%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : ALG203+1 : TPTP v9.2.1. Released v2.7.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n018.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:05:29 AM UTC 2026 % Result : Theorem 0.36s 0.61s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : ALG203+1 : TPTP v9.2.1. Released v2.7.0. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.19/0.35 % Computer : n018.cluster.edu % 0.19/0.35 % Model : x86_64 x86_64 % 0.19/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.19/0.35 % Memory : 8042.1875MB % 0.19/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.19/0.35 % CPULimit : 300 % 0.19/0.35 % WCLimit : 300 % 0.19/0.35 % DateTime : Wed Jun 3 01:41:05 EDT 2026 % 0.19/0.35 % CPUTime : % 0.29/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.36/0.61 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.36/0.61 % SZS status Theorem % 0.36/0.61 % SZS output start Proof % 0.36/0.61 ( % 0.36/0.61 (declare-sort $$unsorted 0) % 0.36/0.61 (declare-const tptp.j (-> $$unsorted $$unsorted)) % 0.36/0.61 (declare-const tptp.h (-> $$unsorted $$unsorted)) % 0.36/0.61 (declare-const tptp.sorti2 (-> $$unsorted Bool)) % 0.36/0.61 (declare-const tptp.op2 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.61 (declare-const tptp.sorti1 (-> $$unsorted Bool)) % 0.36/0.61 (declare-const tptp.op1 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.61 (define @t1 () (@var "V" $$unsorted)) % 0.36/0.61 (define @t2 () (@var "U" $$unsorted)) % 0.36/0.61 (define @t3 () (tptp.sorti1 @t1)) % 0.36/0.61 (define @t4 () (@list @t1)) % 0.36/0.61 (define @t5 () (tptp.sorti1 @t2)) % 0.36/0.61 (define @t6 () (@list @t2)) % 0.36/0.61 (define @t7 () (tptp.sorti2 @t1)) % 0.36/0.61 (define @t8 () (tptp.sorti2 @t2)) % 0.36/0.61 (define @t9 () (tptp.op1 @t1 @t1)) % 0.36/0.61 (define @t10 () (not (= @t9 @t1))) % 0.36/0.61 (define @t11 () (and @t3 @t10)) % 0.36/0.61 (define @t12 () (exists @t4 @t11)) % 0.36/0.61 (define @t13 () (tptp.op1 @t2 @t2)) % 0.36/0.61 (define @t14 () (and @t5 (= @t13 @t2))) % 0.36/0.61 (define @t15 () (exists @t6 @t14)) % 0.36/0.61 (define @t16 () (tptp.op2 @t1 @t1)) % 0.36/0.61 (define @t17 () (not (= @t16 @t1))) % 0.36/0.61 (define @t18 () (and @t7 @t17)) % 0.36/0.61 (define @t19 () (exists @t4 @t18)) % 0.36/0.61 (define @t20 () (tptp.op2 @t2 @t2)) % 0.36/0.61 (define @t21 () (and @t8 (= @t20 @t2))) % 0.36/0.61 (define @t22 () (exists @t6 @t21)) % 0.36/0.61 (define @t23 () (and @t22 @t19)) % 0.36/0.61 (define @t24 () (not @t23)) % 0.36/0.61 (define @t25 () (@var "X2" $$unsorted)) % 0.36/0.61 (define @t26 () (tptp.j (tptp.h @t25))) % 0.36/0.61 (define @t27 () (tptp.sorti1 @t25)) % 0.36/0.61 (define @t28 () (=> @t27 (= @t26 @t25))) % 0.36/0.61 (define @t29 () (@list @t25)) % 0.36/0.61 (define @t30 () (forall @t29 @t28)) % 0.36/0.61 (define @t31 () (@var "X1" $$unsorted)) % 0.36/0.61 (define @t32 () (tptp.h (tptp.j @t31))) % 0.36/0.61 (define @t33 () (tptp.sorti2 @t31)) % 0.36/0.61 (define @t34 () (=> @t33 (= @t32 @t31))) % 0.36/0.61 (define @t35 () (@list @t31)) % 0.36/0.61 (define @t36 () (forall @t35 @t34)) % 0.36/0.61 (define @t37 () (@var "Z" $$unsorted)) % 0.36/0.61 (define @t38 () (@var "Y" $$unsorted)) % 0.36/0.61 (define @t39 () (tptp.j @t38)) % 0.36/0.61 (define @t40 () (= (tptp.j (tptp.op2 @t38 @t37)) (tptp.op1 @t39 (tptp.j @t37)))) % 0.36/0.61 (define @t41 () (tptp.sorti2 @t37)) % 0.36/0.61 (define @t42 () (@list @t37)) % 0.36/0.61 (define @t43 () (forall @t42 (=> @t41 @t40))) % 0.36/0.61 (define @t44 () (tptp.sorti2 @t38)) % 0.36/0.61 (define @t45 () (=> @t44 @t43)) % 0.36/0.61 (define @t46 () (@list @t38)) % 0.36/0.61 (define @t47 () (forall @t46 @t45)) % 0.36/0.61 (define @t48 () (@var "X" $$unsorted)) % 0.36/0.61 (define @t49 () (@var "W" $$unsorted)) % 0.36/0.61 (define @t50 () (tptp.h @t49)) % 0.36/0.61 (define @t51 () (= (tptp.h (tptp.op1 @t49 @t48)) (tptp.op2 @t50 (tptp.h @t48)))) % 0.36/0.61 (define @t52 () (tptp.sorti1 @t48)) % 0.36/0.61 (define @t53 () (@list @t48)) % 0.36/0.61 (define @t54 () (forall @t53 (=> @t52 @t51))) % 0.36/0.61 (define @t55 () (tptp.sorti1 @t49)) % 0.36/0.61 (define @t56 () (=> @t55 @t54)) % 0.36/0.61 (define @t57 () (@list @t49)) % 0.36/0.61 (define @t58 () (forall @t57 @t56)) % 0.36/0.61 (define @t59 () (and @t58 @t47 @t36 @t30)) % 0.36/0.61 (define @t60 () (not @t59)) % 0.36/0.61 (define @t61 () (tptp.sorti1 (tptp.j @t1))) % 0.36/0.61 (define @t62 () (forall @t4 (=> @t7 @t61))) % 0.36/0.61 (define @t63 () (tptp.sorti2 (tptp.h @t2))) % 0.36/0.61 (define @t64 () (forall @t6 (=> @t5 @t63))) % 0.36/0.61 (define @t65 () (and @t64 @t62)) % 0.36/0.61 (define @t66 () (=> @t65 @t60)) % 0.36/0.61 (define @t67 () (not @t66)) % 0.36/0.61 (define @t68 () (= @t2 @t13)) % 0.36/0.61 (define @t69 () (and @t5 @t68)) % 0.36/0.61 (define @t70 () (forall @t6 (not @t69))) % 0.36/0.61 (define @t71 () (not @t70)) % 0.36/0.61 (define @t72 () (@quantifiers_skolemize (forall @t6 (or (not @t5) (not @t68))) 0)) % 0.36/0.61 (define @t73 () (tptp.op1 @t72 @t72)) % 0.36/0.61 (define @t74 () (= @t72 @t73)) % 0.36/0.61 (define @t75 () (not @t74)) % 0.36/0.61 (define @t76 () (tptp.sorti1 @t72)) % 0.36/0.61 (define @t77 () (not @t76)) % 0.36/0.61 (define @t78 () (or @t77 @t75)) % 0.36/0.61 (define @t79 () (@list true)) % 0.36/0.61 (define @t80 () (@list @t78)) % 0.36/0.61 (define @t81 () (= @t25 @t26)) % 0.36/0.61 (define @t82 () (= @t31 @t32)) % 0.36/0.61 (define @t83 () (@var "BOUND_VARIABLE_7641" $$unsorted)) % 0.36/0.61 (define @t84 () (= (tptp.j (tptp.op2 @t38 @t83)) (tptp.op1 @t39 (tptp.j @t83)))) % 0.36/0.61 (define @t85 () (not (tptp.sorti2 @t83))) % 0.36/0.61 (define @t86 () (not @t44)) % 0.36/0.61 (define @t87 () (or @t85 @t84)) % 0.36/0.61 (define @t88 () (or @t86 @t87)) % 0.36/0.61 (define @t89 () (forall (@list @t38 @t83) @t88)) % 0.36/0.61 (define @t90 () (@list @t83)) % 0.36/0.61 (define @t91 () (forall @t90 @t88)) % 0.36/0.61 (define @t92 () (forall @t90 @t87)) % 0.36/0.61 (define @t93 () (or @t86 @t92)) % 0.36/0.61 (define @t94 () (forall @t42 (or (not @t41) @t40))) % 0.36/0.61 (define @t95 () (@var "BOUND_VARIABLE_7618" $$unsorted)) % 0.36/0.61 (define @t96 () (= (tptp.h (tptp.op1 @t49 @t95)) (tptp.op2 @t50 (tptp.h @t95)))) % 0.36/0.61 (define @t97 () (not (tptp.sorti1 @t95))) % 0.36/0.61 (define @t98 () (not @t55)) % 0.36/0.61 (define @t99 () (or @t97 @t96)) % 0.36/0.61 (define @t100 () (or @t98 @t99)) % 0.36/0.61 (define @t101 () (forall (@list @t49 @t95) @t100)) % 0.36/0.61 (define @t102 () (@list @t95)) % 0.36/0.61 (define @t103 () (forall @t102 @t100)) % 0.36/0.61 (define @t104 () (forall @t102 @t99)) % 0.36/0.61 (define @t105 () (or @t98 @t104)) % 0.36/0.61 (define @t106 () (forall @t53 (or (not @t52) @t51))) % 0.36/0.61 (define @t107 () (tptp.h @t72)) % 0.36/0.61 (define @t108 () (tptp.op2 @t107 @t107)) % 0.36/0.61 (define @t109 () (= (tptp.h @t73) @t108)) % 0.36/0.61 (define @t110 () (or @t77 @t77 @t109)) % 0.36/0.61 (define @t111 () (@list false false)) % 0.36/0.61 (define @t112 () (@list @t76 @t110)) % 0.36/0.61 (define @t113 () (= @t1 @t9)) % 0.36/0.61 (define @t114 () (not @t3)) % 0.36/0.61 (define @t115 () (@quantifiers_skolemize (forall @t4 (or @t114 @t113)) 0)) % 0.36/0.61 (define @t116 () (tptp.h @t115)) % 0.36/0.61 (define @t117 () (@list @t115)) % 0.36/0.61 (define @t118 () (not @t113)) % 0.36/0.61 (define @t119 () (and @t3 @t118)) % 0.36/0.61 (define @t120 () (forall @t4 (not @t119))) % 0.36/0.61 (define @t121 () (not @t120)) % 0.36/0.61 (define @t122 () (tptp.sorti1 @t115)) % 0.36/0.61 (define @t123 () (tptp.op1 @t115 @t115)) % 0.36/0.61 (define @t124 () (= @t115 @t123)) % 0.36/0.61 (define @t125 () (not @t122)) % 0.36/0.61 (define @t126 () (or @t125 @t124)) % 0.36/0.61 (define @t127 () (@list @t126)) % 0.36/0.61 (define @t128 () (tptp.sorti2 @t116)) % 0.36/0.61 (define @t129 () (or @t125 @t128)) % 0.36/0.61 (define @t130 () (tptp.j @t116)) % 0.36/0.61 (define @t131 () (tptp.op1 @t130 @t130)) % 0.36/0.61 (define @t132 () (tptp.op2 @t116 @t116)) % 0.36/0.61 (define @t133 () (= (tptp.j @t132) @t131)) % 0.36/0.61 (define @t134 () (not @t128)) % 0.36/0.61 (define @t135 () (or @t134 @t134 @t133)) % 0.36/0.61 (define @t136 () (= @t115 @t130)) % 0.36/0.61 (define @t137 () (or @t125 @t136)) % 0.36/0.61 (define @t138 () (tptp.h @t123)) % 0.36/0.61 (define @t139 () (= @t138 @t132)) % 0.36/0.61 (define @t140 () (or @t125 @t125 @t139)) % 0.36/0.61 (define @t141 () (= @t116 @t132)) % 0.36/0.61 (define @t142 () (and @t139 @t136 @t133 @t141)) % 0.36/0.61 (define @t143 () (not @t141)) % 0.36/0.61 (define @t144 () (or @t134 @t141)) % 0.36/0.61 (define @t145 () (not @t144)) % 0.36/0.61 (define @t146 () (= @t1 @t16)) % 0.36/0.61 (define @t147 () (not @t7)) % 0.36/0.61 (define @t148 () (forall @t4 (or @t147 @t146))) % 0.36/0.61 (define @t149 () (not @t148)) % 0.36/0.61 (define @t150 () (= @t2 @t20)) % 0.36/0.61 (define @t151 () (forall @t6 (or (not @t8) (not @t150)))) % 0.36/0.61 (define @t152 () (not @t146)) % 0.36/0.61 (define @t153 () (and @t7 @t152)) % 0.36/0.61 (define @t154 () (forall @t4 (not @t153))) % 0.36/0.61 (define @t155 () (not @t154)) % 0.36/0.61 (define @t156 () (and @t8 @t150)) % 0.36/0.61 (define @t157 () (forall @t6 (not @t156))) % 0.36/0.61 (define @t158 () (not @t157)) % 0.36/0.61 (define @t159 () (= @t107 @t108)) % 0.36/0.61 (define @t160 () (not @t159)) % 0.36/0.61 (define @t161 () (tptp.sorti2 @t107)) % 0.36/0.61 (define @t162 () (not @t161)) % 0.36/0.61 (define @t163 () (or @t162 @t160)) % 0.36/0.61 (define @t164 () (or @t77 @t161)) % 0.36/0.61 (define @t165 () (not @t109)) % 0.36/0.61 (define @t166 () (and @t160 @t159)) % 0.36/0.61 (assume @p1 (forall @t6 (=> @t5 (forall @t4 (=> @t3 (tptp.sorti1 (tptp.op1 @t2 @t1))))))) % 0.36/0.61 (assume @p2 (forall @t6 (=> @t8 (forall @t4 (=> @t7 (tptp.sorti2 (tptp.op2 @t2 @t1))))))) % 0.36/0.61 (assume @p3 (and @t15 @t12)) % 0.36/0.61 (assume @p4 @t24) % 0.36/0.61 (assume @p5 @t67) % 0.36/0.61 (assume @p6 true) % 0.36/0.61 (step @p7 :rule bool-and-de-morgan :args (@t5 @t68 true)) % 0.36/0.61 (step @p8 :rule cong :premises (@p7) :args (@t70)) % 0.36/0.61 (step @p9 :rule cong :premises (@p8) :args (@t71)) % 0.36/0.61 (step @p10 :rule exists-elim :args ((= (exists @t6 @t69) @t71))) % 0.36/0.61 (step @p11 :rule trans :premises (@p10 @p9)) % 0.36/0.61 (step @p12 :rule eq-symm :args (@t13 @t2)) % 0.36/0.61 (step @p13 :rule refl :args (@t5)) % 0.36/0.61 (step @p14 :rule nary_cong :premises (@p13 @p12) :args (@t14)) % 0.36/0.61 (step @p15 :rule cong :premises (@p14) :args (@t15)) % 0.36/0.61 (step @p16 :rule trans :premises (@p15 @p11)) % 0.36/0.61 (step @p17 :rule and_elim :premises (@p3) :args (0)) % 0.36/0.61 (step @p18 :rule eq_resolve :premises (@p17 @p16)) % 0.36/0.61 (step @p19 :rule skolemize :premises (@p18)) % 0.36/0.61 (step @p20 :rule bool-double-not-elim :args (@t74)) % 0.36/0.61 (step @p21 :rule refl :args (@t78)) % 0.36/0.61 (step @p22 :rule nary_cong :premises (@p21 @p20) :args ((or @t78 (not @t75)))) % 0.36/0.61 (step @p23 :rule cnf_or_neg :args (@t78 1)) % 0.36/0.61 (step @p24 :rule eq_resolve :premises (@p23 @p22)) % 0.36/0.61 (step @p25 :rule reordering :premises (@p24) :args ((or @t74 @t78))) % 0.36/0.61 (step @p26 :rule chain_m_resolution :premises (@p25 @p19) :args (@t74 @t79 @t80)) % 0.36/0.61 (step @p27 :rule bool-impl-elim :args (@t27 @t81)) % 0.36/0.61 (step @p28 :rule cong :premises (@p27) :args ((forall @t29 (=> @t27 @t81)))) % 0.36/0.61 (step @p29 :rule eq-symm :args (@t26 @t25)) % 0.36/0.61 (step @p30 :rule refl :args (@t27)) % 0.36/0.61 (step @p31 :rule cong :premises (@p30 @p29) :args (@t28)) % 0.36/0.61 (step @p32 :rule cong :premises (@p31) :args (@t30)) % 0.36/0.61 (step @p33 :rule trans :premises (@p32 @p28)) % 0.36/0.61 (step @p34 :rule bool-impl-elim :args (@t33 @t82)) % 0.36/0.61 (step @p35 :rule cong :premises (@p34) :args ((forall @t35 (=> @t33 @t82)))) % 0.36/0.61 (step @p36 :rule eq-symm :args (@t32 @t31)) % 0.36/0.61 (step @p37 :rule refl :args (@t33)) % 0.36/0.61 (step @p38 :rule cong :premises (@p37 @p36) :args (@t34)) % 0.36/0.61 (step @p39 :rule cong :premises (@p38) :args (@t36)) % 0.36/0.61 (step @p40 :rule trans :premises (@p39 @p35)) % 0.36/0.61 (step @p41 :rule aci_norm :args ((= @t88 (or @t86 @t85 @t84)))) % 0.36/0.61 (step @p42 :rule cong :premises (@p41) :args (@t89)) % 0.36/0.61 (step @p43 :rule quant-merge-prenex :args ((= (forall @t46 @t91) @t89))) % 0.36/0.61 (step @p44 :rule alpha_equiv :args (@t92 (@list @t83) (@list @t37))) % 0.36/0.61 (step @p45 :rule refl :args (@t86)) % 0.36/0.61 (step @p46 :rule nary_cong :premises (@p45 @p44) :args (@t93)) % 0.36/0.61 (step @p47 :rule quant-miniscope-or :args ((= @t91 @t93))) % 0.36/0.61 (step @p48 :rule trans :premises (@p47 @p46)) % 0.36/0.61 (step @p49 :rule symm :premises (@p48)) % 0.36/0.61 (step @p50 :rule cong :premises (@p49) :args ((forall @t46 (or @t86 @t94)))) % 0.36/0.61 (step @p51 :rule trans :premises (@p50 @p43)) % 0.36/0.61 (step @p52 :rule trans :premises (@p51 @p42)) % 0.36/0.61 (step @p53 :rule bool-impl-elim :args (@t44 @t94)) % 0.36/0.61 (step @p54 :rule cong :premises (@p53) :args ((forall @t46 (=> @t44 @t94)))) % 0.36/0.61 (step @p55 :rule trans :premises (@p54 @p52)) % 0.36/0.61 (step @p56 :rule bool-impl-elim :args (@t41 @t40)) % 0.36/0.61 (step @p57 :rule cong :premises (@p56) :args (@t43)) % 0.36/0.61 (step @p58 :rule refl :args (@t44)) % 0.36/0.61 (step @p59 :rule cong :premises (@p58 @p57) :args (@t45)) % 0.36/0.61 (step @p60 :rule cong :premises (@p59) :args (@t47)) % 0.36/0.61 (step @p61 :rule trans :premises (@p60 @p55)) % 0.36/0.61 (step @p62 :rule aci_norm :args ((= @t100 (or @t98 @t97 @t96)))) % 0.36/0.61 (step @p63 :rule cong :premises (@p62) :args (@t101)) % 0.36/0.61 (step @p64 :rule quant-merge-prenex :args ((= (forall @t57 @t103) @t101))) % 0.36/0.61 (step @p65 :rule alpha_equiv :args (@t104 (@list @t95) (@list @t48))) % 0.36/0.61 (step @p66 :rule refl :args (@t98)) % 0.36/0.61 (step @p67 :rule nary_cong :premises (@p66 @p65) :args (@t105)) % 0.36/0.61 (step @p68 :rule quant-miniscope-or :args ((= @t103 @t105))) % 0.36/0.61 (step @p69 :rule trans :premises (@p68 @p67)) % 0.36/0.61 (step @p70 :rule symm :premises (@p69)) % 0.36/0.61 (step @p71 :rule cong :premises (@p70) :args ((forall @t57 (or @t98 @t106)))) % 0.36/0.61 (step @p72 :rule trans :premises (@p71 @p64)) % 0.36/0.61 (step @p73 :rule trans :premises (@p72 @p63)) % 0.36/0.61 (step @p74 :rule bool-impl-elim :args (@t55 @t106)) % 0.36/0.61 (step @p75 :rule cong :premises (@p74) :args ((forall @t57 (=> @t55 @t106)))) % 0.36/0.61 (step @p76 :rule trans :premises (@p75 @p73)) % 0.36/0.61 (step @p77 :rule bool-impl-elim :args (@t52 @t51)) % 0.36/0.61 (step @p78 :rule cong :premises (@p77) :args (@t54)) % 0.36/0.61 (step @p79 :rule refl :args (@t55)) % 0.36/0.61 (step @p80 :rule cong :premises (@p79 @p78) :args (@t56)) % 0.36/0.61 (step @p81 :rule cong :premises (@p80) :args (@t58)) % 0.36/0.61 (step @p82 :rule trans :premises (@p81 @p76)) % 0.36/0.61 (step @p83 :rule nary_cong :premises (@p82 @p61 @p40 @p33) :args (@t59)) % 0.36/0.61 (step @p84 :rule cong :premises (@p83) :args (@t60)) % 0.36/0.61 (step @p85 :rule bool-impl-elim :args (@t7 @t61)) % 0.36/0.61 (step @p86 :rule cong :premises (@p85) :args (@t62)) % 0.36/0.61 (step @p87 :rule bool-impl-elim :args (@t5 @t63)) % 0.36/0.61 (step @p88 :rule cong :premises (@p87) :args (@t64)) % 0.36/0.61 (step @p89 :rule nary_cong :premises (@p88 @p86) :args (@t65)) % 0.36/0.61 (step @p90 :rule cong :premises (@p89 @p84) :args (@t66)) % 0.36/0.61 (step @p91 :rule cong :premises (@p90) :args (@t67)) % 0.36/0.61 (step @p92 :rule eq_resolve :premises (@p5 @p91)) % 0.36/0.61 (step @p93 :rule not_implies_elim2 :premises (@p92)) % 0.36/0.61 (step @p94 :rule not_not_elim :premises (@p93)) % 0.36/0.61 (step @p95 :rule and_elim :premises (@p94) :args (0)) % 0.36/0.61 (step @p96 :rule instantiate :premises (@p95) :args ((@list @t72 @t72))) % 0.36/0.61 (step @p97 :rule bool-double-not-elim :args (@t76)) % 0.36/0.61 (step @p98 :rule nary_cong :premises (@p21 @p97) :args ((or @t78 (not @t77)))) % 0.36/0.61 (step @p99 :rule cnf_or_neg :args (@t78 0)) % 0.36/0.61 (step @p100 :rule eq_resolve :premises (@p99 @p98)) % 0.36/0.61 (step @p101 :rule reordering :premises (@p100) :args ((or @t76 @t78))) % 0.36/0.61 (step @p102 :rule chain_m_resolution :premises (@p101 @p19) :args (@t76 @t79 @t80)) % 0.36/0.61 (step @p103 :rule cnf_or_pos :args (@t110)) % 0.36/0.61 (step @p104 :rule factoring :premises (@p103)) % 0.36/0.61 (step @p105 :rule reordering :premises (@p104) :args ((or @t77 @t109 (not @t110)))) % 0.36/0.61 (step @p106 :rule chain_m_resolution :premises (@p105 @p102 @p96) :args (@t109 @t111 @t112)) % 0.36/0.61 (step @p107 :rule and_elim :premises (@p94) :args (1)) % 0.36/0.61 (step @p108 :rule instantiate :premises (@p107) :args ((@list @t116 @t116))) % 0.36/0.61 (step @p109 :rule not_implies_elim1 :premises (@p92)) % 0.36/0.61 (step @p110 :rule and_elim :premises (@p109) :args (0)) % 0.36/0.61 (step @p111 :rule instantiate :premises (@p110) :args (@t117)) % 0.36/0.61 (step @p112 :rule bool-double-not-elim :args (@t113)) % 0.36/0.61 (step @p113 :rule refl :args (@t114)) % 0.36/0.61 (step @p114 :rule nary_cong :premises (@p113 @p112) :args ((or @t114 (not @t118)))) % 0.36/0.61 (step @p115 :rule bool-and-de-morgan :args (@t3 @t118 true)) % 0.36/0.61 (step @p116 :rule trans :premises (@p115 @p114)) % 0.36/0.61 (step @p117 :rule cong :premises (@p116) :args (@t120)) % 0.36/0.61 (step @p118 :rule cong :premises (@p117) :args (@t121)) % 0.36/0.61 (step @p119 :rule exists-elim :args ((= (exists @t4 @t119) @t121))) % 0.36/0.61 (step @p120 :rule trans :premises (@p119 @p118)) % 0.36/0.61 (step @p121 :rule eq-symm :args (@t9 @t1)) % 0.36/0.61 (step @p122 :rule cong :premises (@p121) :args (@t10)) % 0.36/0.61 (step @p123 :rule refl :args (@t3)) % 0.36/0.61 (step @p124 :rule nary_cong :premises (@p123 @p122) :args (@t11)) % 0.36/0.61 (step @p125 :rule cong :premises (@p124) :args (@t12)) % 0.36/0.61 (step @p126 :rule trans :premises (@p125 @p120)) % 0.36/0.61 (step @p127 :rule and_elim :premises (@p3) :args (1)) % 0.36/0.61 (step @p128 :rule eq_resolve :premises (@p127 @p126)) % 0.36/0.61 (step @p129 :rule skolemize :premises (@p128)) % 0.36/0.61 (step @p130 :rule bool-double-not-elim :args (@t122)) % 0.36/0.61 (step @p131 :rule refl :args (@t126)) % 0.36/0.61 (step @p132 :rule nary_cong :premises (@p131 @p130) :args ((or @t126 (not @t125)))) % 0.36/0.61 (step @p133 :rule cnf_or_neg :args (@t126 0)) % 0.36/0.61 (step @p134 :rule eq_resolve :premises (@p133 @p132)) % 0.36/0.61 (step @p135 :rule reordering :premises (@p134) :args ((or @t122 @t126))) % 0.36/0.61 (step @p136 :rule chain_m_resolution :premises (@p135 @p129) :args (@t122 @t79 @t127)) % 0.36/0.61 (step @p137 :rule cnf_or_pos :args (@t129)) % 0.36/0.61 (step @p138 :rule reordering :premises (@p137) :args ((or @t125 @t128 (not @t129)))) % 0.36/0.61 (step @p139 :rule chain_m_resolution :premises (@p138 @p136 @p111) :args (@t128 @t111 (@list @t122 @t129))) % 0.36/0.61 (step @p140 :rule cnf_or_pos :args (@t135)) % 0.36/0.61 (step @p141 :rule factoring :premises (@p140)) % 0.36/0.61 (step @p142 :rule reordering :premises (@p141) :args ((or @t134 @t133 (not @t135)))) % 0.36/0.61 (step @p143 :rule chain_m_resolution :premises (@p142 @p139 @p108) :args (@t133 @t111 (@list @t128 @t135))) % 0.36/0.61 (step @p144 :rule and_elim :premises (@p94) :args (3)) % 0.36/0.61 (step @p145 :rule instantiate :premises (@p144) :args (@t117)) % 0.36/0.61 (step @p146 :rule cnf_or_pos :args (@t137)) % 0.36/0.61 (step @p147 :rule reordering :premises (@p146) :args ((or @t125 @t136 (not @t137)))) % 0.36/0.61 (step @p148 :rule chain_m_resolution :premises (@p147 @p136 @p145) :args (@t136 @t111 (@list @t122 @t137))) % 0.36/0.61 (step @p149 :rule instantiate :premises (@p95) :args ((@list @t115 @t115))) % 0.36/0.61 (step @p150 :rule cnf_or_pos :args (@t140)) % 0.36/0.61 (step @p151 :rule factoring :premises (@p150)) % 0.36/0.61 (step @p152 :rule reordering :premises (@p151) :args ((or @t125 @t139 (not @t140)))) % 0.36/0.61 (step @p153 :rule chain_m_resolution :premises (@p152 @p136 @p149) :args (@t139 @t111 (@list @t122 @t140))) % 0.36/0.61 (step @p154 :rule cnf_or_neg :args (@t126 1)) % 0.36/0.61 (step @p155 :rule chain_m_resolution :premises (@p154 @p129) :args ((not @t124) @t79 @t127)) % 0.36/0.61 (assume-push @p276 @t139) % 0.36/0.61 (assume-push @p277 @t136) % 0.36/0.61 (assume-push @p278 @t133) % 0.36/0.61 (assume-push @p279 @t141) % 0.36/0.61 (assume-push @p280 @t136) % 0.36/0.61 (assume-push @p281 @t133) % 0.36/0.61 (assume-push @p282 @t139) % 0.36/0.61 (assume-push @p283 @t141) % 0.36/0.61 (step @p164 :rule symm :premises (@p148)) % 0.36/0.61 (step @p165 :rule cong :premises (@p164 @p164) :args (@t131)) % 0.36/0.61 (step @p166 :rule cong :premises (@p153) :args ((tptp.j @t138))) % 0.36/0.61 (step @p167 :rule symm :premises (@p153)) % 0.36/0.61 (step @p168 :rule trans :premises (@p279 @p167)) % 0.36/0.61 (step @p169 :rule cong :premises (@p168) :args (@t130)) % 0.36/0.61 (step @p170 :rule trans :premises (@p148 @p169 @p166 @p143 @p165)) % 0.36/0.61 (step-pop @p284 :rule scope :premises (@p170)) % 0.36/0.61 (step-pop @p285 :rule scope :premises (@p284)) % 0.36/0.61 (step-pop @p286 :rule scope :premises (@p285)) % 0.36/0.61 (step-pop @p287 :rule scope :premises (@p286)) % 0.36/0.61 (step @p171 :rule process_scope :premises (@p287) :args (@t124)) % 0.36/0.61 (step @p176 :rule and_intro :premises (@p148 @p143 @p153 @p279)) % 0.36/0.61 (step @p177 :rule modus_ponens :premises (@p176 @p171)) % 0.36/0.61 (step-pop @p288 :rule scope :premises (@p177)) % 0.36/0.61 (step-pop @p289 :rule scope :premises (@p288)) % 0.36/0.61 (step-pop @p290 :rule scope :premises (@p289)) % 0.36/0.61 (step-pop @p291 :rule scope :premises (@p290)) % 0.36/0.61 (step @p178 :rule process_scope :premises (@p291) :args (@t124)) % 0.36/0.61 (step @p183 :rule implies_elim :premises (@p178)) % 0.36/0.61 (step @p184 :rule cnf_and_neg :args (@t142)) % 0.36/0.61 (step @p185 :rule resolution :premises (@p184 @p183) :args (true @t142)) % 0.36/0.61 (step @p186 :rule reordering :premises (@p185) :args ((or @t124 (not @t139) (not @t136) (not @t133) @t143))) % 0.36/0.61 (step @p187 :rule chain_m_resolution :premises (@p186 @p155 @p153 @p148 @p143) :args (@t143 (@list true false false false) (@list @t124 @t139 @t136 @t133))) % 0.36/0.61 (step @p188 :rule cnf_or_pos :args (@t144)) % 0.36/0.61 (step @p189 :rule reordering :premises (@p188) :args ((or @t134 @t141 @t145))) % 0.36/0.61 (step @p190 :rule chain_m_resolution :premises (@p189 @p139 @p187) :args (@t145 (@list false true) (@list @t128 @t141))) % 0.36/0.61 (assume-push @p292 @t148) % 0.36/0.61 (step @p192 :rule instantiate :premises (@p292) :args ((@list @t116))) % 0.36/0.61 (step-pop @p293 :rule scope :premises (@p192)) % 0.36/0.61 (step @p193 :rule process_scope :premises (@p293) :args (@t144)) % 0.36/0.61 (step @p195 :rule implies_elim :premises (@p193)) % 0.36/0.61 (step @p196 :rule chain_m_resolution :premises (@p195 @p190) :args (@t149 @t79 (@list @t144))) % 0.36/0.61 (step @p197 :rule bool-double-not-elim :args (@t148)) % 0.36/0.61 (step @p198 :rule bool-double-not-elim :args (@t151)) % 0.36/0.61 (step @p199 :rule nary_cong :premises (@p198 @p197) :args ((or (not (not @t151)) (not @t149)))) % 0.36/0.61 (step @p200 :rule bool-double-not-elim :args (@t146)) % 0.36/0.61 (step @p201 :rule refl :args (@t147)) % 0.36/0.61 (step @p202 :rule nary_cong :premises (@p201 @p200) :args ((or @t147 (not @t152)))) % 0.36/0.61 (step @p203 :rule bool-and-de-morgan :args (@t7 @t152 true)) % 0.36/0.61 (step @p204 :rule trans :premises (@p203 @p202)) % 0.36/0.61 (step @p205 :rule cong :premises (@p204) :args (@t154)) % 0.36/0.61 (step @p206 :rule cong :premises (@p205) :args (@t155)) % 0.36/0.61 (step @p207 :rule exists-elim :args ((= (exists @t4 @t153) @t155))) % 0.36/0.61 (step @p208 :rule trans :premises (@p207 @p206)) % 0.36/0.61 (step @p209 :rule eq-symm :args (@t16 @t1)) % 0.36/0.61 (step @p210 :rule cong :premises (@p209) :args (@t17)) % 0.36/0.61 (step @p211 :rule refl :args (@t7)) % 0.36/0.61 (step @p212 :rule nary_cong :premises (@p211 @p210) :args (@t18)) % 0.36/0.61 (step @p213 :rule cong :premises (@p212) :args (@t19)) % 0.36/0.61 (step @p214 :rule trans :premises (@p213 @p208)) % 0.36/0.61 (step @p215 :rule bool-and-de-morgan :args (@t8 @t150 true)) % 0.36/0.61 (step @p216 :rule cong :premises (@p215) :args (@t157)) % 0.36/0.61 (step @p217 :rule cong :premises (@p216) :args (@t158)) % 0.36/0.61 (step @p218 :rule exists-elim :args ((= (exists @t6 @t156) @t158))) % 0.36/0.61 (step @p219 :rule trans :premises (@p218 @p217)) % 0.36/0.61 (step @p220 :rule eq-symm :args (@t20 @t2)) % 0.36/0.61 (step @p221 :rule refl :args (@t8)) % 0.36/0.61 (step @p222 :rule nary_cong :premises (@p221 @p220) :args (@t21)) % 0.36/0.61 (step @p223 :rule cong :premises (@p222) :args (@t22)) % 0.36/0.61 (step @p224 :rule trans :premises (@p223 @p219)) % 0.36/0.61 (step @p225 :rule nary_cong :premises (@p224 @p214) :args (@t23)) % 0.36/0.61 (step @p226 :rule cong :premises (@p225) :args (@t24)) % 0.36/0.61 (step @p227 :rule eq_resolve :premises (@p4 @p226)) % 0.36/0.61 (step @p228 :rule not_and :premises (@p227)) % 0.36/0.61 (step @p229 :rule eq_resolve :premises (@p228 @p199)) % 0.36/0.61 (step @p230 :rule chain_m_resolution :premises (@p229 @p196) :args (@t151 @t79 (@list @t148))) % 0.36/0.61 (assume-push @p294 @t151) % 0.36/0.61 (step @p232 :rule instantiate :premises (@p294) :args ((@list @t107))) % 0.36/0.61 (step-pop @p295 :rule scope :premises (@p232)) % 0.36/0.61 (step @p233 :rule process_scope :premises (@p295) :args (@t163)) % 0.36/0.61 (step @p235 :rule implies_elim :premises (@p233)) % 0.36/0.61 (step @p236 :rule chain_m_resolution :premises (@p235 @p230) :args (@t163 (@list false) (@list @t151))) % 0.36/0.61 (step @p237 :rule instantiate :premises (@p110) :args ((@list @t72))) % 0.36/0.61 (step @p238 :rule cnf_or_pos :args (@t164)) % 0.36/0.61 (step @p239 :rule reordering :premises (@p238) :args ((or @t77 @t161 (not @t164)))) % 0.36/0.61 (step @p240 :rule chain_m_resolution :premises (@p239 @p102 @p237) :args (@t161 @t111 (@list @t76 @t164))) % 0.36/0.61 (step @p241 :rule cnf_or_pos :args (@t163)) % 0.36/0.61 (step @p242 :rule reordering :premises (@p241) :args ((or @t162 @t160 (not @t163)))) % 0.36/0.61 (step @p243 :rule chain_m_resolution :premises (@p242 @p240 @p236) :args (@t160 @t111 (@list @t161 @t163))) % 0.36/0.61 (step @p244 :rule bool-double-not-elim :args (@t159)) % 0.36/0.61 (step @p245 :rule refl :args (@t165)) % 0.36/0.61 (step @p246 :rule refl :args (@t75)) % 0.36/0.61 (step @p247 :rule nary_cong :premises (@p246 @p245 @p244) :args ((or @t75 @t165 (not @t160)))) % 0.36/0.61 (assume-push @p296 @t160) % 0.36/0.61 (assume-push @p297 @t159) % 0.36/0.61 (step @p250 :rule evaluate :args ((= true false))) % 0.36/0.61 (step @p251 :rule false_intro :premises (@p296)) % 0.36/0.61 (step @p252 :rule chain_m_resolution :premises (@p105 @p102 @p96) :args (@t109 @t111 @t112)) % 0.36/0.61 (step @p253 :rule cong :premises (@p26) :args (@t107)) % 0.36/0.61 (step @p254 :rule trans :premises (@p253 @p252)) % 0.36/0.61 (step @p255 :rule true_intro :premises (@p254)) % 0.36/0.61 (step @p256 :rule symm :premises (@p255)) % 0.36/0.61 (step @p257 :rule trans :premises (@p256 @p251)) % 0.36/0.61 (step @p258 false :rule eq_resolve :premises (@p257 @p250)) % 0.36/0.61 (step-pop @p298 :rule scope :premises (@p258)) % 0.36/0.61 (step-pop @p299 :rule scope :premises (@p298)) % 0.36/0.61 (step @p259 :rule process_scope :premises (@p299) :args (false)) % 0.36/0.61 (assume-push @p300 @t74) % 0.36/0.61 (assume-push @p301 @t109) % 0.36/0.61 (assume-push @p302 @t160) % 0.36/0.61 (step @p253 :rule cong :premises (@p26) :args (@t107)) % 0.36/0.61 (step @p265 :rule trans :premises (@p253 @p106)) % 0.36/0.61 (step @p266 :rule and_intro :premises (@p302 @p265)) % 0.36/0.61 (step-pop @p303 :rule scope :premises (@p266)) % 0.36/0.61 (step-pop @p304 :rule scope :premises (@p303)) % 0.36/0.61 (step-pop @p305 :rule scope :premises (@p304)) % 0.36/0.61 (step @p267 :rule process_scope :premises (@p305) :args (@t166)) % 0.36/0.61 (step @p271 :rule implies_elim :premises (@p267)) % 0.36/0.61 (step @p272 :rule resolution :premises (@p271 @p259) :args (true @t166)) % 0.36/0.61 (step @p273 :rule not_and :premises (@p272)) % 0.36/0.61 (step @p274 :rule eq_resolve :premises (@p273 @p247)) % 0.36/0.61 (step @p275 false :rule chain_m_resolution :premises (@p274 @p243 @p106 @p26) :args (false (@list true false false) (@list @t159 @t109 @t74))) % 0.36/0.61 ) % 0.36/0.61 % SZS output end Proof % 0.36/0.61 % cvc5 exiting %------------------------------------------------------------------------------