 0) % 0.53/0.71 (declare-const tptp.eps (-> (-> $$unsorted Bool) $$unsorted)) % 0.53/0.71 (define tptp.if () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "Z" $$unsorted))) (let ((_let_3 (@var "B" Bool))) (let ((_let_4 (@var "X" $$unsorted))) (lambda (@list _let_3 _let_4 _let_1) (_ tptp.eps (lambda (@list _let_2) (or (and _let_3 (= _let_2 _let_4)) (and (not _let_3) (= _let_2 _let_1))))))))))) % 0.53/0.71 (define @t1 () (@var "P" (-> $$unsorted Bool))) % 0.53/0.71 (define @t2 () (_ tptp.eps @t1)) % 0.53/0.71 (define @t3 () (_ @t1 @t2)) % 0.53/0.71 (define @t4 () (@var "X" $$unsorted)) % 0.53/0.71 (define @t5 () (_ @t1 @t4)) % 0.53/0.71 (define @t6 () (@list @t4)) % 0.53/0.71 (define @t7 () (exists @t6 @t5)) % 0.53/0.71 (define @t8 () (=> @t7 @t3)) % 0.53/0.71 (define @t9 () (@list @t1)) % 0.53/0.71 (define @t10 () (forall @t9 @t8)) % 0.53/0.71 (define @t11 () (@var "Y" $$unsorted)) % 0.53/0.71 (define @t12 () (@var "B" Bool)) % 0.53/0.71 (define @t13 () (_ (_ (_ tptp.if @t12) @t4) @t11)) % 0.53/0.71 (define @t14 () (= @t13 @t11)) % 0.53/0.71 (define @t15 () (= @t13 @t4)) % 0.53/0.71 (define @t16 () (or @t15 @t14)) % 0.53/0.71 (define @t17 () (@list @t12 @t4 @t11)) % 0.53/0.71 (define @t18 () (forall @t17 @t16)) % 0.53/0.71 (define @t19 () (not @t18)) % 0.53/0.71 (define @t20 () (@var "Z" $$unsorted)) % 0.53/0.71 (define @t21 () (not @t12)) % 0.53/0.71 (define @t22 () (and @t21 (= @t20 @t11))) % 0.53/0.71 (define @t23 () (and @t12 (= @t20 @t4))) % 0.53/0.71 (define @t24 () (or @t23 @t22)) % 0.53/0.71 (define @t25 () (@list @t20)) % 0.53/0.71 (define @t26 () (lambda @t25 @t24)) % 0.53/0.71 (define @t27 () (lambda @t17 (_ tptp.eps @t26))) % 0.53/0.71 (define @t28 () (@const 0 $$unsorted)) % 0.53/0.71 (define @t29 () (lambda @t25 (or (and @t12 (= @t4 @t20)) (and @t21 (= @t11 @t20))))) % 0.53/0.71 (define @t30 () (tptp.eps @t29)) % 0.53/0.71 (define @t31 () (forall @t17 (or (= @t4 @t30) (= @t11 @t30)))) % 0.53/0.71 (define @t32 () (@quantifiers_skolemize @t31 2)) % 0.53/0.71 (define @t33 () (@quantifiers_skolemize @t31 0)) % 0.53/0.71 (define @t34 () (not @t33)) % 0.53/0.71 (define @t35 () (and @t34 (= @t32 @t28))) % 0.53/0.71 (define @t36 () (@quantifiers_skolemize @t31 1)) % 0.53/0.71 (define @t37 () (= @t36 @t28)) % 0.53/0.71 (define @t38 () (and @t33 @t37)) % 0.53/0.71 (define @t39 () (not @t37)) % 0.53/0.71 (define @t40 () (tptp.eps @t1)) % 0.53/0.71 (define @t41 () (_ @t1 @t40)) % 0.53/0.71 (define @t42 () (@var "BOUND_VARIABLE_7477" $$unsorted)) % 0.53/0.71 (define @t43 () (not (_ @t1 @t42))) % 0.53/0.71 (define @t44 () (or @t43 @t41)) % 0.53/0.71 (define @t45 () (forall (@list @t1 @t42) @t44)) % 0.53/0.71 (define @t46 () (@list @t42)) % 0.53/0.71 (define @t47 () (forall @t46 @t44)) % 0.53/0.71 (define @t48 () (forall @t46 @t43)) % 0.53/0.71 (define @t49 () (or @t48 @t41)) % 0.53/0.71 (define @t50 () (_ @t1 @t4)) % 0.53/0.71 (define @t51 () (forall @t6 (not @t50))) % 0.53/0.71 (define @t52 () (or @t51 @t3)) % 0.53/0.71 (define @t53 () (not @t51)) % 0.53/0.71 (define @t54 () (not @t5)) % 0.53/0.71 (define @t55 () (forall @t6 @t54)) % 0.53/0.71 (define @t56 () (not @t55)) % 0.53/0.71 (define @t57 () (@var "BOUND_VARIABLE_14776" $$unsorted)) % 0.53/0.71 (define @t58 () (@list @t57)) % 0.53/0.71 (define @t59 () (lambda @t58 (= @t36 @t57))) % 0.53/0.71 (define @t60 () (@purify @t59)) % 0.53/0.71 (define @t61 () (tptp.eps @t59)) % 0.53/0.71 (define @t62 () (= @t36 @t61)) % 0.53/0.71 (define @t63 () (lambda @t58 (= @t57 @t36))) % 0.53/0.71 (define @t64 () (tptp.eps @t63)) % 0.53/0.71 (define @t65 () (_ @t63 @t64)) % 0.53/0.71 (define @t66 () (_ @t63 @t36)) % 0.53/0.71 (define @t67 () (not @t66)) % 0.53/0.71 (define @t68 () (or @t67 @t65)) % 0.53/0.71 (define @t69 () (tptp.eps @t60)) % 0.53/0.71 (define @t70 () (= @t36 @t69)) % 0.53/0.71 (define @t71 () (@list false)) % 0.53/0.71 (define @t72 () (@list @t45)) % 0.53/0.71 (define @t73 () (_ tptp.eps @t29)) % 0.53/0.71 (define @t74 () (= @t11 @t73)) % 0.53/0.71 (define @t75 () (= @t4 @t73)) % 0.53/0.71 (define @t76 () (or @t75 @t74)) % 0.53/0.71 (define @t77 () (lambda (@list @t11) @t73)) % 0.53/0.71 (define @t78 () (lambda (@list @t4 @t11) @t73)) % 0.53/0.71 (define @t79 () (_ (lambda @t17 @t73) @t12)) % 0.53/0.71 (define @t80 () (_ (_ @t79 @t4) @t11)) % 0.53/0.71 (define @t81 () (= @t80 @t11)) % 0.53/0.71 (define @t82 () (= @t80 @t4)) % 0.53/0.71 (define @t83 () (or @t82 @t81)) % 0.53/0.71 (define @t84 () (forall @t17 @t83)) % 0.53/0.71 (define @t85 () (lambda @t25 (or (and @t33 (= @t20 @t36)) (and @t34 (= @t20 @t32))))) % 0.53/0.71 (define @t86 () (@purify @t85)) % 0.53/0.71 (define @t87 () (tptp.eps @t86)) % 0.53/0.71 (define @t88 () (= @t32 @t87)) % 0.53/0.71 (define @t89 () (= @t36 @t87)) % 0.53/0.71 (define @t90 () (or @t89 @t88)) % 0.53/0.71 (define @t91 () (not @t90)) % 0.53/0.71 (define @t92 () (not @t31)) % 0.53/0.71 (define @t93 () (tptp.eps @t85)) % 0.53/0.71 (define @t94 () (= @t32 @t93)) % 0.53/0.71 (define @t95 () (= @t36 @t93)) % 0.53/0.71 (define @t96 () (or @t95 @t94)) % 0.53/0.71 (define @t97 () (not @t96)) % 0.53/0.71 (define @t98 () (and @t34 (= @t32 @t20))) % 0.53/0.71 (define @t99 () (and @t33 (= @t36 @t20))) % 0.53/0.71 (define @t100 () (or @t99 @t98)) % 0.53/0.71 (define @t101 () (lambda @t25 @t100)) % 0.53/0.71 (define @t102 () (tptp.eps @t101)) % 0.53/0.71 (define @t103 () (= @t32 @t102)) % 0.53/0.71 (define @t104 () (= @t36 @t102)) % 0.53/0.71 (define @t105 () (or @t104 @t103)) % 0.53/0.71 (define @t106 () (not @t105)) % 0.53/0.71 (define @t107 () (@list true)) % 0.53/0.71 (define @t108 () (@list @t90)) % 0.53/0.71 (define @t109 () (= @t86 @t60)) % 0.53/0.71 (define @t110 () (and @t70 @t109)) % 0.53/0.71 (define @t111 () (not @t109)) % 0.53/0.71 (define @t112 () (or @t38 @t35)) % 0.53/0.71 (define @t113 () (= (_ @t59 @t28) @t37)) % 0.53/0.71 (define @t114 () (_ @t60 @t28)) % 0.53/0.71 (define @t115 () (and @t34 (= @t28 @t32))) % 0.53/0.71 (define @t116 () (and @t33 (= @t28 @t36))) % 0.53/0.71 (define @t117 () (or @t116 @t115)) % 0.53/0.71 (define @t118 () (_ @t85 @t28)) % 0.53/0.71 (define @t119 () (_ @t86 @t28)) % 0.53/0.71 (define @t120 () (= @t119 @t114)) % 0.53/0.71 (define @t121 () (not @t120)) % 0.53/0.71 (define @t122 () (or @t109 @t121)) % 0.53/0.71 (define @t123 () (= @t37 @t112)) % 0.53/0.71 (define @t124 () (@const 1 $$unsorted)) % 0.53/0.71 (define @t125 () (and @t33 (= @t36 @t124))) % 0.53/0.71 (define @t126 () (not @t125)) % 0.53/0.71 (define @t127 () (lambda @t58 (= @t32 @t57))) % 0.53/0.71 (define @t128 () (@purify @t127)) % 0.53/0.71 (define @t129 () (tptp.eps @t127)) % 0.53/0.71 (define @t130 () (= @t32 @t129)) % 0.53/0.71 (define @t131 () (lambda @t58 (= @t57 @t32))) % 0.53/0.71 (define @t132 () (tptp.eps @t131)) % 0.53/0.71 (define @t133 () (_ @t131 @t132)) % 0.53/0.71 (define @t134 () (_ @t131 @t32)) % 0.53/0.71 (define @t135 () (not @t134)) % 0.53/0.71 (define @t136 () (or @t135 @t133)) % 0.53/0.71 (define @t137 () (tptp.eps @t128)) % 0.53/0.71 (define @t138 () (= @t32 @t137)) % 0.53/0.71 (define @t139 () (= @t86 @t128)) % 0.53/0.71 (define @t140 () (and @t138 @t139)) % 0.53/0.71 (define @t141 () (not @t139)) % 0.53/0.71 (define @t142 () (= @t32 @t124)) % 0.53/0.71 (define @t143 () (and @t34 @t142)) % 0.53/0.71 (define @t144 () (or @t125 @t143)) % 0.53/0.71 (define @t145 () (_ @t127 @t124)) % 0.53/0.71 (define @t146 () (_ @t128 @t124)) % 0.53/0.71 (define @t147 () (and @t34 (= @t124 @t32))) % 0.53/0.71 (define @t148 () (and @t33 (= @t124 @t36))) % 0.53/0.71 (define @t149 () (or @t148 @t147)) % 0.53/0.71 (define @t150 () (_ @t85 @t124)) % 0.53/0.71 (define @t151 () (_ @t86 @t124)) % 0.53/0.71 (define @t152 () (= @t151 @t146)) % 0.53/0.71 (define @t153 () (not @t152)) % 0.53/0.71 (define @t154 () (or @t139 @t153)) % 0.53/0.71 (define @t155 () (= @t142 @t144)) % 0.53/0.71 (define @t156 () (not @t142)) % 0.53/0.71 (define @t157 () (not @t143)) % 0.53/0.71 (assume @p1 @t10) % 0.53/0.71 (assume @p2 @t19) % 0.53/0.71 (assume @p3 true) % 0.53/0.71 (step @p4 (= tptp.if @t27) :rule refl :args (@t27)) % 0.53/0.71 (step @p5 :rule cnf_and_pos :args (@t35 0)) % 0.53/0.71 (step @p6 :rule reordering :premises (@p5) :args ((or @t34 (not @t35)))) % 0.53/0.71 (step @p7 :rule cnf_and_neg :args (@t38)) % 0.53/0.71 (step @p8 :rule reordering :premises (@p7) :args ((or @t34 @t38 @t39))) % 0.53/0.71 (step @p9 :rule quant-merge-prenex :args ((= (forall @t9 @t47) @t45))) % 0.53/0.71 (step @p10 :rule refl :args (@t41)) % 0.53/0.71 (step @p11 :rule alpha_equiv :args (@t48 (@list @t42) (@list @t4))) % 0.53/0.71 (step @p12 :rule nary_cong :premises (@p11 @p10) :args (@t49)) % 0.53/0.71 (step @p13 :rule quant-miniscope-or :args ((= @t47 @t49))) % 0.53/0.71 (step @p14 :rule trans :premises (@p13 @p12)) % 0.53/0.71 (step @p15 :rule symm :premises (@p14)) % 0.53/0.71 (step @p16 :rule cong :premises (@p15) :args ((forall @t9 (or @t51 @t41)))) % 0.53/0.71 (step @p17 :rule trans :premises (@p16 @p9)) % 0.53/0.71 (step @p18 :rule refl :args ((_ @t1 @t2))) % 0.53/0.71 (step @p19 :rule refl :args (@t40)) % 0.53/0.71 (step @p20 :rule cong :premises (@p19) :args (@t41)) % 0.53/0.71 (step @p21 :rule trans :premises (@p20 @p18)) % 0.53/0.71 (step @p22 :rule refl :args (@t1)) % 0.53/0.71 (step @p23 :rule ho_cong :premises (@p22 @p19)) % 0.53/0.71 (step @p24 :rule cong :premises (@p23 @p21) :args ((= (_ @t1 @t40) @t41))) % 0.53/0.71 (step @p25 :rule symm :premises (@p24)) % 0.53/0.71 (step @p26 :rule refl :args (@t3)) % 0.53/0.71 (step @p27 :rule eq_resolve :premises (@p26 @p25)) % 0.53/0.71 (step @p28 :rule refl :args (@t2)) % 0.53/0.71 (step @p29 :rule cong :premises (@p28 @p19) :args ((= @t2 @t40))) % 0.53/0.71 (step @p30 :rule symm :premises (@p29)) % 0.53/0.71 (step @p31 :rule eq_resolve :premises (@p28 @p30)) % 0.53/0.71 (step @p32 :rule ho_cong :premises (@p22 @p31)) % 0.53/0.71 (step @p33 :rule trans :premises (@p32 @p27)) % 0.53/0.71 (step @p34 :rule refl :args (@t51)) % 0.53/0.71 (step @p35 :rule nary_cong :premises (@p34 @p33) :args (@t52)) % 0.53/0.71 (step @p36 :rule cong :premises (@p35) :args ((forall @t9 @t52))) % 0.53/0.71 (step @p37 :rule trans :premises (@p36 @p17)) % 0.53/0.71 (step @p38 :rule bool-double-not-elim :args (@t51)) % 0.53/0.71 (step @p39 :rule nary_cong :premises (@p38 @p26) :args ((or (not @t53) @t3))) % 0.53/0.71 (step @p40 :rule bool-impl-elim :args (@t53 @t3)) % 0.53/0.71 (step @p41 :rule trans :premises (@p40 @p39)) % 0.53/0.71 (step @p42 :rule cong :premises (@p41) :args ((forall @t9 (=> @t53 @t3)))) % 0.53/0.71 (step @p43 :rule trans :premises (@p42 @p37)) % 0.53/0.71 (step @p44 :rule refl :args (@t3)) % 0.53/0.71 (step @p45 :rule refl :args (@t50)) % 0.53/0.71 (step @p46 :rule refl :args (@t5)) % 0.53/0.71 (step @p47 :rule cong :premises (@p46 @p45) :args ((= @t5 @t50))) % 0.53/0.71 (step @p48 :rule symm :premises (@p47)) % 0.53/0.71 (step @p49 :rule eq_resolve :premises (@p46 @p48)) % 0.53/0.71 (step @p50 :rule cong :premises (@p49) :args (@t54)) % 0.53/0.71 (step @p51 :rule cong :premises (@p50) :args (@t55)) % 0.53/0.71 (step @p52 :rule cong :premises (@p51) :args (@t56)) % 0.53/0.71 (step @p53 :rule exists-elim :args ((= @t7 @t56))) % 0.53/0.71 (step @p54 :rule trans :premises (@p53 @p52)) % 0.53/0.71 (step @p55 :rule cong :premises (@p54 @p44) :args (@t8)) % 0.53/0.71 (step @p56 :rule cong :premises (@p55) :args (@t10)) % 0.53/0.71 (step @p57 :rule trans :premises (@p56 @p43)) % 0.53/0.71 (step @p58 :rule eq_resolve :premises (@p1 @p57)) % 0.53/0.71 (step @p59 :rule eq-refl :args (@t59)) % 0.53/0.71 (step @p60 :rule skolem_intro :args (@t60)) % 0.53/0.71 (step @p61 :rule refl :args (@t59)) % 0.53/0.71 (step @p62 :rule cong :premises (@p61 @p60) :args ((= @t59 @t60))) % 0.53/0.71 (step @p63 :rule trans :premises (@p62 @p59)) % 0.53/0.71 (step @p64 :rule true_elim :premises (@p63)) % 0.53/0.71 (step @p65 :rule cong :premises (@p64) :args (@t61)) % 0.53/0.71 (step @p66 :rule refl :args (@t36)) % 0.53/0.71 (step @p67 :rule cong :premises (@p66 @p65) :args (@t62)) % 0.53/0.71 (step @p68 :rule refl :args (@t45)) % 0.53/0.71 (step @p69 :rule cong :premises (@p68 @p67) :args ((=> @t45 @t62))) % 0.53/0.71 (step @p70 :rule aci_norm :args ((= (or false @t62) @t62))) % 0.53/0.71 (step @p71 :rule eq-symm :args (@t61 @t36)) % 0.53/0.71 (step @p72 :rule beta-reduce :args ((= (_ @t63 @t61) (= @t61 @t36)))) % 0.53/0.71 (step @p73 :rule trans :premises (@p72 @p71)) % 0.53/0.71 (step @p74 :rule eq-symm :args (@t57 @t36)) % 0.53/0.71 (step @p75 :rule cong :premises (@p74) :args (@t63)) % 0.53/0.71 (step @p76 :rule cong :premises (@p75) :args (@t64)) % 0.53/0.71 (step @p77 :rule cong :premises (@p76) :args (@t65)) % 0.53/0.71 (step @p78 :rule trans :premises (@p77 @p73)) % 0.53/0.71 (step @p79 :rule evaluate :args ((not true))) % 0.53/0.71 (step @p80 :rule eq-refl :args (@t36)) % 0.53/0.71 (step @p81 :rule beta-reduce :args ((= @t66 (= @t36 @t36)))) % 0.53/0.71 (step @p82 :rule trans :premises (@p81 @p80)) % 0.53/0.71 (step @p83 :rule cong :premises (@p82) :args (@t67)) % 0.53/0.71 (step @p84 :rule trans :premises (@p83 @p79)) % 0.53/0.71 (step @p85 :rule nary_cong :premises (@p84 @p78) :args (@t68)) % 0.53/0.71 (step @p86 :rule trans :premises (@p85 @p70)) % 0.53/0.71 (step @p87 :rule cong :premises (@p68 @p86) :args ((=> @t45 @t68))) % 0.53/0.71 (assume-push @p370 @t45) % 0.53/0.71 (step @p89 :rule instantiate :premises (@p58) :args ((@list @t63 @t36))) % 0.53/0.71 (step-pop @p371 :rule scope :premises (@p89)) % 0.53/0.71 (step @p90 :rule process_scope :premises (@p371) :args (@t68)) % 0.53/0.71 (step @p92 :rule eq_resolve :premises (@p90 @p87)) % 0.53/0.71 (step @p93 :rule eq_resolve :premises (@p92 @p69)) % 0.53/0.71 (step @p94 :rule implies_elim :premises (@p93)) % 0.53/0.71 (step @p95 :rule chain_m_resolution :premises (@p94 @p58) :args (@t70 @t71 @t72)) % 0.53/0.71 (step @p96 :rule refl :args (@t30)) % 0.53/0.71 (step @p97 :rule refl :args (@t73)) % 0.53/0.71 (step @p98 :rule cong :premises (@p97 @p96) :args ((= @t73 @t30))) % 0.53/0.71 (step @p99 :rule symm :premises (@p98)) % 0.53/0.71 (step @p100 :rule eq_resolve :premises (@p97 @p99)) % 0.53/0.71 (step @p101 :rule refl :args (@t11)) % 0.53/0.71 (step @p102 :rule cong :premises (@p101 @p100) :args (@t74)) % 0.53/0.71 (step @p103 :rule refl :args (@t4)) % 0.53/0.71 (step @p104 :rule cong :premises (@p103 @p100) :args (@t75)) % 0.53/0.71 (step @p105 :rule nary_cong :premises (@p104 @p102) :args (@t76)) % 0.53/0.71 (step @p106 :rule cong :premises (@p105) :args ((forall @t17 @t76))) % 0.53/0.71 (step @p107 :rule eq-symm :args (@t73 @t11)) % 0.53/0.71 (step @p108 :rule refl :args (@t11)) % 0.53/0.71 (step @p109 :rule beta-reduce :args ((= (_ @t77 @t11) @t73))) % 0.53/0.71 (step @p110 :rule beta-reduce :args ((= (_ @t78 @t4) @t77))) % 0.53/0.71 (step @p111 :rule refl :args (@t4)) % 0.53/0.71 (step @p112 :rule beta-reduce :args ((= @t79 @t78))) % 0.53/0.71 (step @p113 :rule ho_cong :premises (@p112 @p111)) % 0.53/0.71 (step @p114 :rule trans :premises (@p113 @p110)) % 0.53/0.71 (step @p115 :rule ho_cong :premises (@p114 @p108)) % 0.53/0.71 (step @p116 :rule trans :premises (@p115 @p109)) % 0.53/0.71 (step @p117 :rule cong :premises 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(step @p148 :rule refl :args (@t91)) % 0.53/0.71 (step @p149 :rule bool-double-not-elim :args (@t31)) % 0.53/0.71 (step @p150 :rule nary_cong :premises (@p149 @p148) :args ((or (not @t92) @t91))) % 0.53/0.71 (step @p151 :rule eq-refl :args (@t85)) % 0.53/0.71 (step @p152 :rule skolem_intro :args (@t86)) % 0.53/0.71 (step @p153 :rule refl :args (@t85)) % 0.53/0.71 (step @p154 :rule cong :premises (@p153 @p152) :args ((= @t85 @t86))) % 0.53/0.71 (step @p155 :rule trans :premises (@p154 @p151)) % 0.53/0.71 (step @p156 :rule true_elim :premises (@p155)) % 0.53/0.71 (step @p157 :rule cong :premises (@p156) :args (@t93)) % 0.53/0.71 (step @p158 :rule refl :args (@t32)) % 0.53/0.71 (step @p159 :rule cong :premises (@p158 @p157) :args (@t94)) % 0.53/0.71 (step @p160 :rule cong :premises (@p66 @p157) :args (@t95)) % 0.53/0.71 (step @p161 :rule nary_cong :premises (@p160 @p159) :args (@t96)) % 0.53/0.71 (step @p162 :rule cong :premises (@p161) :args (@t97)) % 0.53/0.71 (step @p163 :rule refl 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:rule cong :premises (@p163 @p177) :args ((=> @t92 @t106))) % 0.53/0.71 (step @p179 :rule trans :premises (@p178 @p164)) % 0.53/0.71 (assume-push @p372 @t92) % 0.53/0.71 (step @p181 :rule skolemize :premises (@p147)) % 0.53/0.71 (step-pop @p373 :rule scope :premises (@p181)) % 0.53/0.71 (step @p182 :rule process_scope :premises (@p373) :args (@t106)) % 0.53/0.71 (step @p184 :rule eq_resolve :premises (@p182 @p179)) % 0.53/0.71 (step @p185 :rule implies_elim :premises (@p184)) % 0.53/0.71 (step @p186 :rule eq_resolve :premises (@p185 @p150)) % 0.53/0.71 (step @p187 :rule chain_m_resolution :premises (@p186 @p147) :args (@t91 @t107 (@list @t31))) % 0.53/0.71 (step @p188 :rule cnf_or_neg :args (@t90 0)) % 0.53/0.71 (step @p189 :rule chain_m_resolution :premises (@p188 @p187) :args ((not @t89) @t107 @t108)) % 0.53/0.71 (assume-push @p374 @t70) % 0.53/0.71 (assume-push @p375 @t109) % 0.53/0.71 (assume-push @p376 @t109) % 0.53/0.71 (assume-push @p377 @t70) % 0.53/0.71 (step @p194 :rule symm 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refl :args (@t109)) % 0.53/0.71 (step @p240 :rule nary_cong :premises (@p239 @p238) :args (@t122)) % 0.53/0.71 ; WARNING: add trust step for TRUST % 0.53/0.71 ; trust TRUST THEORY_LEMMA % 0.53/0.71 (step @p241 :rule trust :premises () :args (@t122)) % 0.53/0.71 (step @p242 :rule eq_resolve :premises (@p241 @p240)) % 0.53/0.71 (step @p243 :rule chain_m_resolution :premises (@p242 @p209) :args ((not @t123) @t107 (@list @t109))) % 0.53/0.71 (step @p244 :rule cnf_equiv_neg2 :args (@t123)) % 0.53/0.71 (step @p245 :rule cnf_or_neg :args (@t112 0)) % 0.53/0.71 (step @p246 :rule chain_m_resolution :premises (@p245 @p244 @p243 @p8) :args ((or @t34 @t39) (@list true true false) (@list @t112 @t123 @t38))) % 0.53/0.71 (step @p247 :rule cnf_and_pos :args (@t38 1)) % 0.53/0.71 (step @p248 :rule reordering :premises (@p247) :args ((or @t37 (not @t38)))) % 0.53/0.71 (step @p249 :rule cnf_equiv_neg1 :args (@t123)) % 0.53/0.71 (step @p250 :rule reordering :premises (@p249) :args ((or @t37 @t112 @t123))) % 0.53/0.71 (step @p251 :rule cnf_or_pos :args (@t112)) % 0.53/0.71 (step @p252 :rule reordering :premises (@p251) :args ((or @t38 @t35 (not @t112)))) % 0.53/0.71 (step @p253 :rule chain_m_resolution :premises (@p252 @p250 @p243 @p248 @p246 @p6) :args (@t34 (@list false true true true true) (@list @t112 @t123 @t38 @t37 @t35))) % 0.53/0.71 (step @p254 :rule cnf_and_pos :args (@t125 0)) % 0.53/0.71 (step @p255 :rule reordering :premises (@p254) :args ((or @t33 @t126))) % 0.53/0.71 (step @p256 :rule chain_m_resolution :premises (@p255 @p253) :args (@t126 @t107 (@list @t33))) % 0.53/0.71 (step @p257 :rule cnf_or_neg :args (@t90 1)) % 0.53/0.71 (step @p258 :rule chain_m_resolution :premises (@p257 @p187) :args ((not @t88) @t107 @t108)) % 0.53/0.71 (step @p259 :rule eq-refl :args (@t127)) % 0.53/0.71 (step @p260 :rule skolem_intro :args (@t128)) % 0.53/0.71 (step @p261 :rule refl :args (@t127)) % 0.53/0.71 (step @p262 :rule cong :premises (@p261 @p260) :args ((= @t127 @t128))) % 0.53/0.71 (step @p263 :rule trans :premises (@p262 @p259)) % 0.53/0.71 (step @p264 :rule true_elim :premises (@p263)) % 0.53/0.71 (step @p265 :rule cong :premises (@p264) :args (@t129)) % 0.53/0.71 (step @p266 :rule cong :premises (@p158 @p265) :args (@t130)) % 0.53/0.71 (step @p267 :rule cong :premises (@p68 @p266) :args ((=> @t45 @t130))) % 0.53/0.71 (step @p268 :rule aci_norm :args ((= (or false @t130) @t130))) % 0.53/0.71 (step @p269 :rule eq-symm :args (@t129 @t32)) % 0.53/0.71 (step @p270 :rule beta-reduce :args ((= (_ @t131 @t129) (= @t129 @t32)))) % 0.53/0.71 (step @p271 :rule trans :premises (@p270 @p269)) % 0.53/0.71 (step @p272 :rule eq-symm :args (@t57 @t32)) % 0.53/0.71 (step @p273 :rule cong :premises (@p272) :args (@t131)) % 0.53/0.71 (step @p274 :rule cong :premises (@p273) :args (@t132)) % 0.53/0.71 (step @p275 :rule cong :premises (@p274) :args (@t133)) % 0.53/0.71 (step @p276 :rule trans :premises (@p275 @p271)) % 0.53/0.71 (step @p277 :rule eq-refl :args (@t32)) % 0.53/0.71 (step @p278 :rule beta-reduce :args ((= @t134 (= @t32 @t32)))) % 0.53/0.71 (step @p279 :rule trans :premises (@p278 @p277)) % 0.53/0.71 (step @p280 :rule cong :premises (@p279) :args (@t135)) % 0.53/0.71 (step @p281 :rule trans :premises (@p280 @p79)) % 0.53/0.71 (step @p282 :rule nary_cong :premises (@p281 @p276) :args (@t136)) % 0.53/0.71 (step @p283 :rule trans :premises (@p282 @p268)) % 0.53/0.71 (step @p284 :rule cong :premises (@p68 @p283) :args ((=> @t45 @t136))) % 0.53/0.71 (assume-push @p382 @t45) % 0.53/0.71 (step @p286 :rule instantiate :premises (@p58) :args ((@list @t131 @t32))) % 0.53/0.71 (step-pop @p383 :rule scope :premises (@p286)) % 0.53/0.71 (step @p287 :rule process_scope :premises (@p383) :args (@t136)) % 0.53/0.71 (step @p289 :rule eq_resolve :premises (@p287 @p284)) % 0.53/0.71 (step @p290 :rule eq_resolve :premises (@p289 @p267)) % 0.53/0.71 (step @p291 :rule implies_elim :premises (@p290)) % 0.53/0.71 (step @p292 :rule chain_m_resolution :premises (@p291 @p58) :args (@t138 @t71 @t72)) % 0.53/0.71 (assume-push @p384 @t138) % 0.53/0.71 (assume-push @p385 @t139) % 0.53/0.71 (assume-push @p386 @t139) % 0.53/0.71 (assume-push @p387 @t138) % 0.53/0.71 (step @p297 :rule symm :premises (@p385)) % 0.53/0.71 (step @p298 :rule cong :premises (@p297) :args (@t137)) % 0.53/0.71 (step @p299 :rule trans :premises (@p292 @p298)) % 0.53/0.71 (step-pop @p388 :rule scope :premises (@p299)) % 0.53/0.71 (step-pop @p389 :rule scope :premises (@p388)) % 0.53/0.71 (step @p300 :rule process_scope :premises (@p389) :args (@t88)) % 0.53/0.71 (step @p303 :rule and_intro :premises (@p385 @p292)) % 0.53/0.71 (step @p304 :rule modus_ponens :premises (@p303 @p300)) % 0.53/0.71 (step-pop @p390 :rule scope :premises (@p304)) % 0.53/0.71 (step-pop @p391 :rule scope :premises (@p390)) % 0.53/0.71 (step @p305 :rule process_scope :premises (@p391) :args (@t88)) % 0.53/0.71 (step @p308 :rule implies_elim :premises (@p305)) % 0.53/0.71 (step @p309 :rule cnf_and_neg :args (@t140)) % 0.53/0.71 (step @p310 :rule resolution :premises (@p309 @p308) :args (true @t140)) % 0.53/0.71 (step @p311 :rule reordering :premises (@p310) :args ((or @t88 (not @t138) @t141))) % 0.53/0.71 (step @p312 :rule chain_m_resolution :premises (@p311 @p292 @p258) :args (@t141 (@list false true) (@list @t138 @t88))) % 0.53/0.71 (step @p313 :rule eq-symm :args (@t144 @t142)) % 0.53/0.71 (step @p314 :rule eq-refl :args (@t142)) % 0.53/0.71 (step @p315 :rule beta-reduce :args ((= @t145 @t142))) % 0.53/0.71 (step @p316 :rule refl :args (@t142)) % 0.53/0.71 (step @p317 :rule cong :premises (@p316 @p315) :args ((= @t142 @t145))) % 0.53/0.71 (step @p318 :rule trans :premises (@p317 @p314)) % 0.53/0.71 (step @p319 :rule eq-symm :args (@t145 @t142)) % 0.53/0.71 (step @p320 :rule trans :premises (@p319 @p318)) % 0.53/0.71 (step @p321 :rule refl :args (@t124)) % 0.53/0.71 (step @p322 :rule ho_cong :premises (@p260 @p321)) % 0.53/0.71 (step @p323 :rule cong :premises (@p322 @p316) :args ((= @t146 @t142))) % 0.53/0.71 (step @p324 :rule trans :premises (@p323 @p320)) % 0.53/0.71 (step @p325 :rule true_elim :premises (@p324)) % 0.53/0.71 (step @p326 :rule eq-refl :args (@t144)) % 0.53/0.71 (step @p327 :rule eq-symm :args (@t124 @t32)) % 0.53/0.71 (step @p328 :rule nary_cong :premises (@p166 @p327) :args (@t147)) % 0.53/0.71 (step @p329 :rule eq-symm :args (@t124 @t36)) % 0.53/0.71 (step @p330 :rule nary_cong :premises (@p169 @p329) :args (@t148)) % 0.53/0.71 (step @p331 :rule nary_cong :premises (@p330 @p328) :args (@t149)) % 0.53/0.71 (step @p332 :rule beta-reduce :args ((= @t150 @t149))) % 0.53/0.71 (step @p333 :rule trans :premises (@p332 @p331)) % 0.53/0.71 (step @p334 :rule refl :args (@t144)) % 0.53/0.71 (step @p335 :rule cong :premises (@p334 @p333) :args ((= @t144 @t150))) % 0.53/0.71 (step @p336 :rule trans :premises (@p335 @p326)) % 0.53/0.71 (step @p337 :rule eq-symm :args (@t150 @t144)) % 0.53/0.71 (step @p338 :rule trans :premises (@p337 @p336)) % 0.53/0.71 (step @p339 :rule ho_cong :premises (@p152 @p321)) % 0.53/0.71 (step @p340 :rule cong :premises (@p339 @p334) :args ((= @t151 @t144))) % 0.53/0.71 (step @p341 :rule trans :premises (@p340 @p338)) % 0.53/0.71 (step @p342 :rule true_elim :premises (@p341)) % 0.53/0.71 (step @p343 :rule cong :premises (@p342 @p325) :args (@t152)) % 0.53/0.71 (step @p344 :rule trans :premises (@p343 @p313)) % 0.53/0.71 (step @p345 :rule cong :premises (@p344) :args (@t153)) % 0.53/0.71 (step @p346 :rule refl :args (@t139)) % 0.53/0.71 (step @p347 :rule nary_cong :premises (@p346 @p345) :args (@t154)) % 0.53/0.71 ; trust TRUST THEORY_LEMMA % 0.53/0.71 (step @p348 :rule trust :premises () :args (@t154)) % 0.53/0.71 (step @p349 :rule eq_resolve :premises (@p348 @p347)) % 0.53/0.71 (step @p350 :rule chain_m_resolution :premises (@p349 @p312) :args ((not @t155) @t107 (@list @t139))) % 0.53/0.71 (step @p351 :rule cnf_equiv_neg2 :args (@t155)) % 0.53/0.71 (step @p352 :rule refl :args (@t156)) % 0.53/0.71 (step @p353 :rule bool-double-not-elim :args (@t33)) % 0.53/0.71 (step @p354 :rule refl :args (@t143)) % 0.53/0.71 (step @p355 :rule nary_cong :premises (@p354 @p353 @p352) :args ((or @t143 (not @t34) @t156))) % 0.53/0.71 (step @p356 :rule cnf_and_neg :args (@t143)) % 0.53/0.71 (step @p357 :rule eq_resolve :premises (@p356 @p355)) % 0.53/0.71 (step @p358 :rule reordering :premises (@p357) :args ((or @t33 @t143 @t156))) % 0.53/0.71 (step @p359 :rule cnf_or_neg :args (@t144 1)) % 0.53/0.71 (step @p360 :rule chain_m_resolution :premises (@p359 @p358 @p253 @p351 @p350) :args (@t156 (@list false true true true) (@list @t143 @t33 @t144 @t155))) % 0.53/0.71 (step @p361 :rule cnf_and_pos :args (@t143 1)) % 0.53/0.71 (step @p362 :rule reordering :premises (@p361) :args ((or @t142 @t157))) % 0.53/0.71 (step @p363 :rule chain_m_resolution :premises (@p362 @p360) :args (@t157 @t107 (@list @t142))) % 0.53/0.71 (step @p364 :rule cnf_equiv_neg1 :args (@t155)) % 0.53/0.71 (step @p365 :rule reordering :premises (@p364) :args ((or @t142 @t144 @t155))) % 0.53/0.71 (step @p366 :rule chain_m_resolution :premises (@p365 @p360 @p350) :args (@t144 (@list true true) (@list @t142 @t155))) % 0.53/0.71 (step @p367 :rule cnf_or_pos :args (@t144)) % 0.53/0.71 (step @p368 :rule reordering :premises (@p367) :args ((or @t125 @t143 (not @t144)))) % 0.53/0.71 (step @p369 false :rule chain_m_resolution :premises (@p368 @p366 @p363 @p256) :args (false (@list false true true) (@list @t144 @t143 @t125))) % 0.53/0.71 ) % 0.53/0.71 % SZS output end Proof % 0.53/0.71 % cvc5 exiting %------------------------------------------------------------------------------