%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : KLE016+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 : n025.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 08:28:05 AM UTC 2026 % Result : Theorem 17.41s 17.62s % Output : Proof 17.41s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : KLE016+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 % 0.17/0.35 % Computer : n025.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Tue Jun 2 05:10:16 EDT 2026 % 0.17/0.35 % CPUTime : % 0.33/0.50 %----Proving TF0_NAR, FOF, or CNF % 17.41/17.62 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 17.41/17.62 --- Run --no-e-matching --full-saturate-quant at 6... % 17.41/17.62 % SZS status Theorem % 17.41/17.62 % SZS output start Proof % 17.41/17.62 ( % 17.41/17.62 (declare-sort $$unsorted 0) % 17.41/17.62 (declare-const tptp.c (-> $$unsorted $$unsorted)) % 17.41/17.62 (declare-const tptp.test (-> $$unsorted Bool)) % 17.41/17.62 (declare-const tptp.complement (-> $$unsorted $$unsorted Bool)) % 17.41/17.62 (declare-const tptp.multiplication (-> $$unsorted $$unsorted $$unsorted)) % 17.41/17.62 (declare-const tptp.leq (-> $$unsorted $$unsorted Bool)) % 17.41/17.62 (declare-const tptp.zero $$unsorted) % 17.41/17.62 (declare-const tptp.one $$unsorted) % 17.41/17.62 (declare-const tptp.addition (-> $$unsorted $$unsorted $$unsorted)) % 17.41/17.62 (define @t1 () (@var "A" $$unsorted)) % 17.41/17.62 (define @t2 () (@var "B" $$unsorted)) % 17.41/17.62 (define @t3 () (tptp.addition @t1 @t2)) % 17.41/17.62 (define @t4 () (@list @t1 @t2)) % 17.41/17.62 (define @t5 () (@var "C" $$unsorted)) % 17.41/17.62 (define @t6 () (tptp.addition @t2 @t5)) % 17.41/17.62 (define @t7 () (forall (@list @t5 @t2 @t1) (= (tptp.addition @t1 @t6) (tptp.addition @t3 @t5)))) % 17.41/17.62 (define @t8 () (tptp.addition @t1 tptp.zero)) % 17.41/17.62 (define @t9 () (@list @t1)) % 17.41/17.62 (define @t10 () (forall @t9 (= @t8 @t1))) % 17.41/17.62 (define @t11 () (tptp.addition @t1 @t1)) % 17.41/17.62 (define @t12 () (forall @t9 (= @t11 @t1))) % 17.41/17.62 (define @t13 () (tptp.multiplication @t1 @t2)) % 17.41/17.62 (define @t14 () (tptp.multiplication @t2 @t5)) % 17.41/17.62 (define @t15 () (@list @t1 @t2 @t5)) % 17.41/17.62 (define @t16 () (tptp.multiplication @t1 tptp.one)) % 17.41/17.62 (define @t17 () (forall @t9 (= @t16 @t1))) % 17.41/17.62 (define @t18 () (tptp.multiplication tptp.one @t1)) % 17.41/17.62 (define @t19 () (forall @t9 (= @t18 @t1))) % 17.41/17.62 (define @t20 () (tptp.multiplication @t1 @t5)) % 17.41/17.62 (define @t21 () (tptp.multiplication @t1 tptp.zero)) % 17.41/17.62 (define @t22 () (forall @t9 (= @t21 tptp.zero))) % 17.41/17.62 (define @t23 () (tptp.multiplication tptp.zero @t1)) % 17.41/17.62 (define @t24 () (forall @t9 (= @t23 tptp.zero))) % 17.41/17.62 (define @t25 () (@var "X0" $$unsorted)) % 17.41/17.62 (define @t26 () (@var "X1" $$unsorted)) % 17.41/17.62 (define @t27 () (tptp.complement @t26 @t25)) % 17.41/17.62 (define @t28 () (@list @t26)) % 17.41/17.62 (define @t29 () (exists @t28 @t27)) % 17.41/17.62 (define @t30 () (tptp.test @t25)) % 17.41/17.62 (define @t31 () (= @t30 @t29)) % 17.41/17.62 (define @t32 () (@list @t25)) % 17.41/17.62 (define @t33 () (forall @t32 @t31)) % 17.41/17.62 (define @t34 () (tptp.addition @t25 @t26)) % 17.41/17.62 (define @t35 () (tptp.multiplication @t26 @t25)) % 17.41/17.62 (define @t36 () (tptp.multiplication @t25 @t26)) % 17.41/17.62 (define @t37 () (and (= @t36 tptp.zero) (= @t35 tptp.zero) (= @t34 tptp.one))) % 17.41/17.62 (define @t38 () (= @t27 @t37)) % 17.41/17.62 (define @t39 () (@list @t25 @t26)) % 17.41/17.62 (define @t40 () (forall @t39 @t38)) % 17.41/17.62 (define @t41 () (tptp.complement @t25 @t26)) % 17.41/17.62 (define @t42 () (tptp.c @t25)) % 17.41/17.62 (define @t43 () (= (= @t42 @t26) @t41)) % 17.41/17.62 (define @t44 () (=> @t30 @t43)) % 17.41/17.62 (define @t45 () (forall @t39 @t44)) % 17.41/17.62 (define @t46 () (not @t30)) % 17.41/17.62 (define @t47 () (= (tptp.c @t36) (tptp.addition @t42 (tptp.c @t26)))) % 17.41/17.62 (define @t48 () (tptp.test @t26)) % 17.41/17.62 (define @t49 () (and @t48 @t30)) % 17.41/17.62 (define @t50 () (forall @t39 (=> @t49 @t47))) % 17.41/17.62 (define @t51 () (not @t50)) % 17.41/17.62 (define @t52 () (not @t48)) % 17.41/17.62 (define @t53 () (or @t52 @t46 @t47)) % 17.41/17.62 (define @t54 () (forall @t39 @t53)) % 17.41/17.62 (define @t55 () (@quantifiers_skolemize @t54 1)) % 17.41/17.62 (define @t56 () (tptp.c @t55)) % 17.41/17.62 (define @t57 () (@quantifiers_skolemize @t54 0)) % 17.41/17.62 (define @t58 () (tptp.c @t57)) % 17.41/17.62 (define @t59 () (tptp.addition @t58 @t56)) % 17.41/17.62 (define @t60 () (tptp.multiplication @t57 @t55)) % 17.41/17.62 (define @t61 () (@list @t60 @t59)) % 17.41/17.62 (define @t62 () (@list @t59)) % 17.41/17.62 (define @t63 () (= @t26 @t42)) % 17.41/17.62 (define @t64 () (= @t41 @t63)) % 17.41/17.62 (define @t65 () (tptp.complement @t55 @t56)) % 17.41/17.62 (define @t66 () (= @t56 @t56)) % 17.41/17.62 (define @t67 () (tptp.test @t55)) % 17.41/17.62 (define @t68 () (not @t67)) % 17.41/17.62 (define @t69 () (or @t68 (= @t65 @t66))) % 17.41/17.62 (define @t70 () (forall @t39 (or @t46 @t64))) % 17.41/17.62 (define @t71 () (@list @t55 @t56)) % 17.41/17.62 (define @t72 () (or @t68 @t65)) % 17.41/17.62 (define @t73 () (@list false)) % 17.41/17.62 (define @t74 () (@list @t70)) % 17.41/17.62 (define @t75 () (tptp.c @t60)) % 17.41/17.62 (define @t76 () (= @t75 @t59)) % 17.41/17.62 (define @t77 () (tptp.test @t57)) % 17.41/17.62 (define @t78 () (not @t77)) % 17.41/17.62 (define @t79 () (or @t68 @t78 @t76)) % 17.41/17.62 (define @t80 () (@list true)) % 17.41/17.62 (define @t81 () (@list @t79)) % 17.41/17.62 (define @t82 () (@list false false)) % 17.41/17.62 (define @t83 () (= tptp.one (tptp.addition @t56 @t55))) % 17.41/17.62 (define @t84 () (tptp.multiplication @t55 @t56)) % 17.41/17.62 (define @t85 () (= tptp.zero @t84)) % 17.41/17.62 (define @t86 () (tptp.multiplication @t56 @t55)) % 17.41/17.62 (define @t87 () (= tptp.zero @t86)) % 17.41/17.62 (define @t88 () (and @t87 @t85 @t83)) % 17.41/17.62 (define @t89 () (= @t65 @t88)) % 17.41/17.62 (define @t90 () (not @t88)) % 17.41/17.62 (define @t91 () (@list @t88)) % 17.41/17.62 (define @t92 () (@list @t56)) % 17.41/17.62 (define @t93 () (@list @t55 @t56 @t56)) % 17.41/17.62 (define @t94 () (tptp.complement @t57 @t58)) % 17.41/17.62 (define @t95 () (= @t58 @t58)) % 17.41/17.62 (define @t96 () (or @t78 (= @t94 @t95))) % 17.41/17.62 (define @t97 () (@list @t57 @t58)) % 17.41/17.62 (define @t98 () (or @t78 @t94)) % 17.41/17.62 (define @t99 () (tptp.addition @t58 @t57)) % 17.41/17.62 (define @t100 () (= tptp.one @t99)) % 17.41/17.62 (define @t101 () (tptp.multiplication @t57 @t58)) % 17.41/17.62 (define @t102 () (= tptp.zero @t101)) % 17.41/17.62 (define @t103 () (= tptp.zero (tptp.multiplication @t58 @t57))) % 17.41/17.62 (define @t104 () (and @t103 @t102 @t100)) % 17.41/17.62 (define @t105 () (= @t94 @t104)) % 17.41/17.62 (define @t106 () (not @t104)) % 17.41/17.62 (define @t107 () (@list @t104)) % 17.41/17.62 (define @t108 () (@list @t57 @t58 @t56)) % 17.41/17.62 (define @t109 () (tptp.addition @t59 @t57)) % 17.41/17.62 (define @t110 () (tptp.addition @t57 @t59)) % 17.41/17.62 (define @t111 () (tptp.multiplication @t59 @t59)) % 17.41/17.62 (define @t112 () (tptp.multiplication @t57 @t59)) % 17.41/17.62 (define @t113 () (tptp.multiplication @t56 @t56)) % 17.41/17.62 (define @t114 () (tptp.multiplication @t56 @t99)) % 17.41/17.62 (define @t115 () (tptp.multiplication @t56 @t58)) % 17.41/17.62 (define @t116 () (@list @t58)) % 17.41/17.62 (define @t117 () (tptp.multiplication @t58 @t56)) % 17.41/17.62 (define @t118 () (tptp.multiplication @t58 @t58)) % 17.41/17.62 (define @t119 () (tptp.multiplication @t58 tptp.one)) % 17.41/17.62 (define @t120 () (tptp.addition @t58 (tptp.addition @t56 @t57))) % 17.41/17.62 (define @t121 () (= @t120 @t109)) % 17.41/17.62 (define @t122 () (@list @t57)) % 17.41/17.62 (define @t123 () (@list @t57 @t57 @t58)) % 17.41/17.62 (define @t124 () (tptp.multiplication @t57 @t57)) % 17.41/17.62 (define @t125 () (tptp.multiplication @t124 @t56)) % 17.41/17.62 (define @t126 () (tptp.multiplication @t101 @t56)) % 17.41/17.62 (define @t127 () (tptp.multiplication @t57 tptp.one)) % 17.41/17.62 (define @t128 () (tptp.multiplication @t57 @t56)) % 17.41/17.62 (define @t129 () (tptp.multiplication @t55 @t58)) % 17.41/17.62 (define @t130 () (tptp.addition @t55 @t57)) % 17.41/17.62 (define @t131 () (tptp.addition @t55 @t56)) % 17.41/17.62 (define @t132 () (@list @t55)) % 17.41/17.62 (define @t133 () (tptp.multiplication @t56 @t57)) % 17.41/17.62 (define @t134 () (tptp.multiplication @t56 @t124)) % 17.41/17.62 (define @t135 () (tptp.multiplication @t56 @t101)) % 17.41/17.62 (define @t136 () (tptp.addition @t57 @t55)) % 17.41/17.62 (define @t137 () (tptp.multiplication @t56 @t136)) % 17.41/17.62 (define @t138 () (tptp.multiplication @t55 @t55)) % 17.41/17.62 (define @t139 () (tptp.addition @t138 (tptp.multiplication tptp.zero @t55))) % 17.41/17.62 (define @t140 () (= tptp.one (tptp.addition @t60 @t59))) % 17.41/17.62 (define @t141 () (= tptp.zero (tptp.multiplication @t59 @t60))) % 17.41/17.62 (define @t142 () (= tptp.zero (tptp.multiplication @t60 @t59))) % 17.41/17.62 (define @t143 () (and @t142 @t141 @t140)) % 17.41/17.62 (define @t144 () (@list false false false)) % 17.41/17.62 (define @t145 () (tptp.complement @t59 @t60)) % 17.41/17.62 (define @t146 () (= @t145 @t143)) % 17.41/17.62 (define @t147 () (tptp.complement @t60 @t59)) % 17.41/17.62 (define @t148 () (= @t147 (= @t59 @t75))) % 17.41/17.62 (define @t149 () (tptp.test @t60)) % 17.41/17.62 (define @t150 () (not @t149)) % 17.41/17.62 (define @t151 () (or @t150 @t148)) % 17.41/17.62 (define @t152 () (= @t76 @t147)) % 17.41/17.62 (define @t153 () (or @t150 @t152)) % 17.41/17.62 (define @t154 () (@list @t59 @t60)) % 17.41/17.62 (define @t155 () (= tptp.one (tptp.addition @t59 @t60))) % 17.41/17.62 (define @t156 () (and @t141 @t142 @t155)) % 17.41/17.62 (define @t157 () (= @t147 @t156)) % 17.41/17.62 (define @t158 () (not @t152)) % 17.41/17.62 (define @t159 () (@list true false)) % 17.41/17.62 (define @t160 () (forall @t28 (not (tptp.complement @t26 @t60)))) % 17.41/17.62 (define @t161 () (not @t160)) % 17.41/17.62 (define @t162 () (= @t149 @t161)) % 17.41/17.62 (define @t163 () (not @t162)) % 17.41/17.62 (assume @p1 (forall @t4 (= @t3 (tptp.addition @t2 @t1)))) % 17.41/17.62 (assume @p2 @t7) % 17.41/17.62 (assume @p3 @t10) % 17.41/17.62 (assume @p4 @t12) % 17.41/17.62 (assume @p5 (forall @t15 (= (tptp.multiplication @t1 @t14) (tptp.multiplication @t13 @t5)))) % 17.41/17.62 (assume @p6 @t17) % 17.41/17.62 (assume @p7 @t19) % 17.41/17.62 (assume @p8 (forall @t15 (= (tptp.multiplication @t1 @t6) (tptp.addition @t13 @t20)))) % 17.41/17.62 (assume @p9 (forall @t15 (= (tptp.multiplication @t3 @t5) (tptp.addition @t20 @t14)))) % 17.41/17.62 (assume @p10 @t22) % 17.41/17.62 (assume @p11 @t24) % 17.41/17.62 (assume @p12 (forall @t4 (= (tptp.leq @t1 @t2) (= @t3 @t2)))) % 17.41/17.62 (assume @p13 @t33) % 17.41/17.62 (assume @p14 @t40) % 17.41/17.62 (assume @p15 @t45) % 17.41/17.62 (assume @p16 (forall @t32 (=> @t46 (= @t42 tptp.zero)))) % 17.41/17.62 (assume @p17 @t51) % 17.41/17.62 (assume @p18 true) % 17.41/17.62 (step @p19 :rule eq-symm :args (@t34 tptp.one)) % 17.41/17.62 (step @p20 :rule eq-symm :args (@t35 tptp.zero)) % 17.41/17.62 (step @p21 :rule eq-symm :args (@t36 tptp.zero)) % 17.41/17.62 (step @p22 :rule nary_cong :premises (@p21 @p20 @p19) :args (@t37)) % 17.41/17.62 (step @p23 :rule refl :args (@t27)) % 17.41/17.62 (step @p24 :rule cong :premises (@p23 @p22) :args (@t38)) % 17.41/17.62 (step @p25 :rule cong :premises (@p24) :args (@t40)) % 17.41/17.62 (step @p26 :rule eq_resolve :premises (@p14 @p25)) % 17.41/17.62 (step @p27 :rule instantiate :premises (@p26) :args (@t61)) % 17.41/17.62 (step @p28 :rule eq-symm :args (@t18 @t1)) % 17.41/17.62 (step @p29 :rule cong :premises (@p28) :args (@t19)) % 17.41/17.62 (step @p30 :rule eq_resolve :premises (@p7 @p29)) % 17.41/17.62 (step @p31 :rule instantiate :premises (@p30) :args (@t62)) % 17.41/17.62 (step @p32 :rule symm :premises (@p31)) % 17.41/17.62 (step @p33 :rule refl :args (@t59)) % 17.41/17.62 (step @p34 :rule instantiate :premises (@p26) :args ((@list @t56 @t55))) % 17.41/17.62 (step @p35 :rule bool-impl-elim :args (@t30 @t64)) % 17.41/17.62 (step @p36 :rule cong :premises (@p35) :args ((forall @t39 (=> @t30 @t64)))) % 17.41/17.62 (step @p37 :rule eq-symm :args (@t63 @t41)) % 17.41/17.62 (step @p38 :rule refl :args (@t41)) % 17.41/17.62 (step @p39 :rule eq-symm :args (@t42 @t26)) % 17.41/17.62 (step @p40 :rule cong :premises (@p39 @p38) :args (@t43)) % 17.41/17.62 (step @p41 :rule trans :premises (@p40 @p37)) % 17.41/17.62 (step @p42 :rule refl :args (@t30)) % 17.41/17.62 (step @p43 :rule cong :premises (@p42 @p41) :args (@t44)) % 17.41/17.62 (step @p44 :rule cong :premises (@p43) :args (@t45)) % 17.41/17.62 (step @p45 :rule trans :premises (@p44 @p36)) % 17.41/17.62 (step @p46 :rule eq_resolve :premises (@p15 @p45)) % 17.41/17.62 (step @p47 :rule bool-eq-true :args (@t65)) % 17.41/17.62 (step @p48 :rule eq-symm :args (true @t65)) % 17.41/17.62 (step @p49 :rule trans :premises (@p48 @p47)) % 17.41/17.62 (step @p50 :rule refl :args (@t65)) % 17.41/17.62 (step @p51 :rule eq-refl :args (@t56)) % 17.41/17.62 (step @p52 :rule cong :premises (@p51 @p50) :args ((= @t66 @t65))) % 17.41/17.62 (step @p53 :rule trans :premises (@p52 @p49)) % 17.41/17.62 (step @p54 :rule eq-symm :args (@t65 @t66)) % 17.41/17.62 (step @p55 :rule trans :premises (@p54 @p53)) % 17.41/17.62 (step @p56 :rule refl :args (@t68)) % 17.41/17.62 (step @p57 :rule nary_cong :premises (@p56 @p55) :args (@t69)) % 17.41/17.62 (step @p58 :rule refl :args (@t70)) % 17.41/17.62 (step @p59 :rule cong :premises (@p58 @p57) :args ((=> @t70 @t69))) % 17.41/17.62 (assume-push @p453 @t70) % 17.41/17.62 (step @p61 :rule instantiate :premises (@p46) :args (@t71)) % 17.41/17.62 (step-pop @p454 :rule scope :premises (@p61)) % 17.41/17.62 (step @p62 :rule process_scope :premises (@p454) :args (@t69)) % 17.41/17.62 (step @p64 :rule eq_resolve :premises (@p62 @p59)) % 17.41/17.62 (step @p65 :rule implies_elim :premises (@p64)) % 17.41/17.62 (step @p66 :rule chain_m_resolution :premises (@p65 @p46) :args (@t72 @t73 @t74)) % 17.41/17.62 (step @p67 :rule aci_norm :args ((= (or (or @t52 @t46) @t47) @t53))) % 17.41/17.62 (step @p68 :rule refl :args (@t47)) % 17.41/17.62 (step @p69 :rule bool-and-de-morgan :args (@t48 @t30 true)) % 17.41/17.62 (step @p70 :rule nary_cong :premises (@p69 @p68) :args ((or (not @t49) @t47))) % 17.41/17.62 (step @p71 :rule trans :premises (@p70 @p67)) % 17.41/17.62 (step @p72 :rule bool-impl-elim :args (@t49 @t47)) % 17.41/17.62 (step @p73 :rule trans :premises (@p72 @p71)) % 17.41/17.62 (step @p74 :rule cong :premises (@p73) :args (@t50)) % 17.41/17.62 (step @p75 :rule cong :premises (@p74) :args (@t51)) % 17.41/17.62 (step @p76 :rule eq_resolve :premises (@p17 @p75)) % 17.41/17.62 (step @p77 :rule skolemize :premises (@p76)) % 17.41/17.62 (step @p78 :rule bool-double-not-elim :args (@t67)) % 17.41/17.62 (step @p79 :rule refl :args (@t79)) % 17.41/17.62 (step @p80 :rule nary_cong :premises (@p79 @p78) :args ((or @t79 (not @t68)))) % 17.41/17.62 (step @p81 :rule cnf_or_neg :args (@t79 0)) % 17.41/17.62 (step @p82 :rule eq_resolve :premises (@p81 @p80)) % 17.41/17.62 (step @p83 :rule reordering :premises (@p82) :args ((or @t67 @t79))) % 17.41/17.62 (step @p84 :rule chain_m_resolution :premises (@p83 @p77) :args (@t67 @t80 @t81)) % 17.41/17.62 (step @p85 :rule cnf_or_pos :args (@t72)) % 17.41/17.62 (step @p86 :rule reordering :premises (@p85) :args ((or @t68 @t65 (not @t72)))) % 17.41/17.62 (step @p87 :rule chain_m_resolution :premises (@p86 @p84 @p66) :args (@t65 @t82 (@list @t67 @t72))) % 17.41/17.62 (step @p88 :rule cnf_equiv_pos1 :args (@t89)) % 17.41/17.62 (step @p89 :rule reordering :premises (@p88) :args ((or (not @t65) @t88 (not @t89)))) % 17.41/17.62 (step @p90 :rule chain_m_resolution :premises (@p89 @p87 @p34) :args (@t88 @t82 (@list @t65 @t89))) % 17.41/17.62 (step @p91 :rule cnf_and_pos :args (@t88 2)) % 17.41/17.62 (step @p92 :rule reordering :premises (@p91) :args ((or @t83 @t90))) % 17.41/17.62 (step @p93 :rule chain_m_resolution :premises (@p92 @p90) :args (@t83 @t73 @t91)) % 17.41/17.62 (step @p94 :rule symm :premises (@p93)) % 17.41/17.62 (step @p95 :rule refl :args (@t55)) % 17.41/17.62 (step @p96 :rule eq-symm :args (@t11 @t1)) % 17.41/17.62 (step @p97 :rule cong :premises (@p96) :args (@t12)) % 17.41/17.62 (step @p98 :rule eq_resolve :premises (@p4 @p97)) % 17.41/17.62 (step @p99 :rule instantiate :premises (@p98) :args (@t92)) % 17.41/17.62 (step @p100 :rule symm :premises (@p99)) % 17.41/17.62 (step @p101 :rule cong 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@p261 @p142 @p260 @p298 @p297 @p156 @p154)) % 17.41/17.62 (step @p300 :rule instantiate :premises (@p5) :args ((@list @t57 @t55 @t59))) % 17.41/17.62 (step @p301 :rule instantiate :premises (@p8) :args ((@list @t55 @t58 @t56))) % 17.41/17.62 (step @p302 :rule symm :premises (@p301)) % 17.41/17.62 (step @p303 :rule refl :args (@t129)) % 17.41/17.62 (step @p304 :rule cong :premises (@p303 @p192) :args ((tptp.addition @t129 tptp.zero))) % 17.41/17.62 (step @p305 :rule cong :premises (@p303 @p232) :args ((tptp.addition @t129 @t101))) % 17.41/17.62 (step @p306 :rule instantiate :premises (@p9) :args ((@list @t55 @t57 @t58))) % 17.41/17.62 (step @p307 :rule trans :premises (@p306 @p305 @p304 @p302)) % 17.41/17.62 (step @p308 :rule cong :premises (@p144 @p307) :args ((tptp.multiplication @t57 (tptp.multiplication @t130 @t58)))) % 17.41/17.62 (step @p309 :rule instantiate :premises (@p5) :args ((@list @t57 @t130 @t58))) % 17.41/17.62 (step @p310 :rule symm :premises (@p309)) % 17.41/17.62 (step @p311 :rule instantiate :premises (@p8) :args ((@list @t57 @t55 @t57))) % 17.41/17.62 (step @p312 :rule symm :premises (@p311)) % 17.41/17.62 (step @p313 :rule symm :premises (@p280)) % 17.41/17.62 (step @p314 :rule cong :premises (@p278 @p232) :args ((tptp.addition @t124 @t101))) % 17.41/17.62 (step @p315 :rule symm :premises (@p273)) % 17.41/17.62 (step @p316 :rule trans :premises (@p137 @p315)) % 17.41/17.62 (step @p317 :rule cong :premises (@p144 @p316) :args (@t127)) % 17.41/17.62 (step @p318 :rule trans :premises (@p271 @p317 @p276 @p314 @p313)) % 17.41/17.62 (step @p319 :rule cong :premises (@p153 @p318) :args ((tptp.addition @t60 @t57))) % 17.41/17.62 (step @p320 :rule cong :premises (@p153 @p272) :args ((tptp.addition @t60 @t127))) % 17.41/17.62 (step @p321 :rule instantiate :premises (@p8) :args ((@list @t57 @t55 tptp.one))) % 17.41/17.62 (step @p322 :rule trans :premises (@p197 @p94)) % 17.41/17.62 (step @p323 :rule cong :premises (@p95 @p322) :args ((tptp.addition @t55 @t131))) % 17.41/17.62 (step @p324 :rule instantiate :premises (@p2) :args ((@list @t56 @t55 @t55))) % 17.41/17.62 (step @p325 :rule symm :premises (@p324)) % 17.41/17.62 (step @p326 :rule instantiate :premises (@p98) :args (@t132)) % 17.41/17.62 (step @p327 :rule cong :premises (@p326 @p140) :args (@t131)) % 17.41/17.62 (step @p328 :rule trans :premises (@p93 @p198 @p327 @p325 @p323)) % 17.41/17.62 (step @p329 :rule cong :premises (@p144 @p328) :args (@t127)) % 17.41/17.62 (step @p330 :rule trans :premises (@p271 @p329 @p321 @p320 @p319 @p312)) % 17.41/17.62 (step @p331 :rule cong :premises (@p330 @p222) :args (@t101)) % 17.41/17.62 (step @p332 :rule trans :premises (@p231 @p331 @p310 @p308 @p300)) % 17.41/17.62 (step @p333 :rule instantiate :premises (@p5) :args ((@list @t59 @t57 @t55))) % 17.41/17.62 (step @p334 :rule symm :premises (@p333)) % 17.41/17.62 (step @p335 :rule instantiate :premises (@p9) :args ((@list @t58 @t56 @t57))) % 17.41/17.62 (step @p336 :rule symm :premises (@p335)) % 17.41/17.62 (step @p337 :rule refl :args (@t133)) % 17.41/17.62 (step @p338 :rule cnf_and_pos :args (@t104 0)) % 17.41/17.62 (step @p339 :rule reordering :premises (@p338) :args ((or @t103 @t106))) % 17.41/17.62 (step @p340 :rule chain_m_resolution :premises (@p339 @p134) :args (@t103 @t73 @t107)) % 17.41/17.62 (step @p341 :rule trans :premises (@p187 @p340)) % 17.41/17.62 (step @p342 :rule cong :premises (@p341 @p337) :args ((tptp.addition @t86 @t133))) % 17.41/17.62 (step @p343 :rule cong :premises (@p140 @p281) :args (@t134)) % 17.41/17.62 (step @p344 :rule symm :premises (@p176)) % 17.41/17.62 (step @p345 :rule cong :premises (@p140 @p232) :args (@t135)) % 17.41/17.62 (step @p346 :rule trans :premises (@p345 @p344)) % 17.41/17.62 (step @p347 :rule trans :premises (@p346 @p186)) % 17.41/17.62 (step @p348 :rule cong :premises (@p347 @p343) :args ((tptp.addition @t135 @t134))) % 17.41/17.62 (step @p349 :rule instantiate :premises (@p8) :args ((@list @t56 @t101 @t124))) % 17.41/17.62 (step @p350 :rule cong :premises (@p140 @p290) :args (@t133)) % 17.41/17.62 (step @p351 :rule trans :premises (@p350 @p349 @p348 @p342 @p336)) % 17.41/17.62 (step @p352 :rule symm :premises (@p350)) % 17.41/17.62 (step @p353 :rule symm :premises (@p349)) % 17.41/17.62 (step @p354 :rule symm :premises (@p348)) % 17.41/17.62 (step @p355 :rule instantiate :premises (@p8) :args ((@list @t56 @t55 @t57))) % 17.41/17.62 (step @p356 :rule instantiate :premises (@p1) :args ((@list @t57 @t55))) % 17.41/17.62 (step @p357 :rule cong :premises (@p140 @p356) :args (@t137)) % 17.41/17.62 (step @p358 :rule trans :premises (@p357 @p355 @p354 @p353 @p352)) % 17.41/17.62 (step @p359 :rule trans :premises (@p358 @p351)) % 17.41/17.62 (step @p360 :rule cong :premises (@p359 @p95) :args ((tptp.multiplication @t137 @t55))) % 17.41/17.62 (step @p361 :rule instantiate :premises (@p5) :args ((@list @t56 @t136 @t55))) % 17.41/17.62 (step @p362 :rule instantiate :premises (@p9) :args ((@list @t57 @t55 @t55))) % 17.41/17.62 (step @p363 :rule symm :premises (@p362)) % 17.41/17.62 (step @p364 :rule instantiate :premises (@p163) :args ((@list @t138))) % 17.41/17.62 (step @p365 :rule symm :premises (@p364)) % 17.41/17.62 (step @p366 :rule instantiate :premises (@p179) :args (@t132)) % 17.41/17.62 (step @p367 :rule symm :premises (@p366)) % 17.41/17.62 (step @p368 :rule refl :args (@t138)) % 17.41/17.62 (step @p369 :rule cong :premises (@p368 @p367) :args (@t139)) % 17.41/17.62 (step @p370 :rule trans :premises (@p193 @p366)) % 17.41/17.62 (step @p371 :rule cong :premises (@p368 @p370) :args ((tptp.addition @t138 @t84))) % 17.41/17.62 (step @p372 :rule instantiate :premises (@p8) :args ((@list @t55 @t55 @t56))) % 17.41/17.62 (step @p373 :rule cong :premises (@p95 @p199) :args ((tptp.multiplication @t55 tptp.one))) % 17.41/17.62 (step @p374 :rule instantiate :premises (@p204) :args (@t132)) % 17.41/17.62 (step @p375 :rule instantiate :premises (@p30) :args (@t132)) % 17.41/17.62 (step @p376 :rule symm :premises (@p375)) % 17.41/17.62 (step @p377 :rule trans :premises (@p376 @p374 @p373 @p372 @p371 @p369 @p365)) % 17.41/17.62 (step @p378 :rule cong :premises (@p153 @p377) :args ((tptp.addition @t60 (tptp.multiplication tptp.one @t55)))) % 17.41/17.62 (step @p379 :rule instantiate :premises (@p9) :args ((@list @t57 tptp.one @t55))) % 17.41/17.62 (step @p380 :rule instantiate :premises (@p1) :args ((@list @t57 tptp.one))) % 17.41/17.62 (step @p381 :rule symm :premises (@p380)) % 17.41/17.62 (step @p382 :rule cong :premises (@p138 @p144) :args ((tptp.addition @t99 @t57))) % 17.41/17.62 (step @p383 :rule instantiate :premises (@p2) :args (@t123)) % 17.41/17.62 (step @p384 :rule instantiate :premises (@p98) :args (@t122)) % 17.41/17.62 (step @p385 :rule cong :premises (@p222 @p384) :args (@t99)) % 17.41/17.62 (step @p386 :rule trans :premises (@p137 @p385 @p383 @p382 @p381)) % 17.41/17.62 (step @p387 :rule trans :premises (@p322 @p386)) % 17.41/17.62 (step @p388 :rule cong :premises (@p387 @p95) :args ((tptp.multiplication @t131 @t55))) % 17.41/17.62 (step @p389 :rule instantiate :premises (@p9) :args ((@list @t55 @t56 @t55))) % 17.41/17.62 (step @p390 :rule symm :premises (@p389)) % 17.41/17.62 (step @p391 :rule trans :premises (@p367 @p186)) % 17.41/17.62 (step @p392 :rule cong :premises (@p368 @p391) :args (@t139)) % 17.41/17.62 (step @p393 :rule trans :premises (@p374 @p373 @p372 @p371 @p392 @p390 @p388 @p379 @p378 @p363)) % 17.41/17.62 (step @p394 :rule cong :premises (@p140 @p393) :args (@t86)) % 17.41/17.62 (step @p395 :rule trans :premises (@p186 @p394 @p361 @p360 @p334)) % 17.41/17.62 (step @p396 :rule cnf_and_neg :args (@t143)) % 17.41/17.62 (step @p397 :rule reordering :premises (@p396) :args ((or (not @t141) (not @t142) @t143 (not @t140)))) % 17.41/17.62 (step @p398 :rule chain_m_resolution :premises (@p397 @p395 @p332 @p299) :args (@t143 @t144 (@list @t141 @t142 @t140))) % 17.41/17.62 (step @p399 :rule cnf_equiv_pos2 :args (@t146)) % 17.41/17.62 (step @p400 :rule reordering :premises (@p399) :args ((or @t145 (not @t143) (not @t146)))) % 17.41/17.62 (step @p401 :rule chain_m_resolution :premises (@p400 @p398 @p27) :args (@t145 @t82 (@list @t143 @t146))) % 17.41/17.62 (step @p402 :rule exists-elim :args ((= @t29 (not (forall @t28 (not @t27)))))) % 17.41/17.62 (step @p403 :rule cong :premises (@p42 @p402) :args (@t31)) % 17.41/17.62 (step @p404 :rule cong :premises (@p403) :args (@t33)) % 17.41/17.62 (step @p405 :rule eq_resolve :premises (@p13 @p404)) % 17.41/17.62 (step @p406 :rule instantiate :premises (@p405) :args ((@list @t60))) % 17.41/17.62 (step @p407 :rule eq-symm :args (@t147 @t76)) % 17.41/17.62 (step @p408 :rule eq-symm :args (@t59 @t75)) % 17.41/17.62 (step @p409 :rule refl :args (@t147)) % 17.41/17.62 (step @p410 :rule cong :premises (@p409 @p408) :args (@t148)) % 17.41/17.62 (step @p411 :rule trans :premises (@p410 @p407)) % 17.41/17.62 (step @p412 :rule refl :args (@t150)) % 17.41/17.62 (step @p413 :rule nary_cong :premises (@p412 @p411) :args (@t151)) % 17.41/17.62 (step @p414 :rule cong :premises (@p58 @p413) :args ((=> @t70 @t151))) % 17.41/17.62 (assume-push @p459 @t70) % 17.41/17.62 (step @p416 :rule instantiate :premises (@p46) :args (@t61)) % 17.41/17.62 (step-pop @p460 :rule scope :premises (@p416)) % 17.41/17.62 (step @p417 :rule process_scope :premises (@p460) :args (@t151)) % 17.41/17.62 (step @p419 :rule eq_resolve :premises (@p417 @p414)) % 17.41/17.62 (step @p420 :rule implies_elim :premises (@p419)) % 17.41/17.62 (step @p421 :rule chain_m_resolution :premises (@p420 @p46) :args (@t153 @t73 @t74)) % 17.41/17.62 (step @p422 :rule instantiate :premises (@p26) :args (@t154)) % 17.41/17.62 (step @p423 :rule instantiate :premises (@p1) :args (@t154)) % 17.41/17.62 (step @p424 :rule symm :premises (@p423)) % 17.41/17.62 (step @p425 :rule trans :premises (@p299 @p424)) % 17.41/17.62 (step @p426 :rule cnf_and_neg :args (@t156)) % 17.41/17.62 (step @p427 :rule chain_m_resolution :premises (@p426 @p395 @p332 @p425) :args (@t156 @t144 (@list @t141 @t142 @t155))) % 17.41/17.62 (step @p428 :rule cnf_equiv_pos2 :args (@t157)) % 17.41/17.62 (step @p429 :rule reordering :premises (@p428) :args ((or @t147 (not @t156) (not @t157)))) % 17.41/17.62 (step @p430 :rule chain_m_resolution :premises (@p429 @p427 @p422) :args (@t147 @t82 (@list @t156 @t157))) % 17.41/17.62 (step @p431 :rule cnf_or_neg :args (@t79 2)) % 17.41/17.62 (step @p432 :rule chain_m_resolution :premises (@p431 @p77) :args ((not @t76) @t80 @t81)) % 17.41/17.62 (step @p433 :rule cnf_equiv_pos2 :args (@t152)) % 17.41/17.62 (step @p434 :rule reordering :premises (@p433) :args ((or @t76 (not @t147) @t158))) % 17.41/17.62 (step @p435 :rule chain_m_resolution :premises (@p434 @p432 @p430) :args (@t158 @t159 (@list @t76 @t147))) % 17.41/17.62 (step @p436 :rule cnf_or_pos :args (@t153)) % 17.41/17.62 (step @p437 :rule reordering :premises (@p436) :args ((or @t150 @t152 (not @t153)))) % 17.41/17.62 (step @p438 :rule chain_m_resolution :premises (@p437 @p435 @p421) :args (@t150 @t159 (@list @t152 @t153))) % 17.41/17.62 (step @p439 :rule bool-double-not-elim :args (@t160)) % 17.41/17.62 (step @p440 :rule refl :args (@t149)) % 17.41/17.62 (step @p441 :rule refl :args (@t163)) % 17.41/17.62 (step @p442 :rule nary_cong :premises (@p441 @p440 @p439) :args ((or @t163 @t149 (not @t161)))) % 17.41/17.62 (step @p443 :rule cnf_equiv_pos2 :args (@t162)) % 17.41/17.62 (step @p444 :rule eq_resolve :premises (@p443 @p442)) % 17.41/17.62 (step @p445 :rule reordering :premises (@p444) :args ((or @t149 @t160 @t163))) % 17.41/17.62 (step @p446 :rule chain_m_resolution :premises (@p445 @p438 @p406) :args (@t160 @t159 (@list @t149 @t162))) % 17.41/17.62 (assume-push @p461 @t160) % 17.41/17.62 (step @p448 :rule instantiate :premises (@p446) :args (@t62)) % 17.41/17.62 (step-pop @p462 :rule scope :premises (@p448)) % 17.41/17.62 (step @p449 :rule process_scope :premises (@p462) :args ((not @t145))) % 17.41/17.62 (step @p451 :rule implies_elim :premises (@p449)) % 17.41/17.62 (step @p452 false :rule chain_m_resolution :premises (@p451 @p446 @p401) :args (false @t82 (@list @t160 @t145))) % 17.41/17.62 ) % 17.41/17.62 % SZS output end Proof % 17.41/17.62 % cvc5 exiting %------------------------------------------------------------------------------