%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : ALG177+1 : TPTP v9.2.1. Released v2.7.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n017.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 08:05:25 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 : ALG177+1 : TPTP v9.2.1. Released v2.7.0. % 0.12/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.18/0.35 % Computer : n017.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 : Wed Jun 3 01:39:31 EDT 2026 % 0.18/0.35 % CPUTime : % 0.29/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.39/0.59 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 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 $$unsorted 0) % 0.39/0.59 (declare-const tptp.j (-> $$unsorted $$unsorted)) % 0.39/0.59 (declare-const tptp.h (-> $$unsorted $$unsorted)) % 0.39/0.59 (declare-const tptp.sorti2 (-> $$unsorted Bool)) % 0.39/0.59 (declare-const tptp.op2 (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.59 (declare-const tptp.sorti1 (-> $$unsorted Bool)) % 0.39/0.59 (declare-const tptp.op1 (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.59 (define @t1 () (@var "V" $$unsorted)) % 0.39/0.59 (define @t2 () (@var "U" $$unsorted)) % 0.39/0.59 (define @t3 () (tptp.op1 @t2 @t1)) % 0.39/0.59 (define @t4 () (tptp.sorti1 @t1)) % 0.39/0.59 (define @t5 () (@list @t1)) % 0.39/0.59 (define @t6 () (tptp.sorti1 @t2)) % 0.39/0.59 (define @t7 () (@list @t2)) % 0.39/0.59 (define @t8 () (tptp.op2 @t2 @t1)) % 0.39/0.59 (define @t9 () (tptp.sorti2 @t1)) % 0.39/0.59 (define @t10 () (tptp.sorti2 @t2)) % 0.39/0.59 (define @t11 () (not (= @t3 @t1))) % 0.39/0.59 (define @t12 () (=> @t4 @t11)) % 0.39/0.59 (define @t13 () (forall @t5 @t12)) % 0.39/0.59 (define @t14 () (and @t6 @t13)) % 0.39/0.59 (define @t15 () (exists @t7 @t14)) % 0.39/0.59 (define @t16 () (not (= @t8 @t1))) % 0.39/0.59 (define @t17 () (=> @t9 @t16)) % 0.39/0.59 (define @t18 () (forall @t5 @t17)) % 0.39/0.59 (define @t19 () (and @t10 @t18)) % 0.39/0.59 (define @t20 () (exists @t7 @t19)) % 0.39/0.59 (define @t21 () (not @t20)) % 0.39/0.59 (define @t22 () (@var "X2" $$unsorted)) % 0.39/0.59 (define @t23 () (tptp.j (tptp.h @t22))) % 0.39/0.59 (define @t24 () (tptp.sorti1 @t22)) % 0.39/0.59 (define @t25 () (=> @t24 (= @t23 @t22))) % 0.39/0.59 (define @t26 () (@list @t22)) % 0.39/0.59 (define @t27 () (forall @t26 @t25)) % 0.39/0.59 (define @t28 () (@var "X1" $$unsorted)) % 0.39/0.59 (define @t29 () (tptp.h (tptp.j @t28))) % 0.39/0.59 (define @t30 () (tptp.sorti2 @t28)) % 0.39/0.59 (define @t31 () (=> @t30 (= @t29 @t28))) % 0.39/0.59 (define @t32 () (@list @t28)) % 0.39/0.59 (define @t33 () (forall @t32 @t31)) % 0.39/0.59 (define @t34 () (@var "Z" $$unsorted)) % 0.39/0.59 (define @t35 () (@var "Y" $$unsorted)) % 0.39/0.59 (define @t36 () (tptp.j @t35)) % 0.39/0.59 (define @t37 () (= (tptp.j (tptp.op2 @t35 @t34)) (tptp.op1 @t36 (tptp.j @t34)))) % 0.39/0.59 (define @t38 () (tptp.sorti2 @t34)) % 0.39/0.59 (define @t39 () (@list @t34)) % 0.39/0.59 (define @t40 () (forall @t39 (=> @t38 @t37))) % 0.39/0.59 (define @t41 () (tptp.sorti2 @t35)) % 0.39/0.59 (define @t42 () (=> @t41 @t40)) % 0.39/0.59 (define @t43 () (@list @t35)) % 0.39/0.59 (define @t44 () (forall @t43 @t42)) % 0.39/0.59 (define @t45 () (@var "X" $$unsorted)) % 0.39/0.59 (define @t46 () (@var "W" $$unsorted)) % 0.39/0.59 (define @t47 () (tptp.h @t46)) % 0.39/0.59 (define @t48 () (= (tptp.h (tptp.op1 @t46 @t45)) (tptp.op2 @t47 (tptp.h @t45)))) % 0.39/0.59 (define @t49 () (tptp.sorti1 @t45)) % 0.39/0.59 (define @t50 () (@list @t45)) % 0.39/0.59 (define @t51 () (forall @t50 (=> @t49 @t48))) % 0.39/0.59 (define @t52 () (tptp.sorti1 @t46)) % 0.39/0.59 (define @t53 () (=> @t52 @t51)) % 0.39/0.59 (define @t54 () (@list @t46)) % 0.39/0.59 (define @t55 () (forall @t54 @t53)) % 0.39/0.59 (define @t56 () (and @t55 @t44 @t33 @t27)) % 0.39/0.59 (define @t57 () (not @t56)) % 0.39/0.59 (define @t58 () (tptp.sorti1 (tptp.j @t1))) % 0.39/0.59 (define @t59 () (forall @t5 (=> @t9 @t58))) % 0.39/0.59 (define @t60 () (tptp.sorti2 (tptp.h @t2))) % 0.39/0.59 (define @t61 () (forall @t7 (=> @t6 @t60))) % 0.39/0.59 (define @t62 () (and @t61 @t59)) % 0.39/0.59 (define @t63 () (=> @t62 @t57)) % 0.39/0.59 (define @t64 () (not @t63)) % 0.39/0.59 (define @t65 () (not (= @t1 @t3))) % 0.39/0.59 (define @t66 () (not @t4)) % 0.39/0.59 (define @t67 () (forall @t5 (or @t66 @t65))) % 0.39/0.59 (define @t68 () (and @t6 @t67)) % 0.39/0.59 (define @t69 () (forall @t7 (not @t68))) % 0.39/0.59 (define @t70 () (not @t69)) % 0.39/0.59 (define @t71 () (@quantifiers_skolemize (forall @t7 (or (not @t6) (not @t67))) 0)) % 0.39/0.59 (define @t72 () (forall @t5 (or @t66 (not (= @t1 (tptp.op1 @t71 @t1)))))) % 0.39/0.59 (define @t73 () (not @t72)) % 0.39/0.59 (define @t74 () (tptp.sorti1 @t71)) % 0.39/0.59 (define @t75 () (not @t74)) % 0.39/0.59 (define @t76 () (or @t75 @t73)) % 0.39/0.59 (define @t77 () (@list true)) % 0.39/0.59 (define @t78 () (@list @t76)) % 0.39/0.59 (define @t79 () (tptp.h @t71)) % 0.39/0.59 (define @t80 () (not @t9)) % 0.39/0.59 (define @t81 () (forall @t5 (or @t80 (not (= @t1 (tptp.op2 @t79 @t1)))))) % 0.39/0.59 (define @t82 () (@quantifiers_skolemize @t81 0)) % 0.39/0.59 (define @t83 () (tptp.j @t82)) % 0.39/0.59 (define @t84 () (= @t22 @t23)) % 0.39/0.59 (define @t85 () (= @t28 @t29)) % 0.39/0.59 (define @t86 () (@var "BOUND_VARIABLE_7621" $$unsorted)) % 0.39/0.59 (define @t87 () (= (tptp.j (tptp.op2 @t35 @t86)) (tptp.op1 @t36 (tptp.j @t86)))) % 0.39/0.59 (define @t88 () (not (tptp.sorti2 @t86))) % 0.39/0.59 (define @t89 () (not @t41)) % 0.39/0.59 (define @t90 () (or @t88 @t87)) % 0.39/0.59 (define @t91 () (or @t89 @t90)) % 0.39/0.59 (define @t92 () (forall (@list @t35 @t86) @t91)) % 0.39/0.59 (define @t93 () (@list @t86)) % 0.39/0.59 (define @t94 () (forall @t93 @t91)) % 0.39/0.59 (define @t95 () (forall @t93 @t90)) % 0.39/0.59 (define @t96 () (or @t89 @t95)) % 0.39/0.59 (define @t97 () (forall @t39 (or (not @t38) @t37))) % 0.39/0.59 (define @t98 () (@var "BOUND_VARIABLE_7598" $$unsorted)) % 0.39/0.59 (define @t99 () (= (tptp.h (tptp.op1 @t46 @t98)) (tptp.op2 @t47 (tptp.h @t98)))) % 0.39/0.59 (define @t100 () (not (tptp.sorti1 @t98))) % 0.39/0.59 (define @t101 () (not @t52)) % 0.39/0.59 (define @t102 () (or @t100 @t99)) % 0.39/0.59 (define @t103 () (or @t101 @t102)) % 0.39/0.59 (define @t104 () (forall (@list @t46 @t98) @t103)) % 0.39/0.59 (define @t105 () (@list @t98)) % 0.39/0.59 (define @t106 () (forall @t105 @t103)) % 0.39/0.59 (define @t107 () (forall @t105 @t102)) % 0.39/0.59 (define @t108 () (or @t101 @t107)) % 0.39/0.59 (define @t109 () (forall @t50 (or (not @t49) @t48))) % 0.39/0.59 (define @t110 () (@list @t71)) % 0.39/0.59 (define @t111 () (tptp.j @t79)) % 0.39/0.59 (define @t112 () (= @t71 @t111)) % 0.39/0.59 (define @t113 () (or @t75 @t112)) % 0.39/0.59 (define @t114 () (@list false false)) % 0.39/0.59 (define @t115 () (tptp.op1 @t111 @t83)) % 0.39/0.59 (define @t116 () (not (= @t1 @t8))) % 0.39/0.59 (define @t117 () (forall @t5 (or @t80 @t116))) % 0.39/0.59 (define @t118 () (and @t10 @t117)) % 0.39/0.59 (define @t119 () (forall @t7 (not @t118))) % 0.39/0.59 (define @t120 () (not @t119)) % 0.39/0.59 (define @t121 () (tptp.sorti2 @t79)) % 0.39/0.59 (define @t122 () (or @t75 @t121)) % 0.39/0.59 (define @t123 () (not @t81)) % 0.39/0.59 (define @t124 () (not @t121)) % 0.39/0.59 (define @t125 () (or @t124 @t123)) % 0.39/0.59 (define @t126 () (tptp.sorti2 @t82)) % 0.39/0.59 (define @t127 () (tptp.op2 @t79 @t82)) % 0.39/0.59 (define @t128 () (= @t82 @t127)) % 0.39/0.59 (define @t129 () (not @t128)) % 0.39/0.59 (define @t130 () (not @t126)) % 0.39/0.59 (define @t131 () (or @t130 @t129)) % 0.39/0.59 (define @t132 () (@list @t131)) % 0.39/0.59 (define @t133 () (= (tptp.j @t127) @t115)) % 0.39/0.59 (define @t134 () (or @t124 @t130 @t133)) % 0.39/0.59 (define @t135 () (tptp.sorti1 @t83)) % 0.39/0.59 (define @t136 () (or @t130 @t135)) % 0.39/0.59 (define @t137 () (= @t83 (tptp.op1 @t71 @t83))) % 0.39/0.59 (define @t138 () (not @t137)) % 0.39/0.59 (define @t139 () (not @t135)) % 0.39/0.59 (define @t140 () (or @t139 @t138)) % 0.39/0.59 (define @t141 () (not @t140)) % 0.39/0.59 (assume @p1 (forall @t7 (=> @t6 (forall @t5 (=> @t4 (tptp.sorti1 @t3)))))) % 0.39/0.59 (assume @p2 (forall @t7 (=> @t10 (forall @t5 (=> @t9 (tptp.sorti2 @t8)))))) % 0.39/0.59 (assume @p3 @t15) % 0.39/0.59 (assume @p4 @t21) % 0.39/0.59 (assume @p5 @t64) % 0.39/0.59 (assume @p6 true) % 0.39/0.59 (step @p7 :rule bool-and-de-morgan :args (@t6 @t67 true)) % 0.39/0.59 (step @p8 :rule cong :premises (@p7) :args (@t69)) % 0.39/0.59 (step @p9 :rule cong :premises (@p8) :args (@t70)) % 0.39/0.59 (step @p10 :rule exists-elim :args ((= (exists @t7 @t68) @t70))) % 0.39/0.59 (step @p11 :rule trans :premises (@p10 @p9)) % 0.39/0.59 (step @p12 :rule bool-impl-elim :args (@t4 @t65)) % 0.39/0.59 (step @p13 :rule cong :premises (@p12) :args ((forall @t5 (=> @t4 @t65)))) % 0.39/0.59 (step @p14 :rule eq-symm :args (@t3 @t1)) % 0.39/0.59 (step @p15 :rule cong :premises (@p14) :args (@t11)) % 0.39/0.59 (step @p16 :rule refl :args (@t4)) % 0.39/0.59 (step @p17 :rule cong :premises (@p16 @p15) :args (@t12)) % 0.39/0.59 (step @p18 :rule cong :premises (@p17) :args (@t13)) % 0.39/0.59 (step @p19 :rule trans :premises (@p18 @p13)) % 0.39/0.59 (step @p20 :rule refl :args (@t6)) % 0.39/0.59 (step @p21 :rule nary_cong :premises (@p20 @p19) :args (@t14)) % 0.39/0.59 (step @p22 :rule cong :premises (@p21) :args (@t15)) % 0.39/0.59 (step @p23 :rule trans :premises (@p22 @p11)) % 0.39/0.59 (step @p24 :rule eq_resolve :premises (@p3 @p23)) % 0.39/0.59 (step @p25 :rule skolemize :premises (@p24)) % 0.39/0.59 (step @p26 :rule bool-double-not-elim :args (@t72)) % 0.39/0.59 (step @p27 :rule refl :args (@t76)) % 0.39/0.59 (step @p28 :rule nary_cong :premises (@p27 @p26) :args ((or @t76 (not @t73)))) % 0.39/0.59 (step @p29 :rule cnf_or_neg :args (@t76 1)) % 0.39/0.59 (step @p30 :rule eq_resolve :premises (@p29 @p28)) % 0.39/0.59 (step @p31 :rule reordering :premises (@p30) :args ((or @t72 @t76))) % 0.39/0.59 (step @p32 :rule chain_m_resolution :premises (@p31 @p25) :args (@t72 @t77 @t78)) % 0.39/0.59 (step @p33 :rule refl :args (@t83)) % 0.39/0.59 (step @p34 :rule bool-impl-elim :args (@t24 @t84)) % 0.39/0.59 (step @p35 :rule cong :premises (@p34) :args ((forall @t26 (=> @t24 @t84)))) % 0.39/0.59 (step @p36 :rule eq-symm :args (@t23 @t22)) % 0.39/0.59 (step @p37 :rule refl :args (@t24)) % 0.39/0.59 (step @p38 :rule cong :premises (@p37 @p36) :args (@t25)) % 0.39/0.59 (step @p39 :rule cong :premises (@p38) :args (@t27)) % 0.39/0.59 (step @p40 :rule trans :premises (@p39 @p35)) % 0.39/0.59 (step @p41 :rule bool-impl-elim :args (@t30 @t85)) % 0.39/0.59 (step @p42 :rule cong :premises (@p41) :args ((forall @t32 (=> @t30 @t85)))) % 0.39/0.59 (step @p43 :rule eq-symm :args (@t29 @t28)) % 0.39/0.59 (step @p44 :rule refl :args (@t30)) % 0.39/0.59 (step @p45 :rule cong :premises (@p44 @p43) :args (@t31)) % 0.39/0.59 (step @p46 :rule cong :premises (@p45) :args (@t33)) % 0.39/0.59 (step @p47 :rule trans :premises (@p46 @p42)) % 0.39/0.59 (step @p48 :rule aci_norm :args ((= @t91 (or @t89 @t88 @t87)))) % 0.39/0.59 (step @p49 :rule cong :premises (@p48) :args (@t92)) % 0.39/0.59 (step @p50 :rule quant-merge-prenex :args ((= (forall @t43 @t94) @t92))) % 0.39/0.59 (step @p51 :rule alpha_equiv :args (@t95 (@list @t86) (@list @t34))) % 0.39/0.59 (step @p52 :rule refl :args (@t89)) % 0.39/0.59 (step @p53 :rule nary_cong :premises (@p52 @p51) :args (@t96)) % 0.39/0.59 (step @p54 :rule quant-miniscope-or :args ((= @t94 @t96))) % 0.39/0.59 (step @p55 :rule trans :premises (@p54 @p53)) % 0.39/0.59 (step @p56 :rule symm :premises (@p55)) % 0.39/0.59 (step @p57 :rule cong :premises (@p56) :args ((forall @t43 (or @t89 @t97)))) % 0.39/0.59 (step @p58 :rule trans :premises (@p57 @p50)) % 0.39/0.59 (step @p59 :rule trans :premises (@p58 @p49)) % 0.39/0.59 (step @p60 :rule bool-impl-elim :args (@t41 @t97)) % 0.39/0.59 (step @p61 :rule cong :premises (@p60) :args ((forall @t43 (=> @t41 @t97)))) % 0.39/0.59 (step @p62 :rule trans :premises (@p61 @p59)) % 0.39/0.59 (step @p63 :rule bool-impl-elim :args (@t38 @t37)) % 0.39/0.59 (step @p64 :rule cong :premises (@p63) :args (@t40)) % 0.39/0.59 (step @p65 :rule refl :args (@t41)) % 0.39/0.59 (step @p66 :rule cong :premises (@p65 @p64) :args (@t42)) % 0.39/0.59 (step @p67 :rule cong :premises (@p66) :args (@t44)) % 0.39/0.59 (step @p68 :rule trans :premises (@p67 @p62)) % 0.39/0.59 (step @p69 :rule aci_norm :args ((= @t103 (or @t101 @t100 @t99)))) % 0.39/0.59 (step @p70 :rule cong :premises (@p69) :args (@t104)) % 0.39/0.59 (step @p71 :rule quant-merge-prenex :args ((= (forall @t54 @t106) @t104))) % 0.39/0.59 (step @p72 :rule alpha_equiv :args (@t107 (@list @t98) (@list @t45))) % 0.39/0.59 (step @p73 :rule refl :args (@t101)) % 0.39/0.59 (step @p74 :rule nary_cong :premises (@p73 @p72) :args (@t108)) % 0.39/0.59 (step @p75 :rule quant-miniscope-or :args ((= @t106 @t108))) % 0.39/0.59 (step @p76 :rule trans :premises (@p75 @p74)) % 0.39/0.59 (step @p77 :rule symm :premises (@p76)) % 0.39/0.59 (step @p78 :rule cong :premises (@p77) :args ((forall @t54 (or @t101 @t109)))) % 0.39/0.59 (step @p79 :rule trans :premises (@p78 @p71)) % 0.39/0.59 (step @p80 :rule trans :premises (@p79 @p70)) % 0.39/0.59 (step @p81 :rule bool-impl-elim :args (@t52 @t109)) % 0.39/0.59 (step @p82 :rule cong :premises (@p81) :args ((forall @t54 (=> @t52 @t109)))) % 0.39/0.59 (step @p83 :rule trans :premises (@p82 @p80)) % 0.39/0.59 (step @p84 :rule bool-impl-elim :args (@t49 @t48)) % 0.39/0.59 (step @p85 :rule cong :premises (@p84) :args (@t51)) % 0.39/0.59 (step @p86 :rule refl :args (@t52)) % 0.39/0.59 (step @p87 :rule cong :premises (@p86 @p85) :args (@t53)) % 0.39/0.59 (step @p88 :rule cong :premises (@p87) :args (@t55)) % 0.39/0.59 (step @p89 :rule trans :premises (@p88 @p83)) % 0.39/0.59 (step @p90 :rule nary_cong :premises (@p89 @p68 @p47 @p40) :args (@t56)) % 0.39/0.59 (step @p91 :rule cong :premises (@p90) :args (@t57)) % 0.39/0.59 (step @p92 :rule bool-impl-elim :args (@t9 @t58)) % 0.39/0.59 (step @p93 :rule cong :premises (@p92) :args (@t59)) % 0.39/0.59 (step @p94 :rule bool-impl-elim :args (@t6 @t60)) % 0.39/0.59 (step @p95 :rule cong :premises (@p94) :args (@t61)) % 0.39/0.59 (step @p96 :rule nary_cong :premises (@p95 @p93) :args (@t62)) % 0.39/0.59 (step @p97 :rule cong :premises (@p96 @p91) :args (@t63)) % 0.39/0.59 (step @p98 :rule cong :premises (@p97) :args (@t64)) % 0.39/0.59 (step @p99 :rule eq_resolve :premises (@p5 @p98)) % 0.39/0.59 (step @p100 :rule not_implies_elim2 :premises (@p99)) % 0.39/0.59 (step @p101 :rule not_not_elim :premises (@p100)) % 0.39/0.59 (step @p102 :rule and_elim :premises (@p101) :args (3)) % 0.39/0.59 (step @p103 :rule instantiate :premises (@p102) :args (@t110)) % 0.39/0.59 (step @p104 :rule bool-double-not-elim :args (@t74)) % 0.39/0.59 (step @p105 :rule nary_cong :premises (@p27 @p104) :args ((or @t76 (not @t75)))) % 0.39/0.59 (step @p106 :rule cnf_or_neg :args (@t76 0)) % 0.39/0.59 (step @p107 :rule eq_resolve :premises (@p106 @p105)) % 0.39/0.59 (step @p108 :rule reordering :premises (@p107) :args ((or @t74 @t76))) % 0.39/0.59 (step @p109 :rule chain_m_resolution :premises (@p108 @p25) :args (@t74 @t77 @t78)) % 0.39/0.59 (step @p110 :rule cnf_or_pos :args (@t113)) % 0.39/0.59 (step @p111 :rule reordering :premises (@p110) :args ((or @t75 @t112 (not @t113)))) % 0.39/0.59 (step @p112 :rule chain_m_resolution :premises (@p111 @p109 @p103) :args (@t112 @t114 (@list @t74 @t113))) % 0.39/0.59 (step @p113 :rule symm :premises (@p112)) % 0.39/0.59 (step @p114 :rule cong :premises (@p113 @p33) :args (@t115)) % 0.39/0.59 (step @p115 :rule and_elim :premises (@p101) :args (1)) % 0.39/0.59 (step @p116 :rule instantiate :premises (@p115) :args ((@list @t79 @t82))) % 0.39/0.59 (step @p117 :rule bool-double-not-elim :args ((forall @t7 (or (not @t10) (not @t117))))) % 0.39/0.59 (step @p118 :rule bool-and-de-morgan :args (@t10 @t117 true)) % 0.39/0.60 (step @p119 :rule cong :premises (@p118) :args (@t119)) % 0.39/0.60 (step @p120 :rule cong :premises (@p119) :args (@t120)) % 0.39/0.60 (step @p121 :rule exists-elim :args ((= (exists @t7 @t118) @t120))) % 0.39/0.60 (step @p122 :rule trans :premises (@p121 @p120)) % 0.39/0.60 (step @p123 :rule bool-impl-elim :args (@t9 @t116)) % 0.39/0.60 (step @p124 :rule cong :premises (@p123) :args ((forall @t5 (=> @t9 @t116)))) % 0.39/0.60 (step @p125 :rule eq-symm :args (@t8 @t1)) % 0.39/0.60 (step @p126 :rule cong :premises (@p125) :args (@t16)) % 0.39/0.60 (step @p127 :rule refl :args (@t9)) % 0.39/0.60 (step @p128 :rule cong :premises (@p127 @p126) :args (@t17)) % 0.39/0.60 (step @p129 :rule cong :premises (@p128) :args (@t18)) % 0.39/0.60 (step @p130 :rule trans :premises (@p129 @p124)) % 0.39/0.60 (step @p131 :rule refl :args (@t10)) % 0.39/0.60 (step @p132 :rule nary_cong :premises (@p131 @p130) :args (@t19)) % 0.39/0.60 (step @p133 :rule cong :premises (@p132) :args (@t20)) % 0.39/0.60 (step @p134 :rule trans :premises (@p133 @p122)) % 0.39/0.60 (step @p135 :rule cong :premises (@p134) :args (@t21)) % 0.39/0.60 (step @p136 :rule trans :premises (@p135 @p117)) % 0.39/0.60 (step @p137 :rule eq_resolve :premises (@p4 @p136)) % 0.39/0.60 (step @p138 :rule instantiate :premises (@p137) :args ((@list @t79))) % 0.39/0.60 (step @p139 :rule not_implies_elim1 :premises (@p99)) % 0.39/0.60 (step @p140 :rule and_elim :premises (@p139) :args (0)) % 0.39/0.60 (step @p141 :rule instantiate :premises (@p140) :args (@t110)) % 0.39/0.60 (step @p142 :rule cnf_or_pos :args (@t122)) % 0.39/0.60 (step @p143 :rule reordering :premises (@p142) :args ((or @t75 @t121 (not @t122)))) % 0.39/0.60 (step @p144 :rule chain_m_resolution :premises (@p143 @p109 @p141) :args (@t121 @t114 (@list @t74 @t122))) % 0.39/0.60 (step @p145 :rule cnf_or_pos :args (@t125)) % 0.39/0.60 (step @p146 :rule reordering :premises (@p145) :args ((or @t124 @t123 (not @t125)))) % 0.39/0.60 (step @p147 :rule chain_m_resolution :premises (@p146 @p144 @p138) :args (@t123 @t114 (@list @t121 @t125))) % 0.39/0.60 (step @p148 :rule skolemize :premises (@p147)) % 0.39/0.60 (step @p149 :rule bool-double-not-elim :args (@t126)) % 0.39/0.60 (step @p150 :rule refl :args (@t131)) % 0.39/0.60 (step @p151 :rule nary_cong :premises (@p150 @p149) :args ((or @t131 (not @t130)))) % 0.39/0.60 (step @p152 :rule cnf_or_neg :args (@t131 0)) % 0.39/0.60 (step @p153 :rule eq_resolve :premises (@p152 @p151)) % 0.39/0.60 (step @p154 :rule reordering :premises (@p153) :args ((or @t126 @t131))) % 0.39/0.60 (step @p155 :rule chain_m_resolution :premises (@p154 @p148) :args (@t126 @t77 @t132)) % 0.39/0.60 (step @p156 :rule cnf_or_pos :args (@t134)) % 0.39/0.60 (step @p157 :rule reordering :premises (@p156) :args ((or @t124 @t130 @t133 (not @t134)))) % 0.39/0.60 (step @p158 :rule chain_m_resolution :premises (@p157 @p144 @p155 @p116) :args (@t133 (@list false false false) (@list @t121 @t126 @t134))) % 0.39/0.60 (step @p159 :rule bool-double-not-elim :args (@t128)) % 0.39/0.60 (step @p160 :rule nary_cong :premises (@p150 @p159) :args ((or @t131 (not @t129)))) % 0.39/0.60 (step @p161 :rule cnf_or_neg :args (@t131 1)) % 0.39/0.60 (step @p162 :rule eq_resolve :premises (@p161 @p160)) % 0.39/0.60 (step @p163 :rule reordering :premises (@p162) :args ((or @t128 @t131))) % 0.39/0.60 (step @p164 :rule chain_m_resolution :premises (@p163 @p148) :args (@t128 @t77 @t132)) % 0.39/0.60 (step @p165 :rule cong :premises (@p164) :args (@t83)) % 0.39/0.60 (step @p166 :rule trans :premises (@p165 @p158 @p114)) % 0.39/0.60 (step @p167 :rule and_elim :premises (@p139) :args (1)) % 0.39/0.60 (step @p168 :rule instantiate :premises (@p167) :args ((@list @t82))) % 0.39/0.60 (step @p169 :rule cnf_or_pos :args (@t136)) % 0.39/0.60 (step @p170 :rule reordering :premises (@p169) :args ((or @t130 @t135 (not @t136)))) % 0.39/0.60 (step @p171 :rule chain_m_resolution :premises (@p170 @p155 @p168) :args (@t135 @t114 (@list @t126 @t136))) % 0.39/0.60 (step @p172 :rule cnf_or_pos :args (@t140)) % 0.39/0.60 (step @p173 :rule reordering :premises (@p172) :args ((or @t139 @t138 @t141))) % 0.39/0.60 (step @p174 :rule chain_m_resolution :premises (@p173 @p171 @p166) :args (@t141 @t114 (@list @t135 @t137))) % 0.39/0.60 (assume-push @p181 @t72) % 0.39/0.60 (step @p176 :rule instantiate :premises (@p32) :args ((@list @t83))) % 0.39/0.60 (step-pop @p182 :rule scope :premises (@p176)) % 0.39/0.60 (step @p177 :rule process_scope :premises (@p182) :args (@t140)) % 0.39/0.60 (step @p179 :rule implies_elim :premises (@p177)) % 0.39/0.60 (step @p180 false :rule chain_m_resolution :premises (@p179 @p174 @p32) :args (false (@list true false) (@list @t140 @t72))) % 0.39/0.60 ) % 0.39/0.60 % SZS output end Proof % 0.39/0.60 % cvc5 exiting %------------------------------------------------------------------------------