%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM459+2 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n029.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 08:39:29 AM UTC 2026 % Result : Theorem 0.71s 1.01s % Output : Proof 0.71s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM459+2 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n029.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 : Tue Jun 2 11:21:47 EDT 2026 % 0.16/0.34 % CPUTime : % 0.30/0.49 %----Proving TF0_NAR, FOF, or CNF % 0.71/1.01 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.71/1.01 % SZS status Theorem % 0.71/1.01 % SZS output start Proof % 0.71/1.01 ( % 0.71/1.01 (declare-sort $$unsorted 0) % 0.71/1.01 (declare-const tptp.xn $$unsorted) % 0.71/1.01 (declare-const tptp.sdtmndt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.71/1.01 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.71/1.01 (declare-const tptp.sdtlseqdt0 (-> $$unsorted $$unsorted Bool)) % 0.71/1.01 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.71/1.01 (declare-const tptp.xm $$unsorted) % 0.71/1.01 (declare-const tptp.sz10 $$unsorted) % 0.71/1.01 (declare-const tptp.sz00 $$unsorted) % 0.71/1.01 (declare-const tptp.aNaturalNumber0 (-> $$unsorted Bool)) % 0.71/1.01 (define @t1 () (@var "W0" $$unsorted)) % 0.71/1.01 (define @t2 () (tptp.aNaturalNumber0 @t1)) % 0.71/1.01 (define @t3 () (@list @t1)) % 0.71/1.01 (define @t4 () (tptp.aNaturalNumber0 tptp.sz00)) % 0.71/1.01 (define @t5 () (@var "W1" $$unsorted)) % 0.71/1.01 (define @t6 () (tptp.sdtpldt0 @t1 @t5)) % 0.71/1.01 (define @t7 () (tptp.aNaturalNumber0 @t6)) % 0.71/1.01 (define @t8 () (tptp.aNaturalNumber0 @t5)) % 0.71/1.01 (define @t9 () (and @t2 @t8)) % 0.71/1.01 (define @t10 () (@list @t1 @t5)) % 0.71/1.01 (define @t11 () (forall @t10 (=> @t9 @t7))) % 0.71/1.01 (define @t12 () (tptp.sdtasdt0 @t1 @t5)) % 0.71/1.01 (define @t13 () (tptp.sdtpldt0 @t5 @t1)) % 0.71/1.01 (define @t14 () (@var "W2" $$unsorted)) % 0.71/1.01 (define @t15 () (tptp.sdtpldt0 @t5 @t14)) % 0.71/1.01 (define @t16 () (= (tptp.sdtpldt0 @t6 @t14) (tptp.sdtpldt0 @t1 @t15))) % 0.71/1.01 (define @t17 () (tptp.aNaturalNumber0 @t14)) % 0.71/1.01 (define @t18 () (and @t2 @t8 @t17)) % 0.71/1.01 (define @t19 () (@list @t1 @t5 @t14)) % 0.71/1.01 (define @t20 () (forall @t19 (=> @t18 @t16))) % 0.71/1.01 (define @t21 () (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1))) % 0.71/1.01 (define @t22 () (tptp.sdtpldt0 @t1 tptp.sz00)) % 0.71/1.01 (define @t23 () (and (= @t22 @t1) @t21)) % 0.71/1.01 (define @t24 () (=> @t2 @t23)) % 0.71/1.01 (define @t25 () (forall @t3 @t24)) % 0.71/1.01 (define @t26 () (tptp.sdtasdt0 @t5 @t1)) % 0.71/1.01 (define @t27 () (tptp.sdtasdt0 @t14 @t1)) % 0.71/1.01 (define @t28 () (tptp.sdtasdt0 @t1 @t14)) % 0.71/1.01 (define @t29 () (= @t5 @t14)) % 0.71/1.01 (define @t30 () (= @t13 (tptp.sdtpldt0 @t14 @t1))) % 0.71/1.01 (define @t31 () (tptp.sdtpldt0 @t1 @t14)) % 0.71/1.01 (define @t32 () (= @t6 @t31)) % 0.71/1.01 (define @t33 () (or @t32 @t30)) % 0.71/1.01 (define @t34 () (=> @t33 @t29)) % 0.71/1.01 (define @t35 () (forall @t19 (=> @t18 @t34))) % 0.71/1.01 (define @t36 () (and @t8 @t17)) % 0.71/1.01 (define @t37 () (= @t1 tptp.sz00)) % 0.71/1.01 (define @t38 () (= @t5 tptp.sz00)) % 0.71/1.01 (define @t39 () (and @t37 @t38)) % 0.71/1.01 (define @t40 () (=> (= @t6 tptp.sz00) @t39)) % 0.71/1.01 (define @t41 () (=> @t9 @t40)) % 0.71/1.01 (define @t42 () (forall @t10 @t41)) % 0.71/1.01 (define @t43 () (and @t17 (= @t31 @t5))) % 0.71/1.01 (define @t44 () (@list @t14)) % 0.71/1.01 (define @t45 () (tptp.sdtlseqdt0 @t1 @t5)) % 0.71/1.01 (define @t46 () (tptp.aNaturalNumber0 tptp.xn)) % 0.71/1.01 (define @t47 () (tptp.aNaturalNumber0 tptp.xm)) % 0.71/1.01 (define @t48 () (= tptp.xm tptp.xn)) % 0.71/1.01 (define @t49 () (tptp.sdtlseqdt0 tptp.xn tptp.xm)) % 0.71/1.01 (define @t50 () (tptp.sdtpldt0 tptp.xn @t1)) % 0.71/1.01 (define @t51 () (and @t2 (= @t50 tptp.xm))) % 0.71/1.01 (define @t52 () (exists @t3 @t51)) % 0.71/1.01 (define @t53 () (tptp.sdtlseqdt0 tptp.xm tptp.xn)) % 0.71/1.01 (define @t54 () (tptp.sdtpldt0 tptp.xm @t1)) % 0.71/1.01 (define @t55 () (and @t2 (= @t54 tptp.xn))) % 0.71/1.01 (define @t56 () (exists @t3 @t55)) % 0.71/1.01 (define @t57 () (and @t56 @t53 @t52 @t49)) % 0.71/1.01 (define @t58 () (=> @t57 @t48)) % 0.71/1.01 (define @t59 () (not @t58)) % 0.71/1.01 (define @t60 () (= tptp.xm @t50)) % 0.71/1.01 (define @t61 () (and @t2 @t60)) % 0.71/1.01 (define @t62 () (forall @t3 (not @t61))) % 0.71/1.01 (define @t63 () (not @t62)) % 0.71/1.01 (define @t64 () (= tptp.xn @t54)) % 0.71/1.01 (define @t65 () (and @t2 @t64)) % 0.71/1.01 (define @t66 () (forall @t3 (not @t65))) % 0.71/1.01 (define @t67 () (not @t66)) % 0.71/1.01 (define @t68 () (not @t2)) % 0.71/1.01 (define @t69 () (@quantifiers_skolemize (forall @t3 (or @t68 (not @t64))) 0)) % 0.71/1.01 (define @t70 () (tptp.sdtpldt0 tptp.xm @t69)) % 0.71/1.01 (define @t71 () (= tptp.xn @t70)) % 0.71/1.01 (define @t72 () (not @t71)) % 0.71/1.01 (define @t73 () (tptp.aNaturalNumber0 @t69)) % 0.71/1.01 (define @t74 () (not @t73)) % 0.71/1.01 (define @t75 () (or @t74 @t72)) % 0.71/1.01 (define @t76 () (@list true)) % 0.71/1.01 (define @t77 () (@list @t75)) % 0.71/1.01 (define @t78 () (@quantifiers_skolemize (forall @t3 (or @t68 (not @t60))) 0)) % 0.71/1.01 (define @t79 () (tptp.sdtpldt0 tptp.xn @t78)) % 0.71/1.01 (define @t80 () (= tptp.xm @t79)) % 0.71/1.01 (define @t81 () (not @t80)) % 0.71/1.01 (define @t82 () (tptp.aNaturalNumber0 @t78)) % 0.71/1.01 (define @t83 () (not @t82)) % 0.71/1.01 (define @t84 () (or @t83 @t81)) % 0.71/1.01 (define @t85 () (@list @t84)) % 0.71/1.01 (define @t86 () (not @t17)) % 0.71/1.01 (define @t87 () (not @t8)) % 0.71/1.01 (define @t88 () (or @t68 @t87 @t86)) % 0.71/1.01 (define @t89 () (not @t18)) % 0.71/1.01 (define @t90 () (tptp.sdtpldt0 @t78 @t69)) % 0.71/1.01 (define @t91 () (tptp.sdtpldt0 tptp.xn @t90)) % 0.71/1.01 (define @t92 () (tptp.sdtpldt0 @t79 @t69)) % 0.71/1.01 (define @t93 () (= @t92 @t91)) % 0.71/1.01 (define @t94 () (not @t46)) % 0.71/1.01 (define @t95 () (or @t94 @t83 @t74 @t93)) % 0.71/1.01 (define @t96 () (@list false false false false)) % 0.71/1.01 (define @t97 () (@list @t46 @t73 @t82 @t95)) % 0.71/1.01 (define @t98 () (and (= @t1 @t22) @t21)) % 0.71/1.01 (define @t99 () (tptp.sdtpldt0 tptp.sz00 tptp.xn)) % 0.71/1.01 (define @t100 () (tptp.sdtpldt0 tptp.xn tptp.sz00)) % 0.71/1.01 (define @t101 () (= tptp.xn @t100)) % 0.71/1.01 (define @t102 () (and @t101 (= tptp.xn @t99))) % 0.71/1.01 (define @t103 () (or @t94 @t102)) % 0.71/1.01 (define @t104 () (@list false false)) % 0.71/1.01 (define @t105 () (@list false)) % 0.71/1.01 (define @t106 () (and (not @t32) (not @t30))) % 0.71/1.01 (define @t107 () (or @t68 @t87 @t86 @t106 @t29)) % 0.71/1.01 (define @t108 () (= tptp.sz00 @t90)) % 0.71/1.01 (define @t109 () (not (= @t99 (tptp.sdtpldt0 @t90 tptp.xn)))) % 0.71/1.01 (define @t110 () (not (= @t100 @t91))) % 0.71/1.01 (define @t111 () (and @t110 @t109)) % 0.71/1.01 (define @t112 () (tptp.aNaturalNumber0 @t90)) % 0.71/1.01 (define @t113 () (not @t112)) % 0.71/1.01 (define @t114 () (not @t4)) % 0.71/1.01 (define @t115 () (or @t94 @t114 @t113 @t111 @t108)) % 0.71/1.01 (define @t116 () (forall @t19 @t107)) % 0.71/1.01 (define @t117 () (= @t91 @t100)) % 0.71/1.01 (define @t118 () (not @t117)) % 0.71/1.01 (define @t119 () (and @t118 @t109)) % 0.71/1.01 (define @t120 () (or @t94 @t114 @t113 @t119 @t108)) % 0.71/1.01 (define @t121 () (and @t37 (= tptp.sz00 @t5))) % 0.71/1.01 (define @t122 () (= tptp.sz00 @t6)) % 0.71/1.01 (define @t123 () (not @t122)) % 0.71/1.01 (define @t124 () (or @t68 @t87 @t123 @t121)) % 0.71/1.01 (define @t125 () (or @t68 @t87)) % 0.71/1.01 (define @t126 () (=> @t122 @t121)) % 0.71/1.01 (define @t127 () (not @t9)) % 0.71/1.01 (define @t128 () (= tptp.sz00 @t69)) % 0.71/1.01 (define @t129 () (and (= @t78 tptp.sz00) @t128)) % 0.71/1.01 (define @t130 () (not @t108)) % 0.71/1.01 (define @t131 () (or @t83 @t74 @t130 @t129)) % 0.71/1.01 (define @t132 () (forall @t10 @t124)) % 0.71/1.01 (define @t133 () (@list @t78 @t69)) % 0.71/1.01 (define @t134 () (and (= tptp.sz00 @t78) @t128)) % 0.71/1.01 (define @t135 () (or @t83 @t74 @t130 @t134)) % 0.71/1.01 (define @t136 () (tptp.sdtpldt0 tptp.xm tptp.sz00)) % 0.71/1.01 (define @t137 () (= tptp.xm @t136)) % 0.71/1.01 (define @t138 () (and @t137 (= tptp.xm (tptp.sdtpldt0 tptp.sz00 tptp.xm)))) % 0.71/1.01 (define @t139 () (not @t47)) % 0.71/1.01 (define @t140 () (or @t139 @t138)) % 0.71/1.01 (define @t141 () (and @t71 @t80 @t137 @t128)) % 0.71/1.01 (define @t142 () (not @t128)) % 0.71/1.01 (define @t143 () (not @t134)) % 0.71/1.01 (define @t144 () (or @t83 @t74 @t112)) % 0.71/1.01 (define @t145 () (not @t101)) % 0.71/1.01 (define @t146 () (not @t93)) % 0.71/1.01 (define @t147 () (= tptp.xn @t91)) % 0.71/1.01 (define @t148 () (and @t118 @t147 @t101 @t71)) % 0.71/1.01 (assume @p1 (forall @t3 (=> @t2 true))) % 0.71/1.01 (assume @p2 @t4) % 0.71/1.01 (assume @p3 (and (tptp.aNaturalNumber0 tptp.sz10) (not (= tptp.sz10 tptp.sz00)))) % 0.71/1.01 (assume @p4 @t11) % 0.71/1.01 (assume @p5 (forall @t10 (=> @t9 (tptp.aNaturalNumber0 @t12)))) % 0.71/1.01 (assume @p6 (forall @t10 (=> @t9 (= @t6 @t13)))) % 0.71/1.01 (assume @p7 @t20) % 0.71/1.01 (assume @p8 @t25) % 0.71/1.01 (assume @p9 (forall @t10 (=> @t9 (= @t12 @t26)))) % 0.71/1.01 (assume @p10 (forall @t19 (=> @t18 (= (tptp.sdtasdt0 @t12 @t14) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t5 @t14)))))) % 0.71/1.01 (assume @p11 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 0.71/1.01 (assume @p12 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 0.71/1.01 (assume @p13 (forall @t19 (=> @t18 (and (= (tptp.sdtasdt0 @t1 @t15) (tptp.sdtpldt0 @t12 @t28)) (= (tptp.sdtasdt0 @t15 @t1) (tptp.sdtpldt0 @t26 @t27)))))) % 0.71/1.01 (assume @p14 @t35) % 0.71/1.01 (assume @p15 (forall @t3 (=> @t2 (=> (not @t37) (forall (@list @t5 @t14) (=> @t36 (=> (or (= @t12 @t28) (= @t26 @t27)) @t29))))))) % 0.71/1.01 (assume @p16 @t42) % 0.71/1.01 (assume @p17 (forall @t10 (=> @t9 (=> (= @t12 tptp.sz00) (or @t37 @t38))))) % 0.71/1.01 (assume @p18 (forall @t10 (=> @t9 (= @t45 (exists @t44 @t43))))) % 0.71/1.01 (assume @p19 (forall @t10 (=> @t9 (=> @t45 (forall @t44 (= (= @t14 (tptp.sdtmndt0 @t5 @t1)) @t43)))))) % 0.71/1.01 (assume @p20 (forall @t3 (=> @t2 (tptp.sdtlseqdt0 @t1 @t1)))) % 0.71/1.01 (assume @p21 (and @t47 @t46)) % 0.71/1.01 (assume @p22 @t59) % 0.71/1.01 (assume @p23 true) % 0.71/1.01 (step @p24 :rule refl :args (@t48)) % 0.71/1.01 (step @p25 :rule refl :args (@t49)) % 0.71/1.01 (step @p26 :rule bool-and-de-morgan :args (@t2 @t60 true)) % 0.71/1.01 (step @p27 :rule cong :premises (@p26) :args (@t62)) % 0.71/1.01 (step @p28 :rule cong :premises (@p27) :args (@t63)) % 0.71/1.01 (step @p29 :rule exists-elim :args ((= (exists @t3 @t61) @t63))) % 0.71/1.01 (step @p30 :rule trans :premises (@p29 @p28)) % 0.71/1.01 (step @p31 :rule eq-symm :args (@t50 tptp.xm)) % 0.71/1.01 (step @p32 :rule refl :args (@t2)) % 0.71/1.01 (step @p33 :rule nary_cong :premises (@p32 @p31) :args (@t51)) % 0.71/1.01 (step @p34 :rule cong :premises (@p33) :args (@t52)) % 0.71/1.01 (step @p35 :rule trans :premises (@p34 @p30)) % 0.71/1.01 (step @p36 :rule refl :args (@t53)) % 0.71/1.01 (step @p37 :rule bool-and-de-morgan :args (@t2 @t64 true)) % 0.71/1.01 (step @p38 :rule cong :premises (@p37) :args (@t66)) % 0.71/1.01 (step @p39 :rule cong :premises (@p38) :args (@t67)) % 0.71/1.01 (step @p40 :rule exists-elim :args ((= (exists @t3 @t65) @t67))) % 0.71/1.01 (step @p41 :rule trans :premises (@p40 @p39)) % 0.71/1.01 (step @p42 :rule eq-symm :args (@t54 tptp.xn)) % 0.71/1.01 (step @p43 :rule nary_cong :premises (@p32 @p42) :args (@t55)) % 0.71/1.01 (step @p44 :rule cong :premises (@p43) :args (@t56)) % 0.71/1.01 (step @p45 :rule trans :premises (@p44 @p41)) % 0.71/1.01 (step @p46 :rule nary_cong :premises (@p45 @p36 @p35 @p25) :args (@t57)) % 0.71/1.01 (step @p47 :rule cong :premises (@p46 @p24) :args (@t58)) % 0.71/1.01 (step @p48 :rule cong :premises (@p47) :args (@t59)) % 0.71/1.01 (step @p49 :rule eq_resolve :premises (@p22 @p48)) % 0.71/1.01 (step @p50 :rule not_implies_elim1 :premises (@p49)) % 0.71/1.01 (step @p51 :rule and_elim :premises (@p50) :args (0)) % 0.71/1.01 (step @p52 :rule skolemize :premises (@p51)) % 0.71/1.01 (step @p53 :rule bool-double-not-elim :args (@t71)) % 0.71/1.01 (step @p54 :rule refl :args (@t75)) % 0.71/1.01 (step @p55 :rule nary_cong :premises (@p54 @p53) :args ((or @t75 (not @t72)))) % 0.71/1.01 (step @p56 :rule cnf_or_neg :args (@t75 1)) % 0.71/1.01 (step @p57 :rule eq_resolve :premises (@p56 @p55)) % 0.71/1.01 (step @p58 :rule reordering :premises (@p57) :args ((or @t71 @t75))) % 0.71/1.01 (step @p59 :rule chain_m_resolution :premises (@p58 @p52) :args (@t71 @t76 @t77)) % 0.71/1.01 (step @p60 :rule and_elim :premises (@p50) :args (2)) % 0.71/1.01 (step @p61 :rule skolemize :premises (@p60)) % 0.71/1.01 (step @p62 :rule bool-double-not-elim :args (@t80)) % 0.71/1.01 (step @p63 :rule refl :args (@t84)) % 0.71/1.01 (step @p64 :rule nary_cong :premises (@p63 @p62) :args ((or @t84 (not @t81)))) % 0.71/1.01 (step @p65 :rule cnf_or_neg :args (@t84 1)) % 0.71/1.01 (step @p66 :rule eq_resolve :premises (@p65 @p64)) % 0.71/1.01 (step @p67 :rule reordering :premises (@p66) :args ((or @t80 @t84))) % 0.71/1.01 (step @p68 :rule chain_m_resolution :premises (@p67 @p61) :args (@t80 @t76 @t85)) % 0.71/1.01 (step @p69 :rule aci_norm :args ((= (or @t88 @t16) (or @t68 @t87 @t86 @t16)))) % 0.71/1.01 (step @p70 :rule refl :args (@t16)) % 0.71/1.01 (step @p71 :rule aci_norm :args ((= (or @t68 (or @t87 @t86)) @t88))) % 0.71/1.01 (step @p72 :rule bool-and-de-morgan :args (@t8 @t17 true)) % 0.71/1.01 (step @p73 :rule refl :args (@t68)) % 0.71/1.01 (step @p74 :rule nary_cong :premises (@p73 @p72) :args ((or @t68 (not @t36)))) % 0.71/1.01 (step @p75 :rule bool-and-de-morgan :args (@t2 @t8 (and @t17))) % 0.71/1.01 (step @p76 :rule trans :premises (@p75 @p74)) % 0.71/1.01 (step @p77 :rule trans :premises (@p76 @p71)) % 0.71/1.01 (step @p78 :rule nary_cong :premises (@p77 @p70) :args ((or @t89 @t16))) % 0.71/1.01 (step @p79 :rule trans :premises (@p78 @p69)) % 0.71/1.01 (step @p80 :rule bool-impl-elim :args (@t18 @t16)) % 0.71/1.01 (step @p81 :rule trans :premises (@p80 @p79)) % 0.71/1.01 (step @p82 :rule cong :premises (@p81) :args (@t20)) % 0.71/1.01 (step @p83 :rule eq_resolve :premises (@p7 @p82)) % 0.71/1.01 (step @p84 :rule instantiate :premises (@p83) :args ((@list tptp.xn @t78 @t69))) % 0.71/1.01 (step @p85 :rule bool-double-not-elim :args (@t82)) % 0.71/1.01 (step @p86 :rule nary_cong :premises (@p63 @p85) :args ((or @t84 (not @t83)))) % 0.71/1.01 (step @p87 :rule cnf_or_neg :args (@t84 0)) % 0.71/1.01 (step @p88 :rule eq_resolve :premises (@p87 @p86)) % 0.71/1.01 (step @p89 :rule reordering :premises (@p88) :args ((or @t82 @t84))) % 0.71/1.01 (step @p90 :rule chain_m_resolution :premises (@p89 @p61) :args (@t82 @t76 @t85)) % 0.71/1.01 (step @p91 :rule bool-double-not-elim :args (@t73)) % 0.71/1.01 (step @p92 :rule nary_cong :premises (@p54 @p91) :args ((or @t75 (not @t74)))) % 0.71/1.01 (step @p93 :rule cnf_or_neg :args (@t75 0)) % 0.71/1.01 (step @p94 :rule eq_resolve :premises (@p93 @p92)) % 0.71/1.01 (step @p95 :rule reordering :premises (@p94) :args ((or @t73 @t75))) % 0.71/1.01 (step @p96 :rule chain_m_resolution :premises (@p95 @p52) :args (@t73 @t76 @t77)) % 0.71/1.01 (step @p97 :rule and_elim :premises (@p21) :args (1)) % 0.71/1.01 (step @p98 :rule cnf_or_pos :args (@t95)) % 0.71/1.01 (step @p99 :rule reordering :premises (@p98) :args ((or @t94 @t74 @t83 @t93 (not @t95)))) % 0.71/1.01 (step @p100 :rule chain_m_resolution :premises (@p99 @p97 @p96 @p90 @p84) :args (@t93 @t96 @t97)) % 0.71/1.01 (step @p101 :rule bool-impl-elim :args (@t2 @t98)) % 0.71/1.01 (step @p102 :rule cong :premises (@p101) :args ((forall @t3 (=> @t2 @t98)))) % 0.71/1.01 (step @p103 :rule refl :args (@t21)) % 0.71/1.01 (step @p104 :rule eq-symm :args (@t22 @t1)) % 0.71/1.01 (step @p105 :rule nary_cong :premises (@p104 @p103) :args (@t23)) % 0.71/1.01 (step @p106 :rule cong :premises (@p32 @p105) :args (@t24)) % 0.71/1.01 (step @p107 :rule cong :premises (@p106) :args (@t25)) % 0.71/1.01 (step @p108 :rule trans :premises (@p107 @p102)) % 0.71/1.01 (step @p109 :rule eq_resolve :premises (@p8 @p108)) % 0.71/1.01 (step @p110 :rule instantiate :premises (@p109) :args ((@list tptp.xn))) % 0.71/1.01 (step @p111 :rule cnf_or_pos :args (@t103)) % 0.71/1.01 (step @p112 :rule reordering :premises (@p111) :args ((or @t94 @t102 (not @t103)))) % 0.71/1.01 (step @p113 :rule chain_m_resolution :premises (@p112 @p97 @p110) :args (@t102 @t104 (@list @t46 @t103))) % 0.71/1.01 (step @p114 :rule cnf_and_pos :args (@t102 0)) % 0.71/1.01 (step @p115 :rule reordering :premises (@p114) :args ((or @t101 (not @t102)))) % 0.71/1.01 (step @p116 :rule chain_m_resolution :premises (@p115 @p113) :args (@t101 @t105 (@list @t102))) % 0.71/1.01 (step @p117 :rule aci_norm :args ((= (or @t88 (or @t106 @t29)) @t107))) % 0.71/1.01 (step @p118 :rule refl :args (@t29)) % 0.71/1.01 (step @p119 :rule bool-or-de-morgan :args (@t32 @t30 false)) % 0.71/1.01 (step @p120 :rule nary_cong :premises (@p119 @p118) :args ((or (not @t33) @t29))) % 0.71/1.01 (step @p121 :rule bool-impl-elim :args (@t33 @t29)) % 0.71/1.01 (step @p122 :rule trans :premises (@p121 @p120)) % 0.71/1.01 (step @p123 :rule nary_cong :premises (@p77 @p122) :args ((or @t89 @t34))) % 0.71/1.01 (step @p124 :rule trans :premises (@p123 @p117)) % 0.71/1.01 (step @p125 :rule bool-impl-elim :args (@t18 @t34)) % 0.71/1.01 (step @p126 :rule trans :premises (@p125 @p124)) % 0.71/1.01 (step @p127 :rule cong :premises (@p126) :args (@t35)) % 0.71/1.01 (step @p128 :rule eq_resolve :premises (@p14 @p127)) % 0.71/1.01 (step @p129 :rule refl :args (@t108)) % 0.71/1.01 (step @p130 :rule refl :args (@t109)) % 0.71/1.01 (step @p131 :rule eq-symm :args (@t100 @t91)) % 0.71/1.01 (step @p132 :rule cong :premises (@p131) :args (@t110)) % 0.71/1.01 (step @p133 :rule nary_cong :premises (@p132 @p130) :args (@t111)) % 0.71/1.01 (step @p134 :rule refl :args (@t113)) % 0.71/1.01 (step @p135 :rule refl :args (@t114)) % 0.71/1.01 (step @p136 :rule refl :args (@t94)) % 0.71/1.01 (step @p137 :rule nary_cong :premises (@p136 @p135 @p134 @p133 @p129) :args (@t115)) % 0.71/1.01 (step @p138 :rule refl :args (@t116)) % 0.71/1.01 (step @p139 :rule cong :premises (@p138 @p137) :args ((=> @t116 @t115))) % 0.71/1.01 (assume-push @p291 @t116) % 0.71/1.01 (step @p141 :rule instantiate :premises (@p128) :args ((@list tptp.xn tptp.sz00 @t90))) % 0.71/1.01 (step-pop @p292 :rule scope :premises (@p141)) % 0.71/1.01 (step @p142 :rule process_scope :premises (@p292) :args (@t115)) % 0.71/1.01 (step @p144 :rule eq_resolve :premises (@p142 @p139)) % 0.71/1.01 (step @p145 :rule implies_elim :premises (@p144)) % 0.71/1.01 (step @p146 :rule chain_m_resolution :premises (@p145 @p128) :args (@t120 @t105 (@list @t116))) % 0.71/1.01 (step @p147 :rule aci_norm :args ((= (or @t125 (or @t123 @t121)) @t124))) % 0.71/1.01 (step @p148 :rule bool-impl-elim :args (@t122 @t121)) % 0.71/1.01 (step @p149 :rule bool-and-de-morgan :args (@t2 @t8 true)) % 0.71/1.01 (step @p150 :rule nary_cong :premises (@p149 @p148) :args ((or @t127 @t126))) % 0.71/1.01 (step @p151 :rule trans :premises (@p150 @p147)) % 0.71/1.01 (step @p152 :rule bool-impl-elim :args (@t9 @t126)) % 0.71/1.01 (step @p153 :rule trans :premises (@p152 @p151)) % 0.71/1.01 (step @p154 :rule cong :premises (@p153) :args ((forall @t10 (=> @t9 @t126)))) % 0.71/1.01 (step @p155 :rule eq-symm :args (@t5 tptp.sz00)) % 0.71/1.01 (step @p156 :rule refl :args (@t37)) % 0.71/1.01 (step @p157 :rule nary_cong :premises (@p156 @p155) :args (@t39)) % 0.71/1.01 (step @p158 :rule eq-symm :args (@t6 tptp.sz00)) % 0.71/1.01 (step @p159 :rule cong :premises (@p158 @p157) :args (@t40)) % 0.71/1.01 (step @p160 :rule refl :args (@t9)) % 0.71/1.01 (step @p161 :rule cong :premises (@p160 @p159) :args (@t41)) % 0.71/1.01 (step @p162 :rule cong :premises (@p161) :args (@t42)) % 0.71/1.01 (step @p163 :rule trans :premises (@p162 @p154)) % 0.71/1.01 (step @p164 :rule eq_resolve :premises (@p16 @p163)) % 0.71/1.01 (step @p165 :rule refl :args (@t128)) % 0.71/1.01 (step @p166 :rule eq-symm :args (@t78 tptp.sz00)) % 0.71/1.01 (step @p167 :rule nary_cong :premises (@p166 @p165) :args (@t129)) % 0.71/1.01 (step @p168 :rule refl :args (@t130)) % 0.71/1.01 (step @p169 :rule refl :args (@t74)) % 0.71/1.01 (step @p170 :rule refl :args (@t83)) % 0.71/1.01 (step @p171 :rule nary_cong :premises (@p170 @p169 @p168 @p167) :args (@t131)) % 0.71/1.01 (step @p172 :rule refl :args (@t132)) % 0.71/1.01 (step @p173 :rule cong :premises (@p172 @p171) :args ((=> @t132 @t131))) % 0.71/1.01 (assume-push @p293 @t132) % 0.71/1.01 (step @p175 :rule instantiate :premises (@p164) :args (@t133)) % 0.71/1.01 (step-pop @p294 :rule scope :premises (@p175)) % 0.71/1.01 (step @p176 :rule process_scope :premises (@p294) :args (@t131)) % 0.71/1.01 (step @p178 :rule eq_resolve :premises (@p176 @p173)) % 0.71/1.01 (step @p179 :rule implies_elim :premises (@p178)) % 0.71/1.01 (step @p180 :rule chain_m_resolution :premises (@p179 @p164) :args (@t135 @t105 (@list @t132))) % 0.71/1.01 (step @p181 :rule not_implies_elim2 :premises (@p49)) % 0.71/1.01 (step @p182 :rule instantiate :premises (@p109) :args ((@list tptp.xm))) % 0.71/1.01 (step @p183 :rule and_elim :premises (@p21) :args (0)) % 0.71/1.01 (step @p184 :rule cnf_or_pos :args (@t140)) % 0.71/1.01 (step @p185 :rule reordering :premises (@p184) :args ((or @t139 @t138 (not @t140)))) % 0.71/1.01 (step @p186 :rule chain_m_resolution :premises (@p185 @p183 @p182) :args (@t138 @t104 (@list @t47 @t140))) % 0.71/1.01 (step @p187 :rule cnf_and_pos :args (@t138 0)) % 0.71/1.01 (step @p188 :rule reordering :premises (@p187) :args ((or @t137 (not @t138)))) % 0.71/1.01 (step @p189 :rule chain_m_resolution :premises (@p188 @p186) :args (@t137 @t105 (@list @t138))) % 0.71/1.01 (assume-push @p295 @t71) % 0.71/1.01 (assume-push @p296 @t80) % 0.71/1.01 (assume-push @p297 @t137) % 0.71/1.01 (assume-push @p298 @t128) % 0.71/1.01 (assume-push @p299 @t71) % 0.71/1.01 (assume-push @p300 @t80) % 0.71/1.01 (assume-push @p301 @t128) % 0.71/1.01 (assume-push @p302 @t137) % 0.71/1.01 (step @p198 :rule symm :premises (@p59)) % 0.71/1.01 (step @p199 :rule refl :args (@t69)) % 0.71/1.01 (step @p200 :rule symm :premises (@p68)) % 0.71/1.01 (step @p201 :rule cong :premises (@p200 @p199) :args (@t92)) % 0.71/1.01 (step @p202 :rule cong :premises (@p68 @p298) :args (@t136)) % 0.71/1.01 (step @p203 :rule trans :premises (@p189 @p202 @p201 @p198)) % 0.71/1.01 (step-pop @p303 :rule scope :premises (@p203)) % 0.71/1.01 (step-pop @p304 :rule scope :premises (@p303)) % 0.71/1.01 (step-pop @p305 :rule scope :premises (@p304)) % 0.71/1.01 (step-pop @p306 :rule scope :premises (@p305)) % 0.71/1.01 (step @p204 :rule process_scope :premises (@p306) :args (@t48)) % 0.71/1.01 (step @p209 :rule and_intro :premises (@p59 @p68 @p298 @p189)) % 0.71/1.01 (step @p210 :rule modus_ponens :premises (@p209 @p204)) % 0.71/1.01 (step-pop @p307 :rule scope :premises (@p210)) % 0.71/1.01 (step-pop @p308 :rule scope :premises (@p307)) % 0.71/1.01 (step-pop @p309 :rule scope :premises (@p308)) % 0.71/1.01 (step-pop @p310 :rule scope :premises (@p309)) % 0.71/1.01 (step @p211 :rule process_scope :premises (@p310) :args (@t48)) % 0.71/1.01 (step @p216 :rule implies_elim :premises (@p211)) % 0.71/1.01 (step @p217 :rule cnf_and_neg :args (@t141)) % 0.71/1.01 (step @p218 :rule resolution :premises (@p217 @p216) :args (true @t141)) % 0.71/1.01 (step @p219 :rule reordering :premises (@p218) :args ((or @t48 @t72 @t81 (not @t137) @t142))) % 0.71/1.01 (step @p220 :rule chain_m_resolution :premises (@p219 @p189 @p68 @p59 @p181) :args (@t142 (@list false false false true) (@list @t137 @t80 @t71 @t48))) % 0.71/1.01 (step @p221 :rule cnf_and_pos :args (@t134 1)) % 0.71/1.01 (step @p222 :rule reordering :premises (@p221) :args ((or @t128 @t143))) % 0.71/1.01 (step @p223 :rule chain_m_resolution :premises (@p222 @p220) :args (@t143 @t76 (@list @t128))) % 0.71/1.01 (step @p224 :rule cnf_or_pos :args (@t135)) % 0.71/1.01 (step @p225 :rule reordering :premises (@p224) :args ((or @t74 @t83 @t130 @t134 (not @t135)))) % 0.71/1.01 (step @p226 :rule chain_m_resolution :premises (@p225 @p96 @p90 @p223 @p180) :args (@t130 (@list false false true false) (@list @t73 @t82 @t134 @t135))) % 0.71/1.01 (step @p227 :rule aci_norm :args ((= (or @t125 @t7) (or @t68 @t87 @t7)))) % 0.71/1.01 (step @p228 :rule refl :args (@t7)) % 0.71/1.01 (step @p229 :rule nary_cong :premises (@p149 @p228) :args ((or @t127 @t7))) % 0.71/1.01 (step @p230 :rule trans :premises (@p229 @p227)) % 0.71/1.01 (step @p231 :rule bool-impl-elim :args (@t9 @t7)) % 0.71/1.01 (step @p232 :rule trans :premises (@p231 @p230)) % 0.71/1.01 (step @p233 :rule cong :premises (@p232) :args (@t11)) % 0.71/1.01 (step @p234 :rule eq_resolve :premises (@p4 @p233)) % 0.71/1.01 (step @p235 :rule instantiate :premises (@p234) :args (@t133)) % 0.71/1.01 (step @p236 :rule cnf_or_pos :args (@t144)) % 0.71/1.01 (step @p237 :rule reordering :premises (@p236) :args ((or @t74 @t83 @t112 (not @t144)))) % 0.71/1.01 (step @p238 :rule chain_m_resolution :premises (@p237 @p96 @p90 @p235) :args (@t112 (@list false false false) (@list @t73 @t82 @t144))) % 0.71/1.01 (step @p239 :rule cnf_or_pos :args (@t120)) % 0.71/1.01 (step @p240 :rule reordering :premises (@p239) :args ((or @t114 @t94 @t113 @t108 @t119 (not @t120)))) % 0.71/1.01 (step @p241 :rule chain_m_resolution :premises (@p240 @p2 @p97 @p238 @p226 @p146) :args (@t119 (@list false false false true false) (@list @t4 @t46 @t112 @t108 @t120))) % 0.71/1.02 (step @p242 :rule cnf_and_pos :args (@t119 0)) % 0.71/1.02 (step @p243 :rule reordering :premises (@p242) :args ((or @t118 (not @t119)))) % 0.71/1.02 (step @p244 :rule chain_m_resolution :premises (@p243 @p241) :args (@t118 @t105 (@list @t119))) % 0.71/1.02 (step @p245 :rule bool-double-not-elim :args (@t117)) % 0.71/1.02 (step @p246 :rule refl :args (@t145)) % 0.71/1.02 (step @p247 :rule refl :args (@t146)) % 0.71/1.02 (step @p248 :rule refl :args (@t81)) % 0.71/1.02 (step @p249 :rule refl :args (@t72)) % 0.71/1.02 (step @p250 :rule nary_cong :premises (@p249 @p248 @p247 @p246 @p245) :args ((or @t72 @t81 @t146 @t145 (not @t118)))) % 0.71/1.02 (assume-push @p311 @t118) % 0.71/1.02 (assume-push @p312 @t147) % 0.71/1.02 (assume-push @p313 @t101) % 0.71/1.02 (assume-push @p314 @t71) % 0.71/1.02 (step @p255 :rule evaluate :args ((= true false))) % 0.71/1.02 (step @p256 :rule false_intro :premises (@p311)) % 0.71/1.02 (step @p198 :rule symm :premises (@p59)) % 0.71/1.02 (step @p257 :rule trans :premises (@p198 @p116)) % 0.71/1.02 (step @p258 :rule chain_m_resolution :premises (@p99 @p97 @p96 @p90 @p84) :args (@t93 @t96 @t97)) % 0.71/1.02 (step @p199 :rule refl :args (@t69)) % 0.71/1.02 (step @p259 :rule cong :premises (@p68 @p199) :args (@t70)) % 0.71/1.02 (step @p260 :rule chain_m_resolution :premises (@p58 @p52) :args (@t71 @t76 @t77)) % 0.71/1.02 (step @p261 :rule trans :premises (@p260 @p259 @p258)) % 0.71/1.02 (step @p262 :rule symm :premises (@p261)) % 0.71/1.02 (step @p263 :rule trans :premises (@p262 @p59 @p257)) % 0.71/1.02 (step @p264 :rule true_intro :premises (@p263)) % 0.71/1.02 (step @p265 :rule symm :premises (@p264)) % 0.71/1.02 (step @p266 :rule trans :premises (@p265 @p256)) % 0.71/1.02 (step @p267 false :rule eq_resolve :premises (@p266 @p255)) % 0.71/1.02 (step-pop @p315 :rule scope :premises (@p267)) % 0.71/1.02 (step-pop @p316 :rule scope :premises (@p315)) % 0.71/1.02 (step-pop @p317 :rule scope :premises (@p316)) % 0.71/1.02 (step-pop @p318 :rule scope :premises (@p317)) % 0.71/1.02 (step @p268 :rule process_scope :premises (@p318) :args (false)) % 0.71/1.02 (assume-push @p319 @t71) % 0.71/1.02 (assume-push @p320 @t80) % 0.71/1.02 (assume-push @p321 @t93) % 0.71/1.02 (assume-push @p322 @t101) % 0.71/1.02 (assume-push @p323 @t118) % 0.71/1.02 (step @p199 :rule refl :args (@t69)) % 0.71/1.02 (step @p259 :rule cong :premises (@p68 @p199) :args (@t70)) % 0.71/1.02 (step @p278 :rule trans :premises (@p59 @p259 @p100)) % 0.71/1.02 (step @p279 :rule and_intro :premises (@p323 @p278 @p116 @p59)) % 0.71/1.02 (step-pop @p324 :rule scope :premises (@p279)) % 0.71/1.02 (step-pop @p325 :rule scope :premises (@p324)) % 0.71/1.02 (step-pop @p326 :rule scope :premises (@p325)) % 0.71/1.02 (step-pop @p327 :rule scope :premises (@p326)) % 0.71/1.02 (step-pop @p328 :rule scope :premises (@p327)) % 0.71/1.02 (step @p280 :rule process_scope :premises (@p328) :args (@t148)) % 0.71/1.02 (step @p286 :rule implies_elim :premises (@p280)) % 0.71/1.02 (step @p287 :rule resolution :premises (@p286 @p268) :args (true @t148)) % 0.71/1.02 (step @p288 :rule not_and :premises (@p287)) % 0.71/1.02 (step @p289 :rule eq_resolve :premises (@p288 @p250)) % 0.71/1.02 (step @p290 false :rule chain_m_resolution :premises (@p289 @p244 @p116 @p100 @p68 @p59) :args (false (@list true false false false false) (@list @t117 @t101 @t93 @t80 @t71))) % 0.71/1.02 ) % 0.71/1.02 % SZS output end Proof % 0.71/1.02 % cvc5 exiting %------------------------------------------------------------------------------