%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : ALG069+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 : n008.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 08:05:09 AM UTC 2026 % Result : Theorem 0.38s 0.58s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ALG069+1 : TPTP v9.2.1. Released v2.7.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n008.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Wed Jun 3 01:39:03 EDT 2026 % 0.16/0.34 % CPUTime : % 0.31/0.49 %----Proving TF0_NAR, FOF, or CNF % 0.38/0.58 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.38/0.58 % SZS status Theorem % 0.38/0.58 % SZS output start Proof % 0.38/0.58 ( % 0.38/0.58 (declare-sort $$unsorted 0) % 0.38/0.58 (declare-const tptp.j (-> $$unsorted $$unsorted)) % 0.38/0.58 (declare-const tptp.h (-> $$unsorted $$unsorted)) % 0.38/0.58 (declare-const tptp.sorti2 (-> $$unsorted Bool)) % 0.38/0.58 (declare-const tptp.op2 (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.58 (declare-const tptp.sorti1 (-> $$unsorted Bool)) % 0.38/0.58 (declare-const tptp.op1 (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.58 (define @t1 () (@var "V" $$unsorted)) % 0.38/0.58 (define @t2 () (@var "U" $$unsorted)) % 0.38/0.58 (define @t3 () (tptp.sorti1 @t1)) % 0.38/0.58 (define @t4 () (@list @t1)) % 0.38/0.58 (define @t5 () (tptp.sorti1 @t2)) % 0.38/0.58 (define @t6 () (@list @t2)) % 0.38/0.58 (define @t7 () (tptp.sorti2 @t1)) % 0.38/0.58 (define @t8 () (tptp.sorti2 @t2)) % 0.38/0.58 (define @t9 () (tptp.op1 @t1 @t1)) % 0.38/0.58 (define @t10 () (and @t3 (= @t9 @t2))) % 0.38/0.58 (define @t11 () (exists @t4 @t10)) % 0.38/0.58 (define @t12 () (=> @t5 @t11)) % 0.38/0.58 (define @t13 () (forall @t6 @t12)) % 0.38/0.58 (define @t14 () (tptp.op2 @t1 @t1)) % 0.38/0.58 (define @t15 () (and @t7 (= @t14 @t2))) % 0.38/0.58 (define @t16 () (exists @t4 @t15)) % 0.38/0.58 (define @t17 () (=> @t8 @t16)) % 0.38/0.58 (define @t18 () (forall @t6 @t17)) % 0.38/0.58 (define @t19 () (not @t18)) % 0.38/0.58 (define @t20 () (@var "X2" $$unsorted)) % 0.38/0.58 (define @t21 () (tptp.j (tptp.h @t20))) % 0.38/0.58 (define @t22 () (tptp.sorti1 @t20)) % 0.38/0.58 (define @t23 () (=> @t22 (= @t21 @t20))) % 0.38/0.58 (define @t24 () (@list @t20)) % 0.38/0.58 (define @t25 () (forall @t24 @t23)) % 0.38/0.58 (define @t26 () (@var "X1" $$unsorted)) % 0.38/0.58 (define @t27 () (tptp.h (tptp.j @t26))) % 0.38/0.58 (define @t28 () (tptp.sorti2 @t26)) % 0.38/0.58 (define @t29 () (=> @t28 (= @t27 @t26))) % 0.38/0.58 (define @t30 () (@list @t26)) % 0.38/0.58 (define @t31 () (forall @t30 @t29)) % 0.38/0.58 (define @t32 () (@var "Z" $$unsorted)) % 0.38/0.58 (define @t33 () (@var "Y" $$unsorted)) % 0.38/0.58 (define @t34 () (tptp.j @t33)) % 0.38/0.58 (define @t35 () (= (tptp.j (tptp.op2 @t33 @t32)) (tptp.op1 @t34 (tptp.j @t32)))) % 0.38/0.58 (define @t36 () (tptp.sorti2 @t32)) % 0.38/0.58 (define @t37 () (@list @t32)) % 0.38/0.58 (define @t38 () (forall @t37 (=> @t36 @t35))) % 0.38/0.58 (define @t39 () (tptp.sorti2 @t33)) % 0.38/0.58 (define @t40 () (=> @t39 @t38)) % 0.38/0.58 (define @t41 () (@list @t33)) % 0.38/0.58 (define @t42 () (forall @t41 @t40)) % 0.38/0.58 (define @t43 () (@var "X" $$unsorted)) % 0.38/0.58 (define @t44 () (@var "W" $$unsorted)) % 0.38/0.58 (define @t45 () (tptp.h @t44)) % 0.38/0.58 (define @t46 () (= (tptp.h (tptp.op1 @t44 @t43)) (tptp.op2 @t45 (tptp.h @t43)))) % 0.38/0.58 (define @t47 () (tptp.sorti1 @t43)) % 0.38/0.58 (define @t48 () (@list @t43)) % 0.38/0.58 (define @t49 () (forall @t48 (=> @t47 @t46))) % 0.38/0.58 (define @t50 () (tptp.sorti1 @t44)) % 0.38/0.58 (define @t51 () (=> @t50 @t49)) % 0.38/0.58 (define @t52 () (@list @t44)) % 0.38/0.58 (define @t53 () (forall @t52 @t51)) % 0.38/0.58 (define @t54 () (and @t53 @t42 @t31 @t25)) % 0.38/0.58 (define @t55 () (not @t54)) % 0.38/0.58 (define @t56 () (tptp.sorti1 (tptp.j @t1))) % 0.38/0.58 (define @t57 () (forall @t4 (=> @t7 @t56))) % 0.38/0.58 (define @t58 () (tptp.sorti2 (tptp.h @t2))) % 0.38/0.58 (define @t59 () (forall @t6 (=> @t5 @t58))) % 0.38/0.58 (define @t60 () (and @t59 @t57)) % 0.38/0.58 (define @t61 () (=> @t60 @t55)) % 0.38/0.58 (define @t62 () (not @t61)) % 0.38/0.58 (define @t63 () (= @t2 @t14)) % 0.38/0.58 (define @t64 () (not @t7)) % 0.38/0.58 (define @t65 () (not (forall @t4 (or @t64 (not @t63))))) % 0.38/0.58 (define @t66 () (and @t7 @t63)) % 0.38/0.58 (define @t67 () (forall @t4 (not @t66))) % 0.38/0.58 (define @t68 () (not @t67)) % 0.38/0.58 (define @t69 () (forall @t6 (or (not @t8) @t65))) % 0.38/0.58 (define @t70 () (@quantifiers_skolemize @t69 0)) % 0.38/0.58 (define @t71 () (forall @t4 (or @t64 (not (= @t14 @t70))))) % 0.38/0.58 (define @t72 () (not @t71)) % 0.38/0.58 (define @t73 () (tptp.sorti2 @t70)) % 0.38/0.58 (define @t74 () (not @t73)) % 0.38/0.58 (define @t75 () (or @t74 @t72)) % 0.38/0.58 (define @t76 () (not @t75)) % 0.38/0.58 (define @t77 () (not @t69)) % 0.38/0.58 (define @t78 () (not (= @t70 @t14))) % 0.38/0.58 (define @t79 () (or @t64 @t78)) % 0.38/0.58 (define @t80 () (forall @t4 @t79)) % 0.38/0.58 (define @t81 () (not @t80)) % 0.38/0.58 (define @t82 () (or @t74 @t81)) % 0.38/0.58 (define @t83 () (not @t82)) % 0.38/0.58 (define @t84 () (@list true)) % 0.38/0.58 (define @t85 () (@list @t75)) % 0.38/0.58 (define @t86 () (= @t20 @t21)) % 0.38/0.58 (define @t87 () (= @t26 @t27)) % 0.38/0.58 (define @t88 () (@var "BOUND_VARIABLE_7619" $$unsorted)) % 0.38/0.58 (define @t89 () (= (tptp.j (tptp.op2 @t33 @t88)) (tptp.op1 @t34 (tptp.j @t88)))) % 0.38/0.58 (define @t90 () (not (tptp.sorti2 @t88))) % 0.38/0.58 (define @t91 () (not @t39)) % 0.38/0.58 (define @t92 () (or @t90 @t89)) % 0.38/0.58 (define @t93 () (or @t91 @t92)) % 0.38/0.58 (define @t94 () (forall (@list @t33 @t88) @t93)) % 0.38/0.58 (define @t95 () (@list @t88)) % 0.38/0.58 (define @t96 () (forall @t95 @t93)) % 0.38/0.58 (define @t97 () (forall @t95 @t92)) % 0.38/0.58 (define @t98 () (or @t91 @t97)) % 0.38/0.58 (define @t99 () (forall @t37 (or (not @t36) @t35))) % 0.38/0.58 (define @t100 () (@var "BOUND_VARIABLE_7596" $$unsorted)) % 0.38/0.58 (define @t101 () (= (tptp.h (tptp.op1 @t44 @t100)) (tptp.op2 @t45 (tptp.h @t100)))) % 0.38/0.58 (define @t102 () (not (tptp.sorti1 @t100))) % 0.38/0.58 (define @t103 () (not @t50)) % 0.38/0.58 (define @t104 () (or @t102 @t101)) % 0.38/0.58 (define @t105 () (or @t103 @t104)) % 0.38/0.58 (define @t106 () (forall (@list @t44 @t100) @t105)) % 0.38/0.58 (define @t107 () (@list @t100)) % 0.38/0.58 (define @t108 () (forall @t107 @t105)) % 0.38/0.58 (define @t109 () (forall @t107 @t104)) % 0.38/0.58 (define @t110 () (or @t103 @t109)) % 0.38/0.58 (define @t111 () (forall @t48 (or (not @t47) @t46))) % 0.38/0.58 (define @t112 () (tptp.j @t70)) % 0.38/0.58 (define @t113 () (not @t3)) % 0.38/0.58 (define @t114 () (forall @t4 (or @t113 (not (= @t9 @t112))))) % 0.38/0.58 (define @t115 () (@quantifiers_skolemize @t114 0)) % 0.38/0.58 (define @t116 () (= @t2 @t9)) % 0.38/0.58 (define @t117 () (not (forall @t4 (or @t113 (not @t116))))) % 0.38/0.58 (define @t118 () (and @t3 @t116)) % 0.38/0.58 (define @t119 () (forall @t4 (not @t118))) % 0.38/0.58 (define @t120 () (not @t119)) % 0.38/0.58 (define @t121 () (not (= @t112 @t9))) % 0.38/0.58 (define @t122 () (or @t113 @t121)) % 0.38/0.58 (define @t123 () (forall @t4 @t122)) % 0.38/0.58 (define @t124 () (not @t123)) % 0.38/0.58 (define @t125 () (tptp.sorti1 @t112)) % 0.38/0.58 (define @t126 () (not @t125)) % 0.38/0.58 (define @t127 () (or @t126 @t124)) % 0.38/0.58 (define @t128 () (forall @t6 (or (not @t5) @t117))) % 0.38/0.58 (define @t129 () (not @t114)) % 0.38/0.58 (define @t130 () (or @t126 @t129)) % 0.38/0.58 (define @t131 () (@list @t70)) % 0.38/0.58 (define @t132 () (or @t74 @t125)) % 0.38/0.58 (define @t133 () (@list false false)) % 0.38/0.58 (define @t134 () (tptp.op1 @t115 @t115)) % 0.38/0.58 (define @t135 () (= @t112 @t134)) % 0.38/0.58 (define @t136 () (not @t135)) % 0.38/0.58 (define @t137 () (tptp.sorti1 @t115)) % 0.38/0.58 (define @t138 () (not @t137)) % 0.38/0.58 (define @t139 () (or @t138 @t136)) % 0.38/0.58 (define @t140 () (not @t139)) % 0.38/0.58 (define @t141 () (not (= @t134 @t112))) % 0.38/0.58 (define @t142 () (or @t138 @t141)) % 0.38/0.58 (define @t143 () (not @t142)) % 0.38/0.58 (define @t144 () (@list @t139)) % 0.38/0.58 (define @t145 () (tptp.h @t115)) % 0.38/0.58 (define @t146 () (tptp.op2 @t145 @t145)) % 0.38/0.58 (define @t147 () (= (tptp.h @t134) @t146)) % 0.38/0.58 (define @t148 () (or @t138 @t138 @t147)) % 0.38/0.58 (define @t149 () (tptp.h @t112)) % 0.38/0.58 (define @t150 () (= @t70 @t149)) % 0.38/0.58 (define @t151 () (or @t74 @t150)) % 0.38/0.58 (define @t152 () (tptp.sorti2 @t145)) % 0.38/0.58 (define @t153 () (or @t138 @t152)) % 0.38/0.58 (define @t154 () (= @t70 @t146)) % 0.38/0.58 (define @t155 () (not @t154)) % 0.38/0.58 (define @t156 () (not @t152)) % 0.38/0.58 (define @t157 () (or @t156 @t155)) % 0.38/0.58 (define @t158 () (not @t157)) % 0.38/0.58 (define @t159 () (not (= @t146 @t70))) % 0.38/0.58 (define @t160 () (or @t156 @t159)) % 0.38/0.58 (assume @p1 (forall @t6 (=> @t5 (forall @t4 (=> @t3 (tptp.sorti1 (tptp.op1 @t2 @t1))))))) % 0.38/0.58 (assume @p2 (forall @t6 (=> @t8 (forall @t4 (=> @t7 (tptp.sorti2 (tptp.op2 @t2 @t1))))))) % 0.38/0.58 (assume @p3 @t13) % 0.38/0.58 (assume @p4 @t19) % 0.38/0.58 (assume @p5 @t62) % 0.38/0.58 (assume @p6 true) % 0.38/0.58 (step @p7 :rule bool-impl-elim :args (@t8 @t65)) % 0.38/0.58 (step @p8 :rule cong :premises (@p7) :args ((forall @t6 (=> @t8 @t65)))) % 0.38/0.58 (step @p9 :rule bool-and-de-morgan :args (@t7 @t63 true)) % 0.38/0.58 (step @p10 :rule cong :premises (@p9) :args (@t67)) % 0.38/0.58 (step @p11 :rule cong :premises (@p10) :args (@t68)) % 0.38/0.58 (step @p12 :rule exists-elim :args ((= (exists @t4 @t66) @t68))) % 0.38/0.58 (step @p13 :rule trans :premises (@p12 @p11)) % 0.38/0.58 (step @p14 :rule eq-symm :args (@t14 @t2)) % 0.38/0.58 (step @p15 :rule refl :args (@t7)) % 0.38/0.58 (step @p16 :rule nary_cong :premises (@p15 @p14) :args (@t15)) % 0.38/0.58 (step @p17 :rule cong :premises (@p16) :args (@t16)) % 0.38/0.58 (step @p18 :rule trans :premises (@p17 @p13)) % 0.38/0.58 (step @p19 :rule refl :args (@t8)) % 0.38/0.58 (step @p20 :rule cong :premises (@p19 @p18) :args (@t17)) % 0.38/0.58 (step @p21 :rule cong :premises (@p20) :args (@t18)) % 0.38/0.58 (step @p22 :rule trans :premises (@p21 @p8)) % 0.38/0.58 (step @p23 :rule cong :premises (@p22) :args (@t19)) % 0.38/0.58 (step @p24 :rule eq_resolve :premises (@p4 @p23)) % 0.38/0.58 (step @p25 :rule refl :args (@t76)) % 0.38/0.58 (step @p26 :rule bool-double-not-elim :args (@t69)) % 0.38/0.58 (step @p27 :rule nary_cong :premises (@p26 @p25) :args ((or (not @t77) @t76))) % 0.38/0.58 (step @p28 :rule eq-symm :args (@t70 @t14)) % 0.38/0.58 (step @p29 :rule cong :premises (@p28) :args (@t78)) % 0.38/0.58 (step @p30 :rule refl :args (@t64)) % 0.38/0.58 (step @p31 :rule nary_cong :premises (@p30 @p29) :args (@t79)) % 0.38/0.58 (step @p32 :rule cong :premises (@p31) :args (@t80)) % 0.38/0.58 (step @p33 :rule cong :premises (@p32) :args (@t81)) % 0.38/0.58 (step @p34 :rule refl :args (@t74)) % 0.38/0.58 (step @p35 :rule nary_cong :premises (@p34 @p33) :args (@t82)) % 0.38/0.58 (step @p36 :rule cong :premises (@p35) :args (@t83)) % 0.38/0.58 (step @p37 :rule refl :args (@t77)) % 0.38/0.58 (step @p38 :rule cong :premises (@p37 @p36) :args ((=> @t77 @t83))) % 0.38/0.58 (assume-push @p236 @t77) % 0.38/0.58 (step @p40 :rule skolemize :premises (@p24)) % 0.38/0.58 (step-pop @p237 :rule scope :premises (@p40)) % 0.38/0.58 (step @p41 :rule process_scope :premises (@p237) :args (@t83)) % 0.38/0.58 (step @p43 :rule eq_resolve :premises (@p41 @p38)) % 0.38/0.58 (step @p44 :rule implies_elim :premises (@p43)) % 0.38/0.58 (step @p45 :rule eq_resolve :premises (@p44 @p27)) % 0.38/0.58 (step @p46 :rule chain_m_resolution :premises (@p45 @p24) :args (@t76 @t84 (@list @t69))) % 0.38/0.58 (step @p47 :rule bool-double-not-elim :args (@t71)) % 0.38/0.58 (step @p48 :rule refl :args (@t75)) % 0.38/0.58 (step @p49 :rule nary_cong :premises (@p48 @p47) :args ((or @t75 (not @t72)))) % 0.38/0.58 (step @p50 :rule cnf_or_neg :args (@t75 1)) % 0.38/0.58 (step @p51 :rule eq_resolve :premises (@p50 @p49)) % 0.38/0.58 (step @p52 :rule reordering :premises (@p51) :args ((or @t71 @t75))) % 0.38/0.58 (step @p53 :rule chain_m_resolution :premises (@p52 @p46) :args (@t71 @t84 @t85)) % 0.38/0.58 (step @p54 :rule bool-impl-elim :args (@t22 @t86)) % 0.38/0.58 (step @p55 :rule cong :premises (@p54) :args ((forall @t24 (=> @t22 @t86)))) % 0.38/0.58 (step @p56 :rule eq-symm :args (@t21 @t20)) % 0.38/0.58 (step @p57 :rule refl :args (@t22)) % 0.38/0.58 (step @p58 :rule cong :premises (@p57 @p56) :args (@t23)) % 0.38/0.58 (step @p59 :rule cong :premises (@p58) :args (@t25)) % 0.38/0.58 (step @p60 :rule trans :premises (@p59 @p55)) % 0.38/0.58 (step @p61 :rule bool-impl-elim :args (@t28 @t87)) % 0.38/0.58 (step @p62 :rule cong :premises (@p61) :args ((forall @t30 (=> @t28 @t87)))) % 0.38/0.58 (step @p63 :rule eq-symm :args (@t27 @t26)) % 0.38/0.58 (step @p64 :rule refl :args (@t28)) % 0.38/0.58 (step @p65 :rule cong :premises (@p64 @p63) :args (@t29)) % 0.38/0.58 (step @p66 :rule cong :premises (@p65) :args (@t31)) % 0.38/0.58 (step @p67 :rule trans :premises (@p66 @p62)) % 0.38/0.58 (step @p68 :rule aci_norm :args ((= @t93 (or @t91 @t90 @t89)))) % 0.38/0.58 (step @p69 :rule cong :premises (@p68) :args (@t94)) % 0.38/0.58 (step @p70 :rule quant-merge-prenex :args ((= (forall @t41 @t96) @t94))) % 0.38/0.58 (step @p71 :rule alpha_equiv :args (@t97 (@list @t88) (@list @t32))) % 0.38/0.58 (step @p72 :rule refl :args (@t91)) % 0.38/0.58 (step @p73 :rule nary_cong :premises (@p72 @p71) :args (@t98)) % 0.38/0.58 (step @p74 :rule quant-miniscope-or :args ((= @t96 @t98))) % 0.38/0.58 (step @p75 :rule trans :premises (@p74 @p73)) % 0.38/0.58 (step @p76 :rule symm :premises (@p75)) % 0.38/0.58 (step @p77 :rule cong :premises (@p76) :args ((forall @t41 (or @t91 @t99)))) % 0.38/0.58 (step @p78 :rule trans :premises (@p77 @p70)) % 0.38/0.58 (step @p79 :rule trans :premises (@p78 @p69)) % 0.38/0.58 (step @p80 :rule bool-impl-elim :args (@t39 @t99)) % 0.38/0.58 (step @p81 :rule cong :premises (@p80) :args ((forall @t41 (=> @t39 @t99)))) % 0.38/0.58 (step @p82 :rule trans :premises (@p81 @p79)) % 0.38/0.58 (step @p83 :rule bool-impl-elim :args (@t36 @t35)) % 0.38/0.58 (step @p84 :rule cong :premises (@p83) :args (@t38)) % 0.38/0.58 (step @p85 :rule refl :args (@t39)) % 0.38/0.58 (step @p86 :rule cong :premises (@p85 @p84) :args (@t40)) % 0.38/0.58 (step @p87 :rule cong :premises (@p86) :args (@t42)) % 0.38/0.58 (step @p88 :rule trans :premises (@p87 @p82)) % 0.38/0.58 (step @p89 :rule aci_norm :args ((= @t105 (or @t103 @t102 @t101)))) % 0.38/0.58 (step @p90 :rule cong :premises (@p89) :args (@t106)) % 0.38/0.58 (step @p91 :rule quant-merge-prenex :args ((= (forall @t52 @t108) @t106))) % 0.38/0.58 (step @p92 :rule alpha_equiv :args (@t109 (@list @t100) (@list @t43))) % 0.38/0.58 (step @p93 :rule refl :args (@t103)) % 0.38/0.58 (step @p94 :rule nary_cong :premises (@p93 @p92) :args (@t110)) % 0.38/0.58 (step @p95 :rule quant-miniscope-or :args ((= @t108 @t110))) % 0.38/0.58 (step @p96 :rule trans :premises (@p95 @p94)) % 0.38/0.58 (step @p97 :rule symm :premises (@p96)) % 0.38/0.58 (step @p98 :rule cong :premises (@p97) :args ((forall @t52 (or @t103 @t111)))) % 0.38/0.58 (step @p99 :rule trans :premises (@p98 @p91)) % 0.38/0.58 (step @p100 :rule trans :premises (@p99 @p90)) % 0.38/0.58 (step @p101 :rule bool-impl-elim :args (@t50 @t111)) % 0.38/0.58 (step @p102 :rule cong :premises (@p101) :args ((forall @t52 (=> @t50 @t111)))) % 0.38/0.58 (step @p103 :rule trans :premises (@p102 @p100)) % 0.38/0.58 (step @p104 :rule bool-impl-elim :args (@t47 @t46)) % 0.38/0.58 (step @p105 :rule cong :premises (@p104) :args (@t49)) % 0.38/0.58 (step @p106 :rule refl :args (@t50)) % 0.38/0.58 (step @p107 :rule cong :premises (@p106 @p105) :args (@t51)) % 0.38/0.58 (step @p108 :rule cong :premises (@p107) :args (@t53)) % 0.38/0.58 (step @p109 :rule trans :premises (@p108 @p103)) % 0.38/0.58 (step @p110 :rule nary_cong :premises (@p109 @p88 @p67 @p60) :args (@t54)) % 0.38/0.58 (step @p111 :rule cong :premises (@p110) :args (@t55)) % 0.38/0.58 (step @p112 :rule bool-impl-elim :args (@t7 @t56)) % 0.38/0.58 (step @p113 :rule cong :premises (@p112) :args (@t57)) % 0.38/0.58 (step @p114 :rule bool-impl-elim :args (@t5 @t58)) % 0.38/0.58 (step @p115 :rule cong :premises (@p114) :args (@t59)) % 0.38/0.58 (step @p116 :rule nary_cong :premises (@p115 @p113) :args (@t60)) % 0.38/0.58 (step @p117 :rule cong :premises (@p116 @p111) :args (@t61)) % 0.38/0.58 (step @p118 :rule cong :premises (@p117) :args (@t62)) % 0.38/0.58 (step @p119 :rule eq_resolve :premises (@p5 @p118)) % 0.38/0.58 (step @p120 :rule not_implies_elim2 :premises (@p119)) % 0.38/0.58 (step @p121 :rule not_not_elim :premises (@p120)) % 0.38/0.58 (step @p122 :rule and_elim :premises (@p121) :args (0)) % 0.38/0.58 (step @p123 :rule instantiate :premises (@p122) :args ((@list @t115 @t115))) % 0.38/0.58 (step @p124 :rule bool-impl-elim :args (@t5 @t117)) % 0.38/0.58 (step @p125 :rule cong :premises (@p124) :args ((forall @t6 (=> @t5 @t117)))) % 0.38/0.58 (step @p126 :rule bool-and-de-morgan :args (@t3 @t116 true)) % 0.38/0.58 (step @p127 :rule cong :premises (@p126) :args (@t119)) % 0.38/0.58 (step @p128 :rule cong :premises (@p127) :args (@t120)) % 0.38/0.58 (step @p129 :rule exists-elim :args ((= (exists @t4 @t118) @t120))) % 0.38/0.58 (step @p130 :rule trans :premises (@p129 @p128)) % 0.38/0.58 (step @p131 :rule eq-symm :args (@t9 @t2)) % 0.38/0.58 (step @p132 :rule refl :args (@t3)) % 0.38/0.58 (step @p133 :rule nary_cong :premises (@p132 @p131) :args (@t10)) % 0.38/0.58 (step @p134 :rule cong :premises (@p133) :args (@t11)) % 0.38/0.58 (step @p135 :rule trans :premises (@p134 @p130)) % 0.38/0.58 (step @p136 :rule refl :args (@t5)) % 0.38/0.58 (step @p137 :rule cong :premises (@p136 @p135) :args (@t12)) % 0.38/0.58 (step @p138 :rule cong :premises (@p137) :args (@t13)) % 0.38/0.58 (step @p139 :rule trans :premises (@p138 @p125)) % 0.38/0.58 (step @p140 :rule eq_resolve :premises (@p3 @p139)) % 0.38/0.58 (step @p141 :rule eq-symm :args (@t112 @t9)) % 0.38/0.58 (step @p142 :rule cong :premises (@p141) :args (@t121)) % 0.38/0.58 (step @p143 :rule refl :args (@t113)) % 0.38/0.58 (step @p144 :rule nary_cong :premises (@p143 @p142) :args (@t122)) % 0.38/0.58 (step @p145 :rule cong :premises (@p144) :args (@t123)) % 0.38/0.58 (step @p146 :rule cong :premises (@p145) :args (@t124)) % 0.38/0.58 (step @p147 :rule refl :args (@t126)) % 0.38/0.58 (step @p148 :rule nary_cong :premises (@p147 @p146) :args (@t127)) % 0.38/0.58 (step @p149 :rule refl :args (@t128)) % 0.38/0.58 (step @p150 :rule cong :premises (@p149 @p148) :args ((=> @t128 @t127))) % 0.38/0.58 (assume-push @p238 @t128) % 0.38/0.58 (step @p152 :rule instantiate :premises (@p140) :args ((@list @t112))) % 0.38/0.58 (step-pop @p239 :rule scope :premises (@p152)) % 0.38/0.58 (step @p153 :rule process_scope :premises (@p239) :args (@t127)) % 0.38/0.58 (step @p155 :rule eq_resolve :premises (@p153 @p150)) % 0.38/0.58 (step @p156 :rule implies_elim :premises (@p155)) % 0.38/0.58 (step @p157 :rule chain_m_resolution :premises (@p156 @p140) :args (@t130 (@list false) (@list @t128))) % 0.38/0.58 (step @p158 :rule not_implies_elim1 :premises (@p119)) % 0.38/0.58 (step @p159 :rule and_elim :premises (@p158) :args (1)) % 0.38/0.58 (step @p160 :rule instantiate :premises (@p159) :args (@t131)) % 0.38/0.58 (step @p161 :rule bool-double-not-elim :args (@t73)) % 0.38/0.58 (step @p162 :rule nary_cong :premises (@p48 @p161) :args ((or @t75 (not @t74)))) % 0.38/0.58 (step @p163 :rule cnf_or_neg :args (@t75 0)) % 0.38/0.58 (step @p164 :rule eq_resolve :premises (@p163 @p162)) % 0.38/0.58 (step @p165 :rule reordering :premises (@p164) :args ((or @t73 @t75))) % 0.38/0.58 (step @p166 :rule chain_m_resolution :premises (@p165 @p46) :args (@t73 @t84 @t85)) % 0.38/0.58 (step @p167 :rule cnf_or_pos :args (@t132)) % 0.38/0.58 (step @p168 :rule reordering :premises (@p167) :args ((or @t74 @t125 (not @t132)))) % 0.38/0.58 (step @p169 :rule chain_m_resolution :premises (@p168 @p166 @p160) :args (@t125 @t133 (@list @t73 @t132))) % 0.38/0.58 (step @p170 :rule cnf_or_pos :args (@t130)) % 0.38/0.58 (step @p171 :rule reordering :premises (@p170) :args ((or @t126 @t129 (not @t130)))) % 0.38/0.58 (step @p172 :rule chain_m_resolution :premises (@p171 @p169 @p157) :args (@t129 @t133 (@list @t125 @t130))) % 0.38/0.58 (step @p173 :rule refl :args (@t140)) % 0.38/0.58 (step @p174 :rule bool-double-not-elim :args (@t114)) % 0.38/0.58 (step @p175 :rule nary_cong :premises (@p174 @p173) :args ((or (not @t129) @t140))) % 0.38/0.58 (step @p176 :rule eq-symm :args (@t134 @t112)) % 0.38/0.58 (step @p177 :rule cong :premises (@p176) :args (@t141)) % 0.38/0.58 (step @p178 :rule refl :args (@t138)) % 0.38/0.58 (step @p179 :rule nary_cong :premises (@p178 @p177) :args (@t142)) % 0.38/0.58 (step @p180 :rule cong :premises (@p179) :args (@t143)) % 0.38/0.58 (step @p181 :rule refl :args (@t129)) % 0.38/0.58 (step @p182 :rule cong :premises (@p181 @p180) :args ((=> @t129 @t143))) % 0.38/0.58 (assume-push @p240 @t129) % 0.38/0.58 (step @p184 :rule skolemize :premises (@p172)) % 0.38/0.58 (step-pop @p241 :rule scope :premises (@p184)) % 0.38/0.58 (step @p185 :rule process_scope :premises (@p241) :args (@t143)) % 0.38/0.58 (step @p187 :rule eq_resolve :premises (@p185 @p182)) % 0.38/0.58 (step @p188 :rule implies_elim :premises (@p187)) % 0.38/0.58 (step @p189 :rule eq_resolve :premises (@p188 @p175)) % 0.38/0.58 (step @p190 :rule chain_m_resolution :premises (@p189 @p172) :args (@t140 @t84 (@list @t114))) % 0.38/0.58 (step @p191 :rule bool-double-not-elim :args (@t137)) % 0.38/0.58 (step @p192 :rule refl :args (@t139)) % 0.38/0.58 (step @p193 :rule nary_cong :premises (@p192 @p191) :args ((or @t139 (not @t138)))) % 0.38/0.58 (step @p194 :rule cnf_or_neg :args (@t139 0)) % 0.38/0.58 (step @p195 :rule eq_resolve :premises (@p194 @p193)) % 0.38/0.58 (step @p196 :rule reordering :premises (@p195) :args ((or @t137 @t139))) % 0.38/0.58 (step @p197 :rule chain_m_resolution :premises (@p196 @p190) :args (@t137 @t84 @t144)) % 0.38/0.58 (step @p198 :rule cnf_or_pos :args (@t148)) % 0.38/0.58 (step @p199 :rule factoring :premises (@p198)) % 0.38/0.58 (step @p200 :rule reordering :premises (@p199) :args ((or @t138 @t147 (not @t148)))) % 0.38/0.58 (step @p201 :rule chain_m_resolution :premises (@p200 @p197 @p123) :args (@t147 @t133 (@list @t137 @t148))) % 0.38/0.58 (step @p202 :rule bool-double-not-elim :args (@t135)) % 0.38/0.58 (step @p203 :rule nary_cong :premises (@p192 @p202) :args ((or @t139 (not @t136)))) % 0.38/0.58 (step @p204 :rule cnf_or_neg :args (@t139 1)) % 0.38/0.58 (step @p205 :rule eq_resolve :premises (@p204 @p203)) % 0.38/0.58 (step @p206 :rule reordering :premises (@p205) :args ((or @t135 @t139))) % 0.38/0.58 (step @p207 :rule chain_m_resolution :premises (@p206 @p190) :args (@t135 @t84 @t144)) % 0.38/0.58 (step @p208 :rule cong :premises (@p207) :args (@t149)) % 0.38/0.58 (step @p209 :rule and_elim :premises (@p121) :args (2)) % 0.38/0.58 (step @p210 :rule instantiate :premises (@p209) :args (@t131)) % 0.38/0.58 (step @p211 :rule cnf_or_pos :args (@t151)) % 0.38/0.58 (step @p212 :rule reordering :premises (@p211) :args ((or @t74 @t150 (not @t151)))) % 0.38/0.58 (step @p213 :rule chain_m_resolution :premises (@p212 @p166 @p210) :args (@t150 @t133 (@list @t73 @t151))) % 0.38/0.58 (step @p214 :rule trans :premises (@p213 @p208 @p201)) % 0.38/0.58 (step @p215 :rule and_elim :premises (@p158) :args (0)) % 0.38/0.58 (step @p216 :rule instantiate :premises (@p215) :args ((@list @t115))) % 0.38/0.58 (step @p217 :rule cnf_or_pos :args (@t153)) % 0.38/0.58 (step @p218 :rule reordering :premises (@p217) :args ((or @t138 @t152 (not @t153)))) % 0.38/0.58 (step @p219 :rule chain_m_resolution :premises (@p218 @p197 @p216) :args (@t152 @t133 (@list @t137 @t153))) % 0.38/0.58 (step @p220 :rule cnf_or_pos :args (@t157)) % 0.38/0.58 (step @p221 :rule reordering :premises (@p220) :args ((or @t156 @t155 @t158))) % 0.38/0.58 (step @p222 :rule chain_m_resolution :premises (@p221 @p219 @p214) :args (@t158 @t133 (@list @t152 @t154))) % 0.38/0.58 (step @p223 :rule eq-symm :args (@t146 @t70)) % 0.38/0.58 (step @p224 :rule cong :premises (@p223) :args (@t159)) % 0.38/0.58 (step @p225 :rule refl :args (@t156)) % 0.38/0.58 (step @p226 :rule nary_cong :premises (@p225 @p224) :args (@t160)) % 0.38/0.58 (step @p227 :rule refl :args (@t71)) % 0.38/0.58 (step @p228 :rule cong :premises (@p227 @p226) :args ((=> @t71 @t160))) % 0.38/0.58 (assume-push @p242 @t71) % 0.38/0.58 (step @p230 :rule instantiate :premises (@p53) :args ((@list @t145))) % 0.38/0.58 (step-pop @p243 :rule scope :premises (@p230)) % 0.38/0.58 (step @p231 :rule process_scope :premises (@p243) :args (@t160)) % 0.38/0.58 (step @p233 :rule eq_resolve :premises (@p231 @p228)) % 0.38/0.58 (step @p234 :rule implies_elim :premises (@p233)) % 0.38/0.58 (step @p235 false :rule chain_m_resolution :premises (@p234 @p222 @p53) :args (false (@list true false) (@list @t157 @t71))) % 0.38/0.58 ) % 0.38/0.58 % SZS output end Proof % 0.38/0.58 % cvc5 exiting %------------------------------------------------------------------------------