%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : ALG040+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 : n020.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 08:05:05 AM UTC 2026 % Result : Theorem 0.37s 0.58s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ALG040+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 : n020.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 01:38:26 EDT 2026 % 0.16/0.34 % CPUTime : % 0.28/0.49 %----Proving TF0_NAR, FOF, or CNF % 0.37/0.58 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.37/0.58 % SZS status Theorem % 0.37/0.58 % SZS output start Proof % 0.37/0.58 ( % 0.37/0.58 (declare-sort $$unsorted 0) % 0.37/0.58 (declare-const tptp.j (-> $$unsorted $$unsorted)) % 0.37/0.58 (declare-const tptp.h (-> $$unsorted $$unsorted)) % 0.37/0.58 (declare-const tptp.sorti2 (-> $$unsorted Bool)) % 0.37/0.58 (declare-const tptp.op2 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.58 (declare-const tptp.sorti1 (-> $$unsorted Bool)) % 0.37/0.58 (declare-const tptp.op1 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.58 (define @t1 () (@var "V" $$unsorted)) % 0.37/0.58 (define @t2 () (@var "U" $$unsorted)) % 0.37/0.58 (define @t3 () (tptp.sorti1 @t1)) % 0.37/0.58 (define @t4 () (@list @t1)) % 0.37/0.58 (define @t5 () (tptp.sorti1 @t2)) % 0.37/0.58 (define @t6 () (@list @t2)) % 0.37/0.58 (define @t7 () (tptp.sorti2 @t1)) % 0.37/0.58 (define @t8 () (tptp.sorti2 @t2)) % 0.37/0.58 (define @t9 () (tptp.op1 @t1 @t1)) % 0.37/0.58 (define @t10 () (=> @t3 (= @t9 @t2))) % 0.37/0.58 (define @t11 () (forall @t4 @t10)) % 0.37/0.58 (define @t12 () (and @t5 @t11)) % 0.37/0.58 (define @t13 () (exists @t6 @t12)) % 0.37/0.58 (define @t14 () (tptp.op2 @t1 @t1)) % 0.37/0.58 (define @t15 () (=> @t7 (= @t14 @t2))) % 0.37/0.58 (define @t16 () (forall @t4 @t15)) % 0.37/0.58 (define @t17 () (and @t8 @t16)) % 0.37/0.58 (define @t18 () (exists @t6 @t17)) % 0.37/0.58 (define @t19 () (not @t18)) % 0.37/0.58 (define @t20 () (@var "X2" $$unsorted)) % 0.37/0.58 (define @t21 () (tptp.j (tptp.h @t20))) % 0.37/0.58 (define @t22 () (tptp.sorti1 @t20)) % 0.37/0.58 (define @t23 () (=> @t22 (= @t21 @t20))) % 0.37/0.58 (define @t24 () (@list @t20)) % 0.37/0.58 (define @t25 () (forall @t24 @t23)) % 0.37/0.58 (define @t26 () (@var "X1" $$unsorted)) % 0.37/0.58 (define @t27 () (tptp.h (tptp.j @t26))) % 0.37/0.58 (define @t28 () (tptp.sorti2 @t26)) % 0.37/0.58 (define @t29 () (=> @t28 (= @t27 @t26))) % 0.37/0.58 (define @t30 () (@list @t26)) % 0.37/0.58 (define @t31 () (forall @t30 @t29)) % 0.37/0.58 (define @t32 () (@var "Z" $$unsorted)) % 0.37/0.58 (define @t33 () (@var "Y" $$unsorted)) % 0.37/0.58 (define @t34 () (tptp.j @t33)) % 0.37/0.58 (define @t35 () (= (tptp.j (tptp.op2 @t33 @t32)) (tptp.op1 @t34 (tptp.j @t32)))) % 0.37/0.58 (define @t36 () (tptp.sorti2 @t32)) % 0.37/0.58 (define @t37 () (@list @t32)) % 0.37/0.58 (define @t38 () (forall @t37 (=> @t36 @t35))) % 0.37/0.58 (define @t39 () (tptp.sorti2 @t33)) % 0.37/0.58 (define @t40 () (=> @t39 @t38)) % 0.37/0.58 (define @t41 () (@list @t33)) % 0.37/0.58 (define @t42 () (forall @t41 @t40)) % 0.37/0.58 (define @t43 () (@var "X" $$unsorted)) % 0.37/0.58 (define @t44 () (@var "W" $$unsorted)) % 0.37/0.58 (define @t45 () (tptp.h @t44)) % 0.37/0.58 (define @t46 () (= (tptp.h (tptp.op1 @t44 @t43)) (tptp.op2 @t45 (tptp.h @t43)))) % 0.37/0.58 (define @t47 () (tptp.sorti1 @t43)) % 0.37/0.58 (define @t48 () (@list @t43)) % 0.37/0.58 (define @t49 () (forall @t48 (=> @t47 @t46))) % 0.37/0.58 (define @t50 () (tptp.sorti1 @t44)) % 0.37/0.58 (define @t51 () (=> @t50 @t49)) % 0.37/0.58 (define @t52 () (@list @t44)) % 0.37/0.58 (define @t53 () (forall @t52 @t51)) % 0.37/0.58 (define @t54 () (and @t53 @t42 @t31 @t25)) % 0.37/0.58 (define @t55 () (not @t54)) % 0.37/0.58 (define @t56 () (tptp.sorti1 (tptp.j @t1))) % 0.37/0.58 (define @t57 () (forall @t4 (=> @t7 @t56))) % 0.37/0.58 (define @t58 () (tptp.sorti2 (tptp.h @t2))) % 0.37/0.58 (define @t59 () (forall @t6 (=> @t5 @t58))) % 0.37/0.58 (define @t60 () (and @t59 @t57)) % 0.37/0.58 (define @t61 () (=> @t60 @t55)) % 0.37/0.58 (define @t62 () (not @t61)) % 0.37/0.58 (define @t63 () (= @t2 @t14)) % 0.37/0.58 (define @t64 () (not @t7)) % 0.37/0.58 (define @t65 () (forall @t4 (or @t64 @t63))) % 0.37/0.58 (define @t66 () (forall @t6 (or (not @t8) (not @t65)))) % 0.37/0.58 (define @t67 () (and @t8 @t65)) % 0.37/0.58 (define @t68 () (forall @t6 (not @t67))) % 0.37/0.58 (define @t69 () (not @t68)) % 0.37/0.58 (define @t70 () (= @t2 @t9)) % 0.37/0.58 (define @t71 () (not @t3)) % 0.37/0.58 (define @t72 () (forall @t4 (or @t71 @t70))) % 0.37/0.58 (define @t73 () (forall @t6 (or (not @t5) (not @t72)))) % 0.37/0.58 (define @t74 () (@quantifiers_skolemize @t73 0)) % 0.37/0.58 (define @t75 () (tptp.h @t74)) % 0.37/0.58 (define @t76 () (or @t64 (= @t75 @t14))) % 0.37/0.58 (define @t77 () (forall @t4 @t76)) % 0.37/0.58 (define @t78 () (not @t77)) % 0.37/0.58 (define @t79 () (tptp.sorti2 @t75)) % 0.37/0.58 (define @t80 () (not @t79)) % 0.37/0.58 (define @t81 () (or @t80 @t78)) % 0.37/0.58 (define @t82 () (forall @t4 (or @t64 (= @t14 @t75)))) % 0.37/0.58 (define @t83 () (not @t82)) % 0.37/0.58 (define @t84 () (or @t80 @t83)) % 0.37/0.58 (define @t85 () (@list false)) % 0.37/0.58 (define @t86 () (= @t20 @t21)) % 0.37/0.58 (define @t87 () (= @t26 @t27)) % 0.37/0.58 (define @t88 () (@var "BOUND_VARIABLE_7619" $$unsorted)) % 0.37/0.58 (define @t89 () (= (tptp.j (tptp.op2 @t33 @t88)) (tptp.op1 @t34 (tptp.j @t88)))) % 0.37/0.58 (define @t90 () (not (tptp.sorti2 @t88))) % 0.37/0.58 (define @t91 () (not @t39)) % 0.37/0.58 (define @t92 () (or @t90 @t89)) % 0.37/0.58 (define @t93 () (or @t91 @t92)) % 0.37/0.58 (define @t94 () (forall (@list @t33 @t88) @t93)) % 0.37/0.58 (define @t95 () (@list @t88)) % 0.37/0.58 (define @t96 () (forall @t95 @t93)) % 0.37/0.58 (define @t97 () (forall @t95 @t92)) % 0.37/0.58 (define @t98 () (or @t91 @t97)) % 0.37/0.58 (define @t99 () (forall @t37 (or (not @t36) @t35))) % 0.37/0.58 (define @t100 () (@var "BOUND_VARIABLE_7596" $$unsorted)) % 0.37/0.58 (define @t101 () (= (tptp.h (tptp.op1 @t44 @t100)) (tptp.op2 @t45 (tptp.h @t100)))) % 0.37/0.58 (define @t102 () (not (tptp.sorti1 @t100))) % 0.37/0.58 (define @t103 () (not @t50)) % 0.37/0.58 (define @t104 () (or @t102 @t101)) % 0.37/0.58 (define @t105 () (or @t103 @t104)) % 0.37/0.58 (define @t106 () (forall (@list @t44 @t100) @t105)) % 0.37/0.58 (define @t107 () (@list @t100)) % 0.37/0.58 (define @t108 () (forall @t107 @t105)) % 0.37/0.58 (define @t109 () (forall @t107 @t104)) % 0.37/0.58 (define @t110 () (or @t103 @t109)) % 0.37/0.58 (define @t111 () (forall @t48 (or (not @t47) @t46))) % 0.37/0.58 (define @t112 () (and @t5 @t72)) % 0.37/0.58 (define @t113 () (forall @t6 (not @t112))) % 0.37/0.58 (define @t114 () (not @t113)) % 0.37/0.58 (define @t115 () (forall @t4 (or @t71 (= @t9 @t74)))) % 0.37/0.58 (define @t116 () (not @t115)) % 0.37/0.58 (define @t117 () (tptp.sorti1 @t74)) % 0.37/0.58 (define @t118 () (not @t117)) % 0.37/0.58 (define @t119 () (or @t118 @t116)) % 0.37/0.58 (define @t120 () (not @t119)) % 0.37/0.58 (define @t121 () (not @t73)) % 0.37/0.58 (define @t122 () (or @t71 (= @t74 @t9))) % 0.37/0.58 (define @t123 () (forall @t4 @t122)) % 0.37/0.58 (define @t124 () (not @t123)) % 0.37/0.58 (define @t125 () (or @t118 @t124)) % 0.37/0.58 (define @t126 () (not @t125)) % 0.37/0.58 (define @t127 () (@list true)) % 0.37/0.58 (define @t128 () (@list @t119)) % 0.37/0.58 (define @t129 () (or @t118 @t79)) % 0.37/0.58 (define @t130 () (@list false false)) % 0.37/0.58 (define @t131 () (@quantifiers_skolemize @t82 0)) % 0.37/0.58 (define @t132 () (tptp.op2 @t131 @t131)) % 0.37/0.58 (define @t133 () (= @t75 @t132)) % 0.37/0.58 (define @t134 () (tptp.sorti2 @t131)) % 0.37/0.58 (define @t135 () (not @t134)) % 0.37/0.58 (define @t136 () (or @t135 @t133)) % 0.37/0.58 (define @t137 () (not @t136)) % 0.37/0.58 (define @t138 () (or @t135 (= @t132 @t75))) % 0.37/0.58 (define @t139 () (not @t138)) % 0.37/0.58 (define @t140 () (@list @t136)) % 0.37/0.58 (define @t141 () (tptp.j @t131)) % 0.37/0.58 (define @t142 () (tptp.op1 @t141 @t141)) % 0.37/0.58 (define @t143 () (tptp.j @t132)) % 0.37/0.58 (define @t144 () (= @t143 @t142)) % 0.37/0.58 (define @t145 () (or @t135 @t135 @t144)) % 0.37/0.58 (define @t146 () (@list @t131)) % 0.37/0.58 (define @t147 () (tptp.h @t141)) % 0.37/0.58 (define @t148 () (= @t131 @t147)) % 0.37/0.58 (define @t149 () (or @t135 @t148)) % 0.37/0.58 (define @t150 () (tptp.sorti1 @t141)) % 0.37/0.58 (define @t151 () (or @t135 @t150)) % 0.37/0.58 (define @t152 () (tptp.op2 @t147 @t147)) % 0.37/0.58 (define @t153 () (= (tptp.h @t142) @t152)) % 0.37/0.58 (define @t154 () (not @t150)) % 0.37/0.58 (define @t155 () (or @t154 @t154 @t153)) % 0.37/0.58 (define @t156 () (or @t154 (= @t142 @t74))) % 0.37/0.58 (define @t157 () (= @t74 @t142)) % 0.37/0.58 (define @t158 () (or @t154 @t157)) % 0.37/0.58 (define @t159 () (and @t144 @t148 @t153 @t157)) % 0.37/0.58 (assume @p1 (forall @t6 (=> @t5 (forall @t4 (=> @t3 (tptp.sorti1 (tptp.op1 @t2 @t1))))))) % 0.37/0.58 (assume @p2 (forall @t6 (=> @t8 (forall @t4 (=> @t7 (tptp.sorti2 (tptp.op2 @t2 @t1))))))) % 0.37/0.58 (assume @p3 @t13) % 0.37/0.58 (assume @p4 @t19) % 0.37/0.58 (assume @p5 @t62) % 0.37/0.58 (assume @p6 true) % 0.37/0.58 (step @p7 :rule bool-double-not-elim :args (@t66)) % 0.37/0.58 (step @p8 :rule bool-and-de-morgan :args (@t8 @t65 true)) % 0.37/0.58 (step @p9 :rule cong :premises (@p8) :args (@t68)) % 0.37/0.58 (step @p10 :rule cong :premises (@p9) :args (@t69)) % 0.37/0.58 (step @p11 :rule exists-elim :args ((= (exists @t6 @t67) @t69))) % 0.37/0.58 (step @p12 :rule trans :premises (@p11 @p10)) % 0.37/0.58 (step @p13 :rule bool-impl-elim :args (@t7 @t63)) % 0.37/0.58 (step @p14 :rule cong :premises (@p13) :args ((forall @t4 (=> @t7 @t63)))) % 0.37/0.58 (step @p15 :rule eq-symm :args (@t14 @t2)) % 0.37/0.58 (step @p16 :rule refl :args (@t7)) % 0.37/0.58 (step @p17 :rule cong :premises (@p16 @p15) :args (@t15)) % 0.37/0.58 (step @p18 :rule cong :premises (@p17) :args (@t16)) % 0.37/0.58 (step @p19 :rule trans :premises (@p18 @p14)) % 0.37/0.58 (step @p20 :rule refl :args (@t8)) % 0.37/0.58 (step @p21 :rule nary_cong :premises (@p20 @p19) :args (@t17)) % 0.37/0.58 (step @p22 :rule cong :premises (@p21) :args (@t18)) % 0.37/0.58 (step @p23 :rule trans :premises (@p22 @p12)) % 0.37/0.58 (step @p24 :rule cong :premises (@p23) :args (@t19)) % 0.37/0.58 (step @p25 :rule trans :premises (@p24 @p7)) % 0.37/0.58 (step @p26 :rule eq_resolve :premises (@p4 @p25)) % 0.37/0.58 (step @p27 :rule eq-symm :args (@t75 @t14)) % 0.37/0.58 (step @p28 :rule refl :args (@t64)) % 0.37/0.58 (step @p29 :rule nary_cong :premises (@p28 @p27) :args (@t76)) % 0.37/0.58 (step @p30 :rule cong :premises (@p29) :args (@t77)) % 0.37/0.58 (step @p31 :rule cong :premises (@p30) :args (@t78)) % 0.37/0.58 (step @p32 :rule refl :args (@t80)) % 0.37/0.58 (step @p33 :rule nary_cong :premises (@p32 @p31) :args (@t81)) % 0.37/0.58 (step @p34 :rule refl :args (@t66)) % 0.37/0.58 (step @p35 :rule cong :premises (@p34 @p33) :args ((=> @t66 @t81))) % 0.37/0.58 (assume-push @p255 @t66) % 0.37/0.58 (step @p37 :rule instantiate :premises (@p26) :args ((@list @t75))) % 0.37/0.58 (step-pop @p256 :rule scope :premises (@p37)) % 0.37/0.58 (step @p38 :rule process_scope :premises (@p256) :args (@t81)) % 0.37/0.58 (step @p40 :rule eq_resolve :premises (@p38 @p35)) % 0.37/0.58 (step @p41 :rule implies_elim :premises (@p40)) % 0.37/0.58 (step @p42 :rule chain_m_resolution :premises (@p41 @p26) :args (@t84 @t85 (@list @t66))) % 0.37/0.58 (step @p43 :rule bool-impl-elim :args (@t22 @t86)) % 0.37/0.58 (step @p44 :rule cong :premises (@p43) :args ((forall @t24 (=> @t22 @t86)))) % 0.37/0.58 (step @p45 :rule eq-symm :args (@t21 @t20)) % 0.37/0.58 (step @p46 :rule refl :args (@t22)) % 0.37/0.58 (step @p47 :rule cong :premises (@p46 @p45) :args (@t23)) % 0.37/0.58 (step @p48 :rule cong :premises (@p47) :args (@t25)) % 0.37/0.58 (step @p49 :rule trans :premises (@p48 @p44)) % 0.37/0.58 (step @p50 :rule bool-impl-elim :args (@t28 @t87)) % 0.37/0.58 (step @p51 :rule cong :premises (@p50) :args ((forall @t30 (=> @t28 @t87)))) % 0.37/0.58 (step @p52 :rule eq-symm :args (@t27 @t26)) % 0.37/0.58 (step @p53 :rule refl :args (@t28)) % 0.37/0.58 (step @p54 :rule cong :premises (@p53 @p52) :args (@t29)) % 0.37/0.58 (step @p55 :rule cong :premises (@p54) :args (@t31)) % 0.37/0.58 (step @p56 :rule trans :premises (@p55 @p51)) % 0.37/0.58 (step @p57 :rule aci_norm :args ((= @t93 (or @t91 @t90 @t89)))) % 0.37/0.58 (step @p58 :rule cong :premises (@p57) :args (@t94)) % 0.37/0.58 (step @p59 :rule quant-merge-prenex :args ((= (forall @t41 @t96) @t94))) % 0.37/0.58 (step @p60 :rule alpha_equiv :args (@t97 (@list @t88) (@list @t32))) % 0.37/0.58 (step @p61 :rule refl :args (@t91)) % 0.37/0.58 (step @p62 :rule nary_cong :premises (@p61 @p60) :args (@t98)) % 0.37/0.58 (step @p63 :rule quant-miniscope-or :args ((= @t96 @t98))) % 0.37/0.58 (step @p64 :rule trans :premises (@p63 @p62)) % 0.37/0.58 (step @p65 :rule symm :premises (@p64)) % 0.37/0.58 (step @p66 :rule cong :premises (@p65) :args ((forall @t41 (or @t91 @t99)))) % 0.37/0.58 (step @p67 :rule trans :premises (@p66 @p59)) % 0.37/0.58 (step @p68 :rule trans :premises (@p67 @p58)) % 0.37/0.58 (step @p69 :rule bool-impl-elim :args (@t39 @t99)) % 0.37/0.58 (step @p70 :rule cong :premises (@p69) :args ((forall @t41 (=> @t39 @t99)))) % 0.37/0.58 (step @p71 :rule trans :premises (@p70 @p68)) % 0.37/0.58 (step @p72 :rule bool-impl-elim :args (@t36 @t35)) % 0.37/0.58 (step @p73 :rule cong :premises (@p72) :args (@t38)) % 0.37/0.58 (step @p74 :rule refl :args (@t39)) % 0.37/0.58 (step @p75 :rule cong :premises (@p74 @p73) :args (@t40)) % 0.37/0.58 (step @p76 :rule cong :premises (@p75) :args (@t42)) % 0.37/0.58 (step @p77 :rule trans :premises (@p76 @p71)) % 0.37/0.58 (step @p78 :rule aci_norm :args ((= @t105 (or @t103 @t102 @t101)))) % 0.37/0.58 (step @p79 :rule cong :premises (@p78) :args (@t106)) % 0.37/0.58 (step @p80 :rule quant-merge-prenex :args ((= (forall @t52 @t108) @t106))) % 0.37/0.58 (step @p81 :rule alpha_equiv :args (@t109 (@list @t100) (@list @t43))) % 0.37/0.58 (step @p82 :rule refl :args (@t103)) % 0.37/0.58 (step @p83 :rule nary_cong :premises (@p82 @p81) :args (@t110)) % 0.37/0.58 (step @p84 :rule quant-miniscope-or :args ((= @t108 @t110))) % 0.37/0.58 (step @p85 :rule trans :premises (@p84 @p83)) % 0.37/0.58 (step @p86 :rule symm :premises (@p85)) % 0.37/0.58 (step @p87 :rule cong :premises (@p86) :args ((forall @t52 (or @t103 @t111)))) % 0.37/0.58 (step @p88 :rule trans :premises (@p87 @p80)) % 0.37/0.58 (step @p89 :rule trans :premises (@p88 @p79)) % 0.37/0.58 (step @p90 :rule bool-impl-elim :args (@t50 @t111)) % 0.37/0.58 (step @p91 :rule cong :premises (@p90) :args ((forall @t52 (=> @t50 @t111)))) % 0.37/0.58 (step @p92 :rule trans :premises (@p91 @p89)) % 0.37/0.58 (step @p93 :rule bool-impl-elim :args (@t47 @t46)) % 0.37/0.58 (step @p94 :rule cong :premises (@p93) :args (@t49)) % 0.37/0.58 (step @p95 :rule refl :args (@t50)) % 0.37/0.58 (step @p96 :rule cong :premises (@p95 @p94) :args (@t51)) % 0.37/0.58 (step @p97 :rule cong :premises (@p96) :args (@t53)) % 0.37/0.58 (step @p98 :rule trans :premises (@p97 @p92)) % 0.37/0.58 (step @p99 :rule nary_cong :premises (@p98 @p77 @p56 @p49) :args (@t54)) % 0.37/0.58 (step @p100 :rule cong :premises (@p99) :args (@t55)) % 0.37/0.58 (step @p101 :rule bool-impl-elim :args (@t7 @t56)) % 0.37/0.58 (step @p102 :rule cong :premises (@p101) :args (@t57)) % 0.37/0.58 (step @p103 :rule bool-impl-elim :args (@t5 @t58)) % 0.37/0.58 (step @p104 :rule cong :premises (@p103) :args (@t59)) % 0.37/0.58 (step @p105 :rule nary_cong :premises (@p104 @p102) :args (@t60)) % 0.37/0.58 (step @p106 :rule cong :premises (@p105 @p100) :args (@t61)) % 0.37/0.58 (step @p107 :rule cong :premises (@p106) :args (@t62)) % 0.37/0.58 (step @p108 :rule eq_resolve :premises (@p5 @p107)) % 0.37/0.58 (step @p109 :rule not_implies_elim1 :premises (@p108)) % 0.37/0.58 (step @p110 :rule and_elim :premises (@p109) :args (0)) % 0.37/0.58 (step @p111 :rule instantiate :premises (@p110) :args ((@list @t74))) % 0.37/0.58 (step @p112 :rule bool-and-de-morgan :args (@t5 @t72 true)) % 0.37/0.58 (step @p113 :rule cong :premises (@p112) :args (@t113)) % 0.37/0.58 (step @p114 :rule cong :premises (@p113) :args (@t114)) % 0.37/0.58 (step @p115 :rule exists-elim :args ((= (exists @t6 @t112) @t114))) % 0.37/0.58 (step @p116 :rule trans :premises (@p115 @p114)) % 0.37/0.58 (step @p117 :rule bool-impl-elim :args (@t3 @t70)) % 0.37/0.58 (step @p118 :rule cong :premises (@p117) :args ((forall @t4 (=> @t3 @t70)))) % 0.37/0.58 (step @p119 :rule eq-symm :args (@t9 @t2)) % 0.37/0.58 (step @p120 :rule refl :args (@t3)) % 0.37/0.58 (step @p121 :rule cong :premises 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0.37/0.58 (step @p152 :rule nary_cong :premises (@p151 @p150) :args ((or @t119 (not @t118)))) % 0.37/0.58 (step @p153 :rule cnf_or_neg :args (@t119 0)) % 0.37/0.58 (step @p154 :rule eq_resolve :premises (@p153 @p152)) % 0.37/0.58 (step @p155 :rule reordering :premises (@p154) :args ((or @t117 @t119))) % 0.37/0.58 (step @p156 :rule chain_m_resolution :premises (@p155 @p149) :args (@t117 @t127 @t128)) % 0.37/0.58 (step @p157 :rule cnf_or_pos :args (@t129)) % 0.37/0.58 (step @p158 :rule reordering :premises (@p157) :args ((or @t118 @t79 (not @t129)))) % 0.37/0.58 (step @p159 :rule chain_m_resolution :premises (@p158 @p156 @p111) :args (@t79 @t130 (@list @t117 @t129))) % 0.37/0.58 (step @p160 :rule cnf_or_pos :args (@t84)) % 0.37/0.58 (step @p161 :rule reordering :premises (@p160) :args ((or @t80 @t83 (not @t84)))) % 0.37/0.58 (step @p162 :rule chain_m_resolution :premises (@p161 @p159 @p42) :args (@t83 @t130 (@list @t79 @t84))) % 0.37/0.58 (step @p163 :rule refl :args (@t137)) % 0.37/0.58 (step @p164 :rule bool-double-not-elim :args (@t82)) % 0.37/0.58 (step @p165 :rule nary_cong :premises (@p164 @p163) :args ((or (not @t83) @t137))) % 0.37/0.58 (step @p166 :rule eq-symm :args (@t132 @t75)) % 0.37/0.58 (step @p167 :rule refl :args (@t135)) % 0.37/0.58 (step @p168 :rule nary_cong :premises (@p167 @p166) :args (@t138)) % 0.37/0.58 (step @p169 :rule cong :premises (@p168) :args (@t139)) % 0.37/0.58 (step @p170 :rule refl :args (@t83)) % 0.37/0.58 (step @p171 :rule cong :premises (@p170 @p169) :args ((=> @t83 @t139))) % 0.37/0.58 (assume-push @p259 @t83) % 0.37/0.58 (step @p173 :rule skolemize :premises (@p162)) % 0.37/0.58 (step-pop @p260 :rule scope :premises (@p173)) % 0.37/0.58 (step @p174 :rule process_scope :premises (@p260) :args (@t139)) % 0.37/0.58 (step @p176 :rule eq_resolve :premises (@p174 @p171)) % 0.37/0.58 (step @p177 :rule implies_elim :premises (@p176)) % 0.37/0.58 (step @p178 :rule eq_resolve :premises (@p177 @p165)) % 0.37/0.58 (step @p179 :rule chain_m_resolution :premises (@p178 @p162) :args (@t137 @t127 (@list @t82))) % 0.37/0.58 (step @p180 :rule cnf_or_neg :args (@t136 1)) % 0.37/0.58 (step @p181 :rule chain_m_resolution :premises (@p180 @p179) :args ((not @t133) @t127 @t140)) % 0.37/0.58 (step @p182 :rule not_implies_elim2 :premises (@p108)) % 0.37/0.58 (step @p183 :rule not_not_elim :premises (@p182)) % 0.37/0.58 (step @p184 :rule and_elim :premises (@p183) :args (1)) % 0.37/0.58 (step @p185 :rule instantiate :premises (@p184) :args ((@list @t131 @t131))) % 0.37/0.58 (step @p186 :rule bool-double-not-elim :args (@t134)) % 0.37/0.58 (step @p187 :rule refl :args (@t136)) % 0.37/0.58 (step @p188 :rule nary_cong :premises (@p187 @p186) :args ((or @t136 (not @t135)))) % 0.37/0.58 (step @p189 :rule cnf_or_neg :args (@t136 0)) % 0.37/0.58 (step @p190 :rule eq_resolve :premises (@p189 @p188)) % 0.37/0.58 (step @p191 :rule reordering :premises (@p190) :args ((or @t134 @t136))) % 0.37/0.58 (step @p192 :rule chain_m_resolution 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:premises (@p109) :args (1)) % 0.37/0.58 (step @p205 :rule instantiate :premises (@p204) :args (@t146)) % 0.37/0.58 (step @p206 :rule cnf_or_pos :args (@t151)) % 0.37/0.58 (step @p207 :rule reordering :premises (@p206) :args ((or @t135 @t150 (not @t151)))) % 0.37/0.58 (step @p208 :rule chain_m_resolution :premises (@p207 @p192 @p205) :args (@t150 @t130 (@list @t134 @t151))) % 0.37/0.58 (step @p209 :rule cnf_or_pos :args (@t155)) % 0.37/0.58 (step @p210 :rule factoring :premises (@p209)) % 0.37/0.58 (step @p211 :rule reordering :premises (@p210) :args ((or @t154 @t153 (not @t155)))) % 0.37/0.58 (step @p212 :rule chain_m_resolution :premises (@p211 @p208 @p203) :args (@t153 @t130 (@list @t150 @t155))) % 0.37/0.58 (step @p213 :rule bool-double-not-elim :args (@t115)) % 0.37/0.58 (step @p214 :rule nary_cong :premises (@p151 @p213) :args ((or @t119 (not @t116)))) % 0.37/0.58 (step @p215 :rule cnf_or_neg :args (@t119 1)) % 0.37/0.58 (step @p216 :rule eq_resolve :premises (@p215 @p214)) % 0.37/0.58 (step @p217 :rule reordering :premises (@p216) :args ((or @t115 @t119))) % 0.37/0.58 (step @p218 :rule chain_m_resolution :premises (@p217 @p149) :args (@t115 @t127 @t128)) % 0.37/0.58 (step @p219 :rule eq-symm :args (@t142 @t74)) % 0.37/0.58 (step @p220 :rule refl :args (@t154)) % 0.37/0.58 (step @p221 :rule nary_cong :premises (@p220 @p219) :args (@t156)) % 0.37/0.58 (step @p222 :rule refl :args (@t115)) % 0.37/0.58 (step @p223 :rule cong :premises (@p222 @p221) :args ((=> @t115 @t156))) % 0.37/0.58 (assume-push @p261 @t115) % 0.37/0.58 (step @p225 :rule instantiate :premises (@p218) :args ((@list @t141))) % 0.37/0.58 (step-pop @p262 :rule scope :premises (@p225)) % 0.37/0.58 (step @p226 :rule process_scope :premises (@p262) :args (@t156)) % 0.37/0.58 (step @p228 :rule eq_resolve :premises (@p226 @p223)) % 0.37/0.58 (step @p229 :rule implies_elim :premises (@p228)) % 0.37/0.58 (step @p230 :rule chain_m_resolution :premises (@p229 @p218) :args (@t158 @t85 (@list @t115))) % 0.37/0.58 (step @p231 :rule cnf_or_pos :args (@t158)) % 0.37/0.58 (step @p232 :rule reordering :premises (@p231) :args ((or @t154 @t157 (not @t158)))) % 0.37/0.58 (step @p233 :rule chain_m_resolution :premises (@p232 @p208 @p230) :args (@t157 @t130 (@list @t150 @t158))) % 0.37/0.58 (assume-push @p263 @t144) % 0.37/0.58 (assume-push @p264 @t148) % 0.37/0.58 (assume-push @p265 @t153) % 0.37/0.58 (assume-push @p266 @t157) % 0.37/0.58 (step @p238 :rule symm :premises (@p201)) % 0.37/0.58 (step @p239 :rule cong :premises (@p238 @p238) :args (@t152)) % 0.37/0.58 (step @p240 :rule cong :premises (@p196) :args ((tptp.h @t143))) % 0.37/0.58 (step @p241 :rule symm :premises (@p196)) % 0.37/0.58 (step @p242 :rule trans :premises (@p233 @p241)) % 0.37/0.58 (step @p243 :rule cong :premises (@p242) :args (@t75)) % 0.37/0.58 (step @p244 :rule trans :premises (@p243 @p240 @p212 @p239)) % 0.37/0.58 (step-pop @p267 :rule scope :premises (@p244)) % 0.37/0.58 (step-pop @p268 :rule scope :premises (@p267)) % 0.37/0.58 (step-pop @p269 :rule scope :premises (@p268)) % 0.37/0.58 (step-pop @p270 :rule scope :premises (@p269)) % 0.37/0.58 (step @p245 :rule process_scope :premises (@p270) :args (@t133)) % 0.37/0.58 (step @p250 :rule implies_elim :premises (@p245)) % 0.37/0.58 (step @p251 :rule cnf_and_neg :args (@t159)) % 0.37/0.58 (step @p252 :rule resolution :premises (@p251 @p250) :args (true @t159)) % 0.37/0.58 (step @p253 :rule reordering :premises (@p252) :args ((or @t133 (not @t144) (not @t148) (not @t153) (not @t157)))) % 0.37/0.58 (step @p254 false :rule chain_m_resolution :premises (@p253 @p233 @p212 @p201 @p196 @p181) :args (false (@list false false false false true) (@list @t157 @t153 @t148 @t144 @t133))) % 0.37/0.58 ) % 0.37/0.58 % SZS output end Proof % 0.37/0.58 % cvc5 exiting %------------------------------------------------------------------------------