%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : KLE015+1 : 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 : n015.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 2.54s 2.74s % Output : Proof 2.54s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : KLE015+1 : 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 % 0.17/0.34 % Computer : n015.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 05:10:19 EDT 2026 % 0.17/0.34 % CPUTime : % 0.33/0.49 %----Proving TF0_NAR, FOF, or CNF % 2.54/2.74 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 2.54/2.74 % SZS status Theorem % 2.54/2.74 % SZS output start Proof % 2.54/2.74 ( % 2.54/2.74 (declare-sort $$unsorted 0) % 2.54/2.74 (declare-const tptp.c (-> $$unsorted $$unsorted)) % 2.54/2.74 (declare-const tptp.test (-> $$unsorted Bool)) % 2.54/2.74 (declare-const tptp.complement (-> $$unsorted $$unsorted Bool)) % 2.54/2.74 (declare-const tptp.multiplication (-> $$unsorted $$unsorted $$unsorted)) % 2.54/2.74 (declare-const tptp.leq (-> $$unsorted $$unsorted Bool)) % 2.54/2.74 (declare-const tptp.zero $$unsorted) % 2.54/2.74 (declare-const tptp.one $$unsorted) % 2.54/2.74 (declare-const tptp.addition (-> $$unsorted $$unsorted $$unsorted)) % 2.54/2.74 (define @t1 () (@var "A" $$unsorted)) % 2.54/2.74 (define @t2 () (@var "B" $$unsorted)) % 2.54/2.74 (define @t3 () (tptp.addition @t1 @t2)) % 2.54/2.74 (define @t4 () (@list @t1 @t2)) % 2.54/2.74 (define @t5 () (forall @t4 (= @t3 (tptp.addition @t2 @t1)))) % 2.54/2.74 (define @t6 () (@var "C" $$unsorted)) % 2.54/2.74 (define @t7 () (tptp.addition @t2 @t6)) % 2.54/2.74 (define @t8 () (forall (@list @t6 @t2 @t1) (= (tptp.addition @t1 @t7) (tptp.addition @t3 @t6)))) % 2.54/2.74 (define @t9 () (tptp.addition @t1 tptp.zero)) % 2.54/2.74 (define @t10 () (@list @t1)) % 2.54/2.74 (define @t11 () (forall @t10 (= @t9 @t1))) % 2.54/2.74 (define @t12 () (tptp.addition @t1 @t1)) % 2.54/2.74 (define @t13 () (forall @t10 (= @t12 @t1))) % 2.54/2.74 (define @t14 () (tptp.multiplication @t1 @t2)) % 2.54/2.74 (define @t15 () (tptp.multiplication @t2 @t6)) % 2.54/2.74 (define @t16 () (@list @t1 @t2 @t6)) % 2.54/2.74 (define @t17 () (forall @t16 (= (tptp.multiplication @t1 @t15) (tptp.multiplication @t14 @t6)))) % 2.54/2.74 (define @t18 () (tptp.multiplication tptp.one @t1)) % 2.54/2.74 (define @t19 () (forall @t10 (= @t18 @t1))) % 2.54/2.74 (define @t20 () (tptp.multiplication @t1 @t6)) % 2.54/2.74 (define @t21 () (tptp.multiplication tptp.zero @t1)) % 2.54/2.74 (define @t22 () (forall @t10 (= @t21 tptp.zero))) % 2.54/2.74 (define @t23 () (@var "X0" $$unsorted)) % 2.54/2.74 (define @t24 () (@var "X1" $$unsorted)) % 2.54/2.74 (define @t25 () (tptp.complement @t24 @t23)) % 2.54/2.74 (define @t26 () (@list @t24)) % 2.54/2.74 (define @t27 () (exists @t26 @t25)) % 2.54/2.74 (define @t28 () (tptp.test @t23)) % 2.54/2.74 (define @t29 () (= @t28 @t27)) % 2.54/2.74 (define @t30 () (@list @t23)) % 2.54/2.74 (define @t31 () (forall @t30 @t29)) % 2.54/2.74 (define @t32 () (tptp.addition @t23 @t24)) % 2.54/2.74 (define @t33 () (tptp.multiplication @t24 @t23)) % 2.54/2.74 (define @t34 () (tptp.multiplication @t23 @t24)) % 2.54/2.74 (define @t35 () (and (= @t34 tptp.zero) (= @t33 tptp.zero) (= @t32 tptp.one))) % 2.54/2.74 (define @t36 () (= @t25 @t35)) % 2.54/2.74 (define @t37 () (@list @t23 @t24)) % 2.54/2.74 (define @t38 () (forall @t37 @t36)) % 2.54/2.74 (define @t39 () (tptp.complement @t23 @t24)) % 2.54/2.74 (define @t40 () (tptp.c @t23)) % 2.54/2.74 (define @t41 () (= (= @t40 @t24) @t39)) % 2.54/2.74 (define @t42 () (=> @t28 @t41)) % 2.54/2.74 (define @t43 () (forall @t37 @t42)) % 2.54/2.74 (define @t44 () (not @t28)) % 2.54/2.74 (define @t45 () (tptp.multiplication (tptp.multiplication @t32 @t40) (tptp.c @t24))) % 2.54/2.74 (define @t46 () (tptp.test @t24)) % 2.54/2.74 (define @t47 () (and @t46 @t28)) % 2.54/2.74 (define @t48 () (=> @t47 (= @t45 tptp.zero))) % 2.54/2.74 (define @t49 () (forall @t37 @t48)) % 2.54/2.74 (define @t50 () (not @t49)) % 2.54/2.74 (define @t51 () (= tptp.zero @t45)) % 2.54/2.74 (define @t52 () (not @t46)) % 2.54/2.74 (define @t53 () (or @t52 @t44 @t51)) % 2.54/2.74 (define @t54 () (forall @t37 @t53)) % 2.54/2.74 (define @t55 () (@quantifiers_skolemize @t54 1)) % 2.54/2.74 (define @t56 () (tptp.c @t55)) % 2.54/2.74 (define @t57 () (@quantifiers_skolemize @t54 0)) % 2.54/2.74 (define @t58 () (tptp.c @t57)) % 2.54/2.74 (define @t59 () (tptp.multiplication (tptp.addition @t57 @t55) @t58)) % 2.54/2.74 (define @t60 () (= tptp.zero (tptp.multiplication @t59 @t56))) % 2.54/2.74 (define @t61 () (tptp.test @t57)) % 2.54/2.74 (define @t62 () (not @t61)) % 2.54/2.74 (define @t63 () (tptp.test @t55)) % 2.54/2.74 (define @t64 () (not @t63)) % 2.54/2.74 (define @t65 () (or @t64 @t62 @t60)) % 2.54/2.74 (define @t66 () (not @t60)) % 2.54/2.74 (define @t67 () (@list true)) % 2.54/2.74 (define @t68 () (@list @t65)) % 2.54/2.74 (define @t69 () (tptp.multiplication @t55 @t58)) % 2.54/2.74 (define @t70 () (tptp.multiplication @t57 @t58)) % 2.54/2.74 (define @t71 () (forall @t26 (not (tptp.complement @t24 @t55)))) % 2.54/2.74 (define @t72 () (@quantifiers_skolemize @t71 0)) % 2.54/2.74 (define @t73 () (@list @t55 @t72)) % 2.54/2.74 (define @t74 () (not @t71)) % 2.54/2.74 (define @t75 () (= @t63 @t74)) % 2.54/2.74 (define @t76 () (@list false false)) % 2.54/2.74 (define @t77 () (tptp.complement @t72 @t55)) % 2.54/2.74 (define @t78 () (not @t77)) % 2.54/2.74 (define @t79 () (not @t78)) % 2.54/2.74 (define @t80 () (= tptp.one (tptp.addition @t55 @t72))) % 2.54/2.74 (define @t81 () (= tptp.zero (tptp.multiplication @t72 @t55))) % 2.54/2.74 (define @t82 () (= tptp.zero (tptp.multiplication @t55 @t72))) % 2.54/2.74 (define @t83 () (and @t82 @t81 @t80)) % 2.54/2.74 (define @t84 () (= @t77 @t83)) % 2.54/2.74 (define @t85 () (not @t83)) % 2.54/2.74 (define @t86 () (@list false)) % 2.54/2.74 (define @t87 () (@list @t83)) % 2.54/2.74 (define @t88 () (tptp.addition @t57 @t58)) % 2.54/2.74 (define @t89 () (tptp.addition @t58 @t57)) % 2.54/2.74 (define @t90 () (= @t88 @t89)) % 2.54/2.74 (define @t91 () (@list @t57 @t58)) % 2.54/2.74 (define @t92 () (= @t89 @t88)) % 2.54/2.74 (define @t93 () (tptp.multiplication @t69 @t56)) % 2.54/2.74 (define @t94 () (tptp.multiplication @t70 @t56)) % 2.54/2.74 (define @t95 () (tptp.multiplication @t58 @t56)) % 2.54/2.74 (define @t96 () (tptp.multiplication @t55 @t95)) % 2.54/2.74 (define @t97 () (= @t96 @t93)) % 2.54/2.74 (define @t98 () (@list @t55 @t58 @t56)) % 2.54/2.74 (define @t99 () (= @t93 @t96)) % 2.54/2.74 (define @t100 () (= @t24 @t40)) % 2.54/2.74 (define @t101 () (= @t39 @t100)) % 2.54/2.74 (define @t102 () (tptp.complement @t57 @t58)) % 2.54/2.74 (define @t103 () (= @t102 (= @t58 @t58))) % 2.54/2.74 (define @t104 () (or @t62 @t103)) % 2.54/2.74 (define @t105 () (forall @t37 (or @t44 @t101))) % 2.54/2.74 (define @t106 () (or @t62 @t102)) % 2.54/2.74 (define @t107 () (@list @t105)) % 2.54/2.74 (define @t108 () (= tptp.one @t89)) % 2.54/2.74 (define @t109 () (= tptp.zero @t70)) % 2.54/2.74 (define @t110 () (and (= tptp.zero (tptp.multiplication @t58 @t57)) @t109 @t108)) % 2.54/2.74 (define @t111 () (= @t102 @t110)) % 2.54/2.74 (define @t112 () (not @t110)) % 2.54/2.74 (define @t113 () (@list @t110)) % 2.54/2.74 (define @t114 () (@list @t56)) % 2.54/2.74 (define @t115 () (tptp.complement @t55 @t72)) % 2.54/2.74 (define @t116 () (= @t115 (= @t72 @t56))) % 2.54/2.74 (define @t117 () (or @t64 @t116)) % 2.54/2.74 (define @t118 () (= @t56 @t72)) % 2.54/2.74 (define @t119 () (= @t115 @t118)) % 2.54/2.74 (define @t120 () (or @t64 @t119)) % 2.54/2.74 (define @t121 () (= tptp.one (tptp.addition @t72 @t55))) % 2.54/2.74 (define @t122 () (and @t81 @t82 @t121)) % 2.54/2.74 (define @t123 () (not @t82)) % 2.54/2.74 (define @t124 () (= @t115 @t122)) % 2.54/2.74 (define @t125 () (tptp.addition @t58 @t58)) % 2.54/2.74 (define @t126 () (tptp.addition @t57 @t125)) % 2.54/2.74 (define @t127 () (tptp.addition @t88 @t58)) % 2.54/2.74 (define @t128 () (= @t126 @t127)) % 2.54/2.74 (define @t129 () (= @t127 @t126)) % 2.54/2.74 (define @t130 () (tptp.multiplication @t55 @t56)) % 2.54/2.74 (define @t131 () (tptp.addition @t96 @t130)) % 2.54/2.74 (define @t132 () (tptp.addition @t95 @t56)) % 2.54/2.74 (define @t133 () (tptp.multiplication @t55 @t132)) % 2.54/2.74 (define @t134 () (= @t133 @t131)) % 2.54/2.74 (define @t135 () (not @t134)) % 2.54/2.74 (define @t136 () (not @t129)) % 2.54/2.74 (define @t137 () (tptp.multiplication @t127 @t56)) % 2.54/2.74 (define @t138 () (= @t137 (tptp.addition (tptp.multiplication @t88 @t56) @t95))) % 2.54/2.74 (define @t139 () (not @t138)) % 2.54/2.74 (define @t140 () (= @t58 @t125)) % 2.54/2.74 (define @t141 () (not @t140)) % 2.54/2.74 (define @t142 () (tptp.addition @t56 @t95)) % 2.54/2.74 (define @t143 () (= @t142 @t132)) % 2.54/2.74 (define @t144 () (not @t143)) % 2.54/2.74 (define @t145 () (not @t118)) % 2.54/2.74 (define @t146 () (tptp.multiplication tptp.zero @t56)) % 2.54/2.74 (define @t147 () (= tptp.zero @t146)) % 2.54/2.74 (define @t148 () (not @t147)) % 2.54/2.74 (define @t149 () (tptp.multiplication tptp.one @t56)) % 2.54/2.74 (define @t150 () (= @t56 @t149)) % 2.54/2.74 (define @t151 () (not @t150)) % 2.54/2.74 (define @t152 () (= @t56 (tptp.addition @t56 tptp.zero))) % 2.54/2.74 (define @t153 () (not @t152)) % 2.54/2.74 (define @t154 () (not @t99)) % 2.54/2.74 (define @t155 () (tptp.addition @t94 @t93)) % 2.54/2.74 (define @t156 () (= @t155 (tptp.addition @t93 @t94))) % 2.54/2.74 (define @t157 () (not @t156)) % 2.54/2.74 (define @t158 () (not @t92)) % 2.54/2.74 (define @t159 () (not @t108)) % 2.54/2.74 (define @t160 () (not @t109)) % 2.54/2.74 (define @t161 () (tptp.addition @t70 @t69)) % 2.54/2.74 (define @t162 () (tptp.multiplication @t161 @t56)) % 2.54/2.74 (define @t163 () (= @t162 @t155)) % 2.54/2.74 (define @t164 () (not @t163)) % 2.54/2.74 (define @t165 () (= @t59 @t161)) % 2.54/2.74 (define @t166 () (not @t165)) % 2.54/2.74 (define @t167 () (and @t66 @t165 @t163 @t82 @t109 @t108 @t92 @t156 @t99 @t152 @t150 @t147 @t118 @t143 @t140 @t138 @t129)) % 2.54/2.74 (assume @p1 @t5) % 2.54/2.74 (assume @p2 @t8) % 2.54/2.74 (assume @p3 @t11) % 2.54/2.74 (assume @p4 @t13) % 2.54/2.74 (assume @p5 @t17) % 2.54/2.74 (assume @p6 (forall @t10 (= (tptp.multiplication @t1 tptp.one) @t1))) % 2.54/2.74 (assume @p7 @t19) % 2.54/2.74 (assume @p8 (forall @t16 (= (tptp.multiplication @t1 @t7) (tptp.addition @t14 @t20)))) % 2.54/2.74 (assume @p9 (forall @t16 (= (tptp.multiplication @t3 @t6) (tptp.addition @t20 @t15)))) % 2.54/2.74 (assume @p10 (forall @t10 (= (tptp.multiplication @t1 tptp.zero) tptp.zero))) % 2.54/2.74 (assume @p11 @t22) % 2.54/2.74 (assume @p12 (forall @t4 (= (tptp.leq @t1 @t2) (= @t3 @t2)))) % 2.54/2.74 (assume @p13 @t31) % 2.54/2.74 (assume @p14 @t38) % 2.54/2.74 (assume @p15 @t43) % 2.54/2.74 (assume @p16 (forall @t30 (=> @t44 (= @t40 tptp.zero)))) % 2.54/2.74 (assume @p17 @t50) % 2.54/2.74 (assume @p18 true) % 2.54/2.74 (step @p19 :rule aci_norm :args ((= (or (or @t52 @t44) @t51) @t53))) % 2.54/2.74 (step @p20 :rule refl :args (@t51)) % 2.54/2.74 (step @p21 :rule bool-and-de-morgan :args (@t46 @t28 true)) % 2.54/2.74 (step @p22 :rule nary_cong :premises (@p21 @p20) :args ((or (not @t47) @t51))) % 2.54/2.74 (step @p23 :rule trans :premises (@p22 @p19)) % 2.54/2.74 (step @p24 :rule bool-impl-elim :args (@t47 @t51)) % 2.54/2.74 (step @p25 :rule trans :premises (@p24 @p23)) % 2.54/2.74 (step @p26 :rule cong :premises (@p25) :args ((forall @t37 (=> @t47 @t51)))) % 2.54/2.74 (step @p27 :rule eq-symm :args (@t45 tptp.zero)) % 2.54/2.74 (step @p28 :rule refl :args (@t47)) % 2.54/2.74 (step @p29 :rule cong :premises (@p28 @p27) :args (@t48)) % 2.54/2.74 (step @p30 :rule cong :premises (@p29) :args (@t49)) % 2.54/2.74 (step @p31 :rule trans :premises (@p30 @p26)) % 2.54/2.74 (step @p32 :rule cong :premises (@p31) :args (@t50)) % 2.54/2.74 (step @p33 :rule eq_resolve :premises (@p17 @p32)) % 2.54/2.74 (step @p34 :rule skolemize :premises (@p33)) % 2.54/2.74 (step @p35 :rule cnf_or_neg :args (@t65 2)) % 2.54/2.74 (step @p36 :rule chain_m_resolution :premises (@p35 @p34) :args (@t66 @t67 @t68)) % 2.54/2.74 (step @p37 :rule instantiate :premises (@p9) :args ((@list @t57 @t55 @t58))) % 2.54/2.74 (step @p38 :rule instantiate :premises (@p9) :args ((@list @t70 @t69 @t56))) % 2.54/2.74 (step @p39 :rule eq-symm :args (@t32 tptp.one)) % 2.54/2.74 (step @p40 :rule eq-symm :args (@t33 tptp.zero)) % 2.54/2.74 (step @p41 :rule eq-symm :args (@t34 tptp.zero)) % 2.54/2.74 (step @p42 :rule nary_cong :premises (@p41 @p40 @p39) :args (@t35)) % 2.54/2.74 (step @p43 :rule refl :args (@t25)) % 2.54/2.74 (step @p44 :rule cong :premises (@p43 @p42) :args (@t36)) % 2.54/2.74 (step @p45 :rule cong :premises (@p44) :args (@t38)) % 2.54/2.74 (step @p46 :rule eq_resolve :premises (@p14 @p45)) % 2.54/2.74 (step @p47 :rule instantiate :premises (@p46) :args (@t73)) % 2.54/2.74 (step @p48 :rule exists-elim :args ((= @t27 (not (forall @t26 (not @t25)))))) % 2.54/2.74 (step @p49 :rule refl :args (@t28)) % 2.54/2.74 (step @p50 :rule cong :premises (@p49 @p48) :args (@t29)) % 2.54/2.74 (step @p51 :rule cong :premises (@p50) :args (@t31)) % 2.54/2.74 (step @p52 :rule eq_resolve :premises (@p13 @p51)) % 2.54/2.74 (step @p53 :rule instantiate :premises (@p52) :args ((@list @t55))) % 2.54/2.74 (step @p54 :rule bool-double-not-elim :args (@t63)) % 2.54/2.74 (step @p55 :rule refl :args (@t65)) % 2.54/2.74 (step @p56 :rule nary_cong :premises (@p55 @p54) :args ((or @t65 (not @t64)))) % 2.54/2.74 (step @p57 :rule cnf_or_neg :args (@t65 0)) % 2.54/2.74 (step @p58 :rule eq_resolve :premises (@p57 @p56)) % 2.54/2.74 (step @p59 :rule reordering :premises (@p58) :args ((or @t63 @t65))) % 2.54/2.74 (step @p60 :rule chain_m_resolution :premises (@p59 @p34) :args (@t63 @t67 @t68)) % 2.54/2.74 (step @p61 :rule cnf_equiv_pos1 :args (@t75)) % 2.54/2.74 (step @p62 :rule reordering :premises (@p61) :args ((or @t64 @t74 (not @t75)))) % 2.54/2.74 (step @p63 :rule chain_m_resolution :premises (@p62 @p60 @p53) :args (@t74 @t76 (@list @t63 @t75))) % 2.54/2.74 (step @p64 :rule refl :args (@t77)) % 2.54/2.74 (step @p65 :rule bool-double-not-elim :args (@t71)) % 2.54/2.74 (step @p66 :rule nary_cong :premises (@p65 @p64) :args ((or (not @t74) @t77))) % 2.54/2.74 (step @p67 :rule bool-double-not-elim :args (@t77)) % 2.54/2.74 (step @p68 :rule refl :args (@t74)) % 2.54/2.74 (step @p69 :rule cong :premises (@p68 @p67) :args ((=> @t74 @t79))) % 2.54/2.74 (assume-push @p316 @t74) % 2.54/2.74 (step @p71 :rule skolemize :premises (@p63)) % 2.54/2.74 (step-pop @p317 :rule scope :premises (@p71)) % 2.54/2.74 (step @p72 :rule process_scope :premises (@p317) :args (@t79)) % 2.54/2.74 (step @p74 :rule eq_resolve :premises (@p72 @p69)) % 2.54/2.74 (step @p75 :rule implies_elim :premises (@p74)) % 2.54/2.74 (step @p76 :rule eq_resolve :premises (@p75 @p66)) % 2.54/2.74 (step @p77 :rule chain_m_resolution :premises (@p76 @p63) :args (@t77 @t67 (@list @t71))) % 2.54/2.74 (step @p78 :rule cnf_equiv_pos1 :args (@t84)) % 2.54/2.74 (step @p79 :rule reordering :premises (@p78) :args ((or @t78 @t83 (not @t84)))) % 2.54/2.74 (step @p80 :rule chain_m_resolution :premises (@p79 @p77 @p47) :args (@t83 @t76 (@list @t77 @t84))) % 2.54/2.74 (step @p81 :rule cnf_and_pos :args (@t83 0)) % 2.54/2.74 (step @p82 :rule reordering :premises (@p81) :args ((or @t82 @t85))) % 2.54/2.74 (step @p83 :rule chain_m_resolution :premises (@p82 @p80) :args (@t82 @t86 @t87)) % 2.54/2.74 (step @p84 :rule eq-symm :args (@t88 @t89)) % 2.54/2.74 (step @p85 :rule refl :args (@t5)) % 2.54/2.74 (step @p86 :rule cong :premises (@p85 @p84) :args ((=> @t5 @t90))) % 2.54/2.74 (assume-push @p318 @t5) % 2.54/2.74 (step @p88 :rule instantiate :premises (@p1) :args (@t91)) % 2.54/2.74 (step-pop @p319 :rule scope :premises (@p88)) % 2.54/2.74 (step @p89 :rule process_scope :premises (@p319) :args (@t90)) % 2.54/2.74 (step @p91 :rule eq_resolve :premises (@p89 @p86)) % 2.54/2.74 (step @p92 :rule implies_elim :premises (@p91)) % 2.54/2.74 (step @p93 :rule chain_m_resolution :premises (@p92 @p1) :args (@t92 @t86 (@list @t5))) % 2.54/2.74 (step @p94 :rule instantiate :premises (@p1) :args ((@list @t94 @t93))) % 2.54/2.74 (step @p95 :rule eq-symm :args (@t96 @t93)) % 2.54/2.74 (step @p96 :rule refl :args (@t17)) % 2.54/2.74 (step @p97 :rule cong :premises (@p96 @p95) :args ((=> @t17 @t97))) % 2.54/2.74 (assume-push @p320 @t17) % 2.54/2.74 (step @p99 :rule instantiate :premises (@p5) :args (@t98)) % 2.54/2.74 (step-pop @p321 :rule scope :premises (@p99)) % 2.54/2.74 (step @p100 :rule process_scope :premises (@p321) :args (@t97)) % 2.54/2.74 (step @p102 :rule eq_resolve :premises (@p100 @p97)) % 2.54/2.74 (step @p103 :rule implies_elim :premises (@p102)) % 2.54/2.74 (step @p104 :rule chain_m_resolution :premises (@p103 @p5) :args (@t99 @t86 (@list @t17))) % 2.54/2.74 (step @p105 :rule instantiate :premises (@p46) :args ((@list @t58 @t57))) % 2.54/2.74 (step @p106 :rule bool-impl-elim :args (@t28 @t101)) % 2.54/2.74 (step @p107 :rule cong :premises (@p106) :args ((forall @t37 (=> @t28 @t101)))) % 2.54/2.74 (step @p108 :rule eq-symm :args (@t100 @t39)) % 2.54/2.74 (step @p109 :rule refl :args (@t39)) % 2.54/2.74 (step @p110 :rule eq-symm :args (@t40 @t24)) % 2.54/2.74 (step @p111 :rule cong :premises (@p110 @p109) :args (@t41)) % 2.54/2.74 (step @p112 :rule trans :premises (@p111 @p108)) % 2.54/2.74 (step @p113 :rule cong :premises (@p49 @p112) :args (@t42)) % 2.54/2.74 (step @p114 :rule cong :premises (@p113) :args (@t43)) % 2.54/2.74 (step @p115 :rule trans :premises (@p114 @p107)) % 2.54/2.74 (step @p116 :rule eq_resolve :premises (@p15 @p115)) % 2.54/2.74 (step @p117 :rule bool-eq-true :args (@t102)) % 2.54/2.74 (step @p118 :rule eq-refl :args (@t58)) % 2.54/2.74 (step @p119 :rule refl :args (@t102)) % 2.54/2.74 (step @p120 :rule cong :premises (@p119 @p118) :args (@t103)) % 2.54/2.74 (step @p121 :rule trans :premises (@p120 @p117)) % 2.54/2.74 (step @p122 :rule refl :args (@t62)) % 2.54/2.74 (step @p123 :rule nary_cong :premises (@p122 @p121) :args (@t104)) % 2.54/2.74 (step @p124 :rule refl :args (@t105)) % 2.54/2.74 (step @p125 :rule cong :premises (@p124 @p123) :args ((=> @t105 @t104))) % 2.54/2.74 (assume-push @p322 @t105) % 2.54/2.74 (step @p127 :rule instantiate :premises (@p116) :args (@t91)) % 2.54/2.74 (step-pop @p323 :rule scope :premises (@p127)) % 2.54/2.74 (step @p128 :rule process_scope :premises (@p323) :args (@t104)) % 2.54/2.74 (step @p130 :rule eq_resolve :premises (@p128 @p125)) % 2.54/2.74 (step @p131 :rule implies_elim :premises (@p130)) % 2.54/2.74 (step @p132 :rule chain_m_resolution :premises (@p131 @p116) :args (@t106 @t86 @t107)) % 2.54/2.74 (step @p133 :rule bool-double-not-elim :args (@t61)) % 2.54/2.74 (step @p134 :rule nary_cong :premises (@p55 @p133) :args ((or @t65 (not @t62)))) % 2.54/2.74 (step @p135 :rule cnf_or_neg :args (@t65 1)) % 2.54/2.74 (step @p136 :rule eq_resolve :premises (@p135 @p134)) % 2.54/2.74 (step @p137 :rule reordering :premises (@p136) :args ((or @t61 @t65))) % 2.54/2.74 (step @p138 :rule chain_m_resolution :premises (@p137 @p34) :args (@t61 @t67 @t68)) % 2.54/2.74 (step @p139 :rule cnf_or_pos :args (@t106)) % 2.54/2.74 (step @p140 :rule reordering :premises (@p139) :args ((or @t62 @t102 (not @t106)))) % 2.54/2.74 (step @p141 :rule chain_m_resolution :premises (@p140 @p138 @p132) :args (@t102 @t76 (@list @t61 @t106))) % 2.54/2.74 (step @p142 :rule cnf_equiv_pos1 :args (@t111)) % 2.54/2.74 (step @p143 :rule reordering :premises (@p142) :args ((or @t110 (not @t102) (not @t111)))) % 2.54/2.74 (step @p144 :rule chain_m_resolution :premises (@p143 @p141 @p105) :args (@t110 @t76 (@list @t102 @t111))) % 2.54/2.74 (step @p145 :rule cnf_and_pos :args (@t110 1)) % 2.54/2.74 (step @p146 :rule reordering :premises (@p145) :args ((or 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(@t22)) % 2.54/2.74 (step @p161 :rule eq_resolve :premises (@p11 @p160)) % 2.54/2.74 (step @p162 :rule instantiate :premises (@p161) :args (@t114)) % 2.54/2.74 (step @p163 :rule eq-symm :args (@t72 @t56)) % 2.54/2.74 (step @p164 :rule refl :args (@t115)) % 2.54/2.74 (step @p165 :rule cong :premises (@p164 @p163) :args (@t116)) % 2.54/2.74 (step @p166 :rule refl :args (@t64)) % 2.54/2.74 (step @p167 :rule nary_cong :premises (@p166 @p165) :args (@t117)) % 2.54/2.74 (step @p168 :rule cong :premises (@p124 @p167) :args ((=> @t105 @t117))) % 2.54/2.74 (assume-push @p324 @t105) % 2.54/2.74 (step @p170 :rule instantiate :premises (@p116) :args (@t73)) % 2.54/2.74 (step-pop @p325 :rule scope :premises (@p170)) % 2.54/2.74 (step @p171 :rule process_scope :premises (@p325) :args (@t117)) % 2.54/2.74 (step @p173 :rule eq_resolve :premises (@p171 @p168)) % 2.54/2.74 (step @p174 :rule implies_elim :premises (@p173)) % 2.54/2.74 (step @p175 :rule chain_m_resolution :premises (@p174 @p116) :args 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@p188 :rule cnf_and_neg :args (@t122)) % 2.54/2.74 (step @p189 :rule reordering :premises (@p188) :args ((or @t123 (not @t81) @t122 (not @t121)))) % 2.54/2.74 (step @p190 :rule chain_m_resolution :premises (@p189 @p83 @p187 @p184) :args (@t122 (@list false false false) (@list @t82 @t81 @t121))) % 2.54/2.74 (step @p191 :rule cnf_equiv_pos2 :args (@t124)) % 2.54/2.74 (step @p192 :rule reordering :premises (@p191) :args ((or @t115 (not @t122) (not @t124)))) % 2.54/2.74 (step @p193 :rule chain_m_resolution :premises (@p192 @p190 @p179) :args (@t115 @t76 (@list @t122 @t124))) % 2.54/2.74 (step @p194 :rule cnf_equiv_pos1 :args (@t119)) % 2.54/2.74 (step @p195 :rule reordering :premises (@p194) :args ((or (not @t115) @t118 (not @t119)))) % 2.54/2.74 (step @p196 :rule chain_m_resolution :premises (@p195 @p193 @p178) :args (@t118 @t76 (@list @t115 @t119))) % 2.54/2.74 (step @p197 :rule instantiate :premises (@p1) :args ((@list @t56 @t95))) % 2.54/2.74 (step @p198 :rule eq-symm :args (@t12 @t1)) % 2.54/2.74 (step @p199 :rule cong :premises (@p198) :args (@t13)) % 2.54/2.74 (step @p200 :rule eq_resolve :premises (@p4 @p199)) % 2.54/2.74 (step @p201 :rule instantiate :premises (@p200) :args ((@list @t58))) % 2.54/2.74 (step @p202 :rule instantiate :premises (@p9) :args ((@list @t88 @t58 @t56))) % 2.54/2.74 (step @p203 :rule eq-symm :args (@t126 @t127)) % 2.54/2.74 (step @p204 :rule refl :args (@t8)) % 2.54/2.74 (step @p205 :rule cong :premises (@p204 @p203) :args ((=> @t8 @t128))) % 2.54/2.74 (assume-push @p326 @t8) % 2.54/2.74 (step @p207 :rule instantiate :premises (@p2) :args ((@list @t58 @t58 @t57))) % 2.54/2.74 (step-pop @p327 :rule scope :premises (@p207)) % 2.54/2.74 (step @p208 :rule process_scope :premises (@p327) :args (@t128)) % 2.54/2.74 (step @p210 :rule eq_resolve :premises (@p208 @p205)) % 2.54/2.74 (step @p211 :rule implies_elim :premises (@p210)) % 2.54/2.74 (step @p212 :rule chain_m_resolution :premises (@p211 @p2) :args (@t129 @t86 (@list @t8))) % 2.54/2.74 (step @p213 :rule instantiate :premises (@p8) :args ((@list @t55 @t95 @t56))) % 2.54/2.74 (step @p214 :rule refl :args (@t135)) % 2.54/2.74 (step @p215 :rule refl :args (@t136)) % 2.54/2.74 (step @p216 :rule refl :args (@t139)) % 2.54/2.74 (step @p217 :rule refl :args (@t141)) % 2.54/2.74 (step @p218 :rule refl :args (@t144)) % 2.54/2.74 (step @p219 :rule refl :args (@t145)) % 2.54/2.74 (step @p220 :rule refl :args (@t148)) % 2.54/2.74 (step @p221 :rule refl :args (@t151)) % 2.54/2.74 (step @p222 :rule refl :args (@t153)) % 2.54/2.74 (step @p223 :rule refl :args (@t154)) % 2.54/2.74 (step @p224 :rule refl :args (@t157)) % 2.54/2.74 (step @p225 :rule refl :args (@t158)) % 2.54/2.74 (step @p226 :rule refl :args (@t159)) % 2.54/2.74 (step @p227 :rule refl :args (@t160)) % 2.54/2.74 (step @p228 :rule refl :args (@t123)) % 2.54/2.74 (step @p229 :rule refl :args (@t164)) % 2.54/2.74 (step @p230 :rule refl :args (@t166)) % 2.54/2.74 (step @p231 :rule bool-double-not-elim :args (@t60)) % 2.54/2.74 (step @p232 :rule nary_cong :premises (@p231 @p230 @p229 @p228 @p227 @p226 @p225 @p224 @p223 @p222 @p221 @p220 @p219 @p218 @p217 @p216 @p215 @p214) :args ((or (not @t66) @t166 @t164 @t123 @t160 @t159 @t158 @t157 @t154 @t153 @t151 @t148 @t145 @t144 @t141 @t139 @t136 @t135))) % 2.54/2.74 (assume-push @p328 @t66) % 2.54/2.74 (assume-push @p329 @t165) % 2.54/2.74 (assume-push @p330 @t163) % 2.54/2.74 (assume-push @p331 @t82) % 2.54/2.74 (assume-push @p332 @t109) % 2.54/2.74 (assume-push @p333 @t108) % 2.54/2.74 (assume-push @p334 @t92) % 2.54/2.74 (assume-push @p335 @t156) % 2.54/2.74 (assume-push @p336 @t99) % 2.54/2.74 (assume-push @p337 @t152) % 2.54/2.74 (assume-push @p338 @t150) % 2.54/2.74 (assume-push @p339 @t147) % 2.54/2.74 (assume-push @p340 @t118) % 2.54/2.74 (assume-push @p341 @t143) % 2.54/2.74 (assume-push @p342 @t140) % 2.54/2.74 (assume-push @p343 @t138) % 2.54/2.74 (assume-push @p344 @t129) % 2.54/2.74 (step @p250 :rule false_intro :premises (@p36)) % 2.54/2.74 (step @p251 :rule refl :args (@t56)) % 2.54/2.74 (step @p252 :rule symm :premises (@p37)) % 2.54/2.74 (step @p253 :rule cong :premises (@p252 @p251) :args (@t162)) % 2.54/2.74 (step @p254 :rule symm :premises (@p38)) % 2.54/2.74 (step @p255 :rule symm :premises (@p94)) % 2.54/2.74 (step @p256 :rule cong :premises (@p147 @p251) :args (@t146)) % 2.54/2.74 (step @p257 :rule symm :premises (@p83)) % 2.54/2.74 (step @p258 :rule refl :args (@t55)) % 2.54/2.74 (step @p259 :rule cong :premises (@p258 @p196) :args (@t130)) % 2.54/2.74 (step @p260 :rule trans :premises (@p259 @p257 @p162 @p256)) % 2.54/2.74 (step @p99 :rule instantiate :premises (@p5) :args (@t98)) % 2.54/2.74 (step @p261 :rule cong :premises (@p99 @p260) :args (@t131)) % 2.54/2.74 (step @p262 :rule trans :premises (@p261 @p255 @p254 @p253)) % 2.54/2.74 (step @p263 :rule symm :premises (@p158)) % 2.54/2.74 (step @p264 :rule symm :premises (@p150)) % 2.54/2.74 (step @p88 :rule instantiate :premises (@p1) :args (@t91)) % 2.54/2.74 (step @p265 :rule symm :premises (@p201)) % 2.54/2.74 (step @p266 :rule refl :args (@t57)) % 2.54/2.74 (step @p267 :rule cong :premises (@p266 @p265) :args (@t126)) % 2.54/2.74 (step @p268 :rule trans :premises (@p212 @p267 @p88)) % 2.54/2.74 (step @p269 :rule trans :premises (@p268 @p264)) % 2.54/2.74 (step @p270 :rule cong :premises (@p269 @p251) :args (@t137)) % 2.54/2.74 (step @p271 :rule trans :premises (@p270 @p263)) % 2.54/2.74 (step @p272 :rule cong :premises (@p258 @p271) :args ((tptp.multiplication @t55 @t137))) % 2.54/2.74 (step @p273 :rule symm :premises (@p202)) % 2.54/2.74 (step @p274 :rule refl :args (@t95)) % 2.54/2.74 (step @p275 :rule trans :premises (@p150 @p93)) % 2.54/2.74 (step @p276 :rule cong :premises (@p275 @p251) :args (@t149)) % 2.54/2.74 (step @p277 :rule symm :premises (@p154)) % 2.54/2.74 (step @p278 :rule symm :premises (@p147)) % 2.54/2.74 (step @p279 :rule cong :premises (@p251 @p278) :args ((tptp.addition @t56 @t70))) % 2.54/2.74 (step @p280 :rule 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@p347 :rule scope :premises (@p346)) % 2.54/2.74 (step-pop @p348 :rule scope :premises (@p347)) % 2.54/2.74 (step-pop @p349 :rule scope :premises (@p348)) % 2.54/2.74 (step-pop @p350 :rule scope :premises (@p349)) % 2.54/2.74 (step-pop @p351 :rule scope :premises (@p350)) % 2.54/2.74 (step-pop @p352 :rule scope :premises (@p351)) % 2.54/2.74 (step-pop @p353 :rule scope :premises (@p352)) % 2.54/2.74 (step-pop @p354 :rule scope :premises (@p353)) % 2.54/2.74 (step-pop @p355 :rule scope :premises (@p354)) % 2.54/2.74 (step-pop @p356 :rule scope :premises (@p355)) % 2.54/2.74 (step-pop @p357 :rule scope :premises (@p356)) % 2.54/2.74 (step-pop @p358 :rule scope :premises (@p357)) % 2.54/2.74 (step-pop @p359 :rule scope :premises (@p358)) % 2.54/2.74 (step-pop @p360 :rule scope :premises (@p359)) % 2.54/2.74 (step-pop @p361 :rule scope :premises (@p360)) % 2.54/2.74 (step @p293 :rule process_scope :premises (@p361) :args (@t135)) % 2.54/2.74 (step @p311 :rule implies_elim :premises (@p293)) % 2.54/2.74 (step @p312 :rule cnf_and_neg :args (@t167)) % 2.54/2.74 (step @p313 :rule resolution :premises (@p312 @p311) :args (true @t167)) % 2.54/2.75 (step @p314 :rule eq_resolve :premises (@p313 @p232)) % 2.54/2.75 (step @p315 false :rule chain_m_resolution :premises (@p314 @p213 @p212 @p202 @p201 @p197 @p196 @p162 @p158 @p154 @p150 @p147 @p104 @p94 @p93 @p83 @p38 @p37 @p36) :args (false (@list false false false false false false false false false false false false false false false false false true) (@list @t134 @t129 @t138 @t140 @t143 @t118 @t147 @t150 @t152 @t108 @t109 @t99 @t156 @t92 @t82 @t163 @t165 @t60))) % 2.54/2.75 ) % 2.54/2.75 % SZS output end Proof % 2.54/2.76 % cvc5 exiting %------------------------------------------------------------------------------