%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : COM020+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 : n023.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 08:10:26 AM UTC 2026 % Result : Theorem 18.13s 18.35s % Output : Proof 18.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : COM020+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 % 0.18/0.34 % Computer : n023.cluster.edu % 0.18/0.34 % Model : x86_64 x86_64 % 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.34 % Memory : 8042.1875MB % 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.34 % CPULimit : 300 % 0.18/0.34 % WCLimit : 300 % 0.18/0.34 % DateTime : Mon Jun 1 20:29:28 EDT 2026 % 0.18/0.34 % CPUTime : % 0.33/0.49 %----Proving TF0_NAR, FOF, or CNF % 18.13/18.35 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 18.13/18.35 --- Run --no-e-matching --full-saturate-quant at 6... % 18.13/18.35 % SZS status Theorem % 18.13/18.35 % SZS output start Proof % 18.13/18.35 ( % 18.13/18.35 (declare-sort $$unsorted 0) % 18.13/18.35 (declare-const tptp.xv $$unsorted) % 18.13/18.35 (declare-const tptp.xu $$unsorted) % 18.13/18.35 (declare-const tptp.xa $$unsorted) % 18.13/18.35 (declare-const tptp.xb $$unsorted) % 18.13/18.35 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 18.13/18.35 (declare-const tptp.aRewritingSystem0 (-> $$unsorted Bool)) % 18.13/18.35 (declare-const tptp.sdtmndtplgtdt0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 18.13/18.35 (declare-const tptp.sdtmndtasgtdt0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 18.13/18.35 (declare-const tptp.xw $$unsorted) % 18.13/18.35 (declare-const tptp.xc $$unsorted) % 18.13/18.35 (declare-const tptp.aReductOfIn0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 18.13/18.35 (declare-const tptp.isLocallyConfluent0 (-> $$unsorted Bool)) % 18.13/18.35 (declare-const tptp.xd $$unsorted) % 18.13/18.35 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 18.13/18.35 (declare-const tptp.isConfluent0 (-> $$unsorted Bool)) % 18.13/18.35 (declare-const tptp.xR $$unsorted) % 18.13/18.35 (declare-const tptp.isTerminating0 (-> $$unsorted Bool)) % 18.13/18.35 (declare-const tptp.aNormalFormOfIn0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 18.13/18.35 (define @t1 () (@var "W0" $$unsorted)) % 18.13/18.35 (define @t2 () (tptp.aElement0 @t1)) % 18.13/18.35 (define @t3 () (@list @t1)) % 18.13/18.35 (define @t4 () (tptp.aRewritingSystem0 @t1)) % 18.13/18.35 (define @t5 () (@var "W2" $$unsorted)) % 18.13/18.35 (define @t6 () (tptp.aElement0 @t5)) % 18.13/18.35 (define @t7 () (@var "W1" $$unsorted)) % 18.13/18.35 (define @t8 () (tptp.aReductOfIn0 @t5 @t1 @t7)) % 18.13/18.35 (define @t9 () (@list @t5)) % 18.13/18.35 (define @t10 () (tptp.aRewritingSystem0 @t7)) % 18.13/18.35 (define @t11 () (and @t2 @t10)) % 18.13/18.35 (define @t12 () (@list @t1 @t7)) % 18.13/18.35 (define @t13 () (tptp.aElement0 @t7)) % 18.13/18.35 (define @t14 () (tptp.sdtmndtplgtdt0 @t1 @t7 @t5)) % 18.13/18.35 (define @t15 () (and @t2 @t10 @t6)) % 18.13/18.35 (define @t16 () (@list @t1 @t7 @t5)) % 18.13/18.35 (define @t17 () (@var "W3" $$unsorted)) % 18.13/18.35 (define @t18 () (tptp.sdtmndtplgtdt0 @t17 @t7 @t5)) % 18.13/18.35 (define @t19 () (tptp.aReductOfIn0 @t17 @t1 @t7)) % 18.13/18.35 (define @t20 () (tptp.aElement0 @t17)) % 18.13/18.35 (define @t21 () (and @t20 @t19 @t18)) % 18.13/18.35 (define @t22 () (@list @t17)) % 18.13/18.35 (define @t23 () (exists @t22 @t21)) % 18.13/18.35 (define @t24 () (or @t8 @t23)) % 18.13/18.35 (define @t25 () (= @t14 @t24)) % 18.13/18.35 (define @t26 () (=> @t15 @t25)) % 18.13/18.35 (define @t27 () (forall @t16 @t26)) % 18.13/18.35 (define @t28 () (and @t2 @t10 @t6 @t20)) % 18.13/18.35 (define @t29 () (@list @t1 @t7 @t5 @t17)) % 18.13/18.35 (define @t30 () (tptp.sdtmndtasgtdt0 @t1 @t7 @t5)) % 18.13/18.35 (define @t31 () (tptp.sdtmndtasgtdt0 @t1 @t7 @t17)) % 18.13/18.35 (define @t32 () (tptp.sdtmndtasgtdt0 @t5 @t7 @t17)) % 18.13/18.35 (define @t33 () (and @t30 @t32)) % 18.13/18.35 (define @t34 () (=> @t33 @t31)) % 18.13/18.35 (define @t35 () (forall @t29 (=> @t28 @t34))) % 18.13/18.35 (define @t36 () (@var "W4" $$unsorted)) % 18.13/18.35 (define @t37 () (exists (@list @t36) (and (tptp.aElement0 @t36) (tptp.sdtmndtasgtdt0 @t5 @t1 @t36) (tptp.sdtmndtasgtdt0 @t17 @t1 @t36)))) % 18.13/18.35 (define @t38 () (@list @t7 @t5 @t17)) % 18.13/18.35 (define @t39 () (tptp.iLess0 @t5 @t7)) % 18.13/18.35 (define @t40 () (tptp.sdtmndtplgtdt0 @t7 @t1 @t5)) % 18.13/18.35 (define @t41 () (=> @t40 @t39)) % 18.13/18.35 (define @t42 () (and @t13 @t6)) % 18.13/18.35 (define @t43 () (@list @t7 @t5)) % 18.13/18.35 (define @t44 () (forall @t43 (=> @t42 @t41))) % 18.13/18.35 (define @t45 () (tptp.isTerminating0 @t1)) % 18.13/18.35 (define @t46 () (= @t45 @t44)) % 18.13/18.35 (define @t47 () (=> @t4 @t46)) % 18.13/18.35 (define @t48 () (forall @t3 @t47)) % 18.13/18.35 (define @t49 () (tptp.aReductOfIn0 @t17 @t5 @t7)) % 18.13/18.35 (define @t50 () (exists @t22 @t49)) % 18.13/18.35 (define @t51 () (not @t50)) % 18.13/18.35 (define @t52 () (and @t6 @t30 @t51)) % 18.13/18.35 (define @t53 () (tptp.aNormalFormOfIn0 @t5 @t1 @t7)) % 18.13/18.35 (define @t54 () (= @t53 @t52)) % 18.13/18.35 (define @t55 () (forall @t9 @t54)) % 18.13/18.35 (define @t56 () (=> @t11 @t55)) % 18.13/18.35 (define @t57 () (forall @t12 @t56)) % 18.13/18.35 (define @t58 () (tptp.aRewritingSystem0 tptp.xR)) % 18.13/18.35 (define @t59 () (tptp.isTerminating0 tptp.xR)) % 18.13/18.35 (define @t60 () (tptp.aElement0 tptp.xb)) % 18.13/18.35 (define @t61 () (tptp.aElement0 tptp.xa)) % 18.13/18.35 (define @t62 () (tptp.sdtmndtasgtdt0 @t5 tptp.xR @t17)) % 18.13/18.35 (define @t63 () (tptp.sdtmndtasgtdt0 @t7 tptp.xR @t17)) % 18.13/18.35 (define @t64 () (and @t20 @t63 @t62)) % 18.13/18.35 (define @t65 () (exists @t22 @t64)) % 18.13/18.35 (define @t66 () (tptp.iLess0 @t1 tptp.xa)) % 18.13/18.35 (define @t67 () (=> @t66 @t65)) % 18.13/18.35 (define @t68 () (tptp.sdtmndtasgtdt0 @t1 tptp.xR @t5)) % 18.13/18.35 (define @t69 () (tptp.sdtmndtasgtdt0 @t1 tptp.xR @t7)) % 18.13/18.35 (define @t70 () (and @t2 @t13 @t6 @t69 @t68)) % 18.13/18.35 (define @t71 () (=> @t70 @t67)) % 18.13/18.35 (define @t72 () (forall @t16 @t71)) % 18.13/18.35 (define @t73 () (tptp.sdtmndtasgtdt0 tptp.xu tptp.xR tptp.xb)) % 18.13/18.35 (define @t74 () (tptp.aReductOfIn0 tptp.xu tptp.xa tptp.xR)) % 18.13/18.35 (define @t75 () (tptp.aElement0 tptp.xu)) % 18.13/18.35 (define @t76 () (tptp.sdtmndtasgtdt0 tptp.xu tptp.xR tptp.xw)) % 18.13/18.35 (define @t77 () (tptp.aElement0 tptp.xw)) % 18.13/18.35 (define @t78 () (tptp.aNormalFormOfIn0 tptp.xd tptp.xw tptp.xR)) % 18.13/18.35 (define @t79 () (tptp.sdtmndtasgtdt0 tptp.xd tptp.xR @t1)) % 18.13/18.35 (define @t80 () (tptp.sdtmndtasgtdt0 tptp.xb tptp.xR @t1)) % 18.13/18.35 (define @t81 () (and @t2 @t80 @t79)) % 18.13/18.35 (define @t82 () (exists @t3 @t81)) % 18.13/18.35 (define @t83 () (not @t82)) % 18.13/18.35 (define @t84 () (not @t32)) % 18.13/18.35 (define @t85 () (not @t30)) % 18.13/18.35 (define @t86 () (not @t20)) % 18.13/18.35 (define @t87 () (not @t6)) % 18.13/18.35 (define @t88 () (not @t10)) % 18.13/18.35 (define @t89 () (not @t2)) % 18.13/18.35 (define @t90 () (or @t89 @t88 @t87 @t86 @t85 @t84 @t31)) % 18.13/18.35 (define @t91 () (or @t85 @t84 @t31)) % 18.13/18.35 (define @t92 () (or @t89 @t88 @t87 @t86)) % 18.13/18.35 (define @t93 () (not @t62)) % 18.13/18.35 (define @t94 () (not @t63)) % 18.13/18.35 (define @t95 () (or @t86 @t94 @t93)) % 18.13/18.35 (define @t96 () (not (forall @t22 @t95))) % 18.13/18.35 (define @t97 () (not @t66)) % 18.13/18.35 (define @t98 () (not @t68)) % 18.13/18.35 (define @t99 () (not @t69)) % 18.13/18.35 (define @t100 () (not @t13)) % 18.13/18.35 (define @t101 () (or @t89 @t100 @t87 @t99 @t98)) % 18.13/18.35 (define @t102 () (=> @t66 @t96)) % 18.13/18.35 (define @t103 () (forall @t22 (not @t64))) % 18.13/18.35 (define @t104 () (not @t103)) % 18.13/18.35 (define @t105 () (not @t40)) % 18.13/18.35 (define @t106 () (or @t100 @t87 @t105 @t39)) % 18.13/18.35 (define @t107 () (= @t45 (forall @t43 @t106))) % 18.13/18.35 (define @t108 () (forall @t43 (or @t100 @t87 (not (tptp.sdtmndtplgtdt0 @t7 tptp.xR @t5)) @t39))) % 18.13/18.35 (define @t109 () (= @t59 @t108)) % 18.13/18.35 (define @t110 () (not @t58)) % 18.13/18.35 (define @t111 () (or @t110 @t109)) % 18.13/18.35 (define @t112 () (@list false false)) % 18.13/18.35 (define @t113 () (not @t18)) % 18.13/18.35 (define @t114 () (not @t19)) % 18.13/18.35 (define @t115 () (or @t86 @t114 @t113)) % 18.13/18.35 (define @t116 () (= @t14 (or @t8 (not (forall @t22 @t115))))) % 18.13/18.35 (define @t117 () (or @t89 @t88 @t87)) % 18.13/18.35 (define @t118 () (forall @t22 (not @t21))) % 18.13/18.35 (define @t119 () (not @t118)) % 18.13/18.35 (define @t120 () (or @t74 (not (forall @t22 (or @t86 (not (tptp.aReductOfIn0 @t17 tptp.xa tptp.xR)) (not (tptp.sdtmndtplgtdt0 @t17 tptp.xR tptp.xu))))))) % 18.13/18.35 (define @t121 () (tptp.sdtmndtplgtdt0 tptp.xa tptp.xR tptp.xu)) % 18.13/18.35 (define @t122 () (= @t121 @t120)) % 18.13/18.35 (define @t123 () (not @t75)) % 18.13/18.35 (define @t124 () (not @t61)) % 18.13/18.35 (define @t125 () (or @t124 @t110 @t123 @t122)) % 18.13/18.35 (define @t126 () (@list false false false false)) % 18.13/18.35 (define @t127 () (@list false)) % 18.13/18.35 (define @t128 () (tptp.iLess0 tptp.xu tptp.xa)) % 18.13/18.35 (define @t129 () (not @t121)) % 18.13/18.35 (define @t130 () (or @t124 @t123 @t129 @t128)) % 18.13/18.35 (define @t131 () (not @t79)) % 18.13/18.35 (define @t132 () (not @t80)) % 18.13/18.35 (define @t133 () (or @t89 @t132 @t131)) % 18.13/18.35 (define @t134 () (forall @t3 @t133)) % 18.13/18.35 (define @t135 () (forall @t3 (not @t81))) % 18.13/18.35 (define @t136 () (not @t135)) % 18.13/18.35 (define @t137 () (forall @t22 (or @t86 (not (tptp.sdtmndtasgtdt0 tptp.xb tptp.xR @t17)) (not (tptp.sdtmndtasgtdt0 tptp.xd tptp.xR @t17))))) % 18.13/18.35 (define @t138 () (@var "BOUND_VARIABLE_7719" $$unsorted)) % 18.13/18.35 (define @t139 () (= (tptp.aNormalFormOfIn0 @t138 @t1 @t7) (and (tptp.aElement0 @t138) (tptp.sdtmndtasgtdt0 @t1 @t7 @t138) (forall @t22 (not (tptp.aReductOfIn0 @t17 @t138 @t7)))))) % 18.13/18.35 (define @t140 () (or @t89 @t88 @t139)) % 18.13/18.35 (define @t141 () (@list @t138)) % 18.13/18.35 (define @t142 () (forall @t141 @t140)) % 18.13/18.35 (define @t143 () (forall @t141 @t139)) % 18.13/18.35 (define @t144 () (or @t89 @t88 @t143)) % 18.13/18.35 (define @t145 () (forall @t22 (not @t49))) % 18.13/18.35 (define @t146 () (forall @t9 (= @t53 (and @t6 @t30 @t145)))) % 18.13/18.35 (define @t147 () (or @t89 @t88 @t146)) % 18.13/18.35 (define @t148 () (tptp.sdtmndtasgtdt0 tptp.xw tptp.xR tptp.xd)) % 18.13/18.35 (define @t149 () (tptp.aElement0 tptp.xd)) % 18.13/18.35 (define @t150 () (and @t149 @t148 (forall @t22 (not (tptp.aReductOfIn0 @t17 tptp.xd tptp.xR))))) % 18.13/18.35 (define @t151 () (= @t78 @t150)) % 18.13/18.35 (define @t152 () (not @t77)) % 18.13/18.35 (define @t153 () (or @t152 @t110 @t151)) % 18.13/18.35 (define @t154 () (not @t150)) % 18.13/18.35 (define @t155 () (@list @t150)) % 18.13/18.35 (define @t156 () (not @t137)) % 18.13/18.35 (define @t157 () (not @t128)) % 18.13/18.35 (define @t158 () (tptp.sdtmndtasgtdt0 tptp.xu tptp.xR tptp.xd)) % 18.13/18.35 (define @t159 () (not @t158)) % 18.13/18.35 (define @t160 () (not @t73)) % 18.13/18.35 (define @t161 () (not @t149)) % 18.13/18.35 (define @t162 () (not @t60)) % 18.13/18.35 (define @t163 () (or @t123 @t162 @t161 @t160 @t159 @t157 @t156)) % 18.13/18.35 (define @t164 () (not @t148)) % 18.13/18.35 (define @t165 () (not @t76)) % 18.13/18.35 (define @t166 () (or @t123 @t110 @t152 @t161 @t165 @t164 @t158)) % 18.13/18.35 (define @t167 () (not @t166)) % 18.13/18.35 (define @t168 () (forall @t29 @t90)) % 18.13/18.35 (assume @p1 (forall @t3 (=> @t2 true))) % 18.13/18.35 (assume @p2 (forall @t3 (=> @t4 true))) % 18.13/18.35 (assume @p3 (forall @t12 (=> @t11 (forall @t9 (=> @t8 @t6))))) % 18.13/18.35 (assume @p4 (forall @t12 (=> (and @t2 @t13) (=> (tptp.iLess0 @t1 @t7) true)))) % 18.13/18.35 (assume @p5 (forall @t16 (=> @t15 (=> @t14 true)))) % 18.13/18.35 (assume @p6 @t27) % 18.13/18.35 (assume @p7 (forall @t29 (=> @t28 (=> (and @t14 (tptp.sdtmndtplgtdt0 @t5 @t7 @t17)) (tptp.sdtmndtplgtdt0 @t1 @t7 @t17))))) % 18.13/18.35 (assume @p8 (forall @t16 (=> @t15 (= @t30 (or (= @t1 @t5) @t14))))) % 18.13/18.35 (assume @p9 @t35) % 18.13/18.35 (assume @p10 (forall @t3 (=> @t4 (= (tptp.isConfluent0 @t1) (forall @t38 (=> (and @t13 @t6 @t20 (tptp.sdtmndtasgtdt0 @t7 @t1 @t5) (tptp.sdtmndtasgtdt0 @t7 @t1 @t17)) @t37)))))) % 18.13/18.35 (assume @p11 (forall @t3 (=> @t4 (= (tptp.isLocallyConfluent0 @t1) (forall @t38 (=> (and @t13 @t6 @t20 (tptp.aReductOfIn0 @t5 @t7 @t1) (tptp.aReductOfIn0 @t17 @t7 @t1)) @t37)))))) % 18.13/18.35 (assume @p12 @t48) % 18.13/18.35 (assume @p13 @t57) % 18.13/18.35 (assume @p14 (forall @t3 (=> (and @t4 @t45) (forall (@list @t7) (=> @t13 (exists @t9 (tptp.aNormalFormOfIn0 @t5 @t7 @t1))))))) % 18.13/18.35 (assume @p15 @t58) % 18.13/18.35 (assume @p16 (and (tptp.isLocallyConfluent0 tptp.xR) @t59)) % 18.13/18.35 (assume @p17 (and @t61 @t60 (tptp.aElement0 tptp.xc))) % 18.13/18.35 (assume @p18 @t72) % 18.13/18.35 (assume @p19 (and (tptp.sdtmndtplgtdt0 tptp.xa tptp.xR tptp.xb) (tptp.sdtmndtplgtdt0 tptp.xa tptp.xR tptp.xc))) % 18.13/18.35 (assume @p20 (and @t75 @t74 @t73)) % 18.13/18.35 (assume @p21 (and (tptp.aElement0 tptp.xv) (tptp.aReductOfIn0 tptp.xv tptp.xa tptp.xR) (tptp.sdtmndtasgtdt0 tptp.xv tptp.xR tptp.xc))) % 18.13/18.35 (assume @p22 (and @t77 @t76 (tptp.sdtmndtasgtdt0 tptp.xv tptp.xR tptp.xw))) % 18.13/18.35 (assume @p23 @t78) % 18.13/18.35 (assume @p24 @t83) % 18.13/18.35 (assume @p25 true) % 18.13/18.35 (step @p26 :rule aci_norm :args ((= (or @t92 @t91) @t90))) % 18.13/18.35 (step @p27 :rule aci_norm :args ((= (or (or @t85 @t84) @t31) @t91))) % 18.13/18.35 (step @p28 :rule refl :args (@t31)) % 18.13/18.35 (step @p29 :rule bool-and-de-morgan :args (@t30 @t32 true)) % 18.13/18.35 (step @p30 :rule nary_cong :premises (@p29 @p28) :args ((or (not @t33) @t31))) % 18.13/18.35 (step @p31 :rule trans :premises (@p30 @p27)) % 18.13/18.35 (step @p32 :rule bool-impl-elim :args (@t33 @t31)) % 18.13/18.35 (step @p33 :rule trans :premises (@p32 @p31)) % 18.13/18.35 (step @p34 :rule aci_norm :args ((= (or @t89 (or @t88 (or @t87 @t86))) @t92))) % 18.13/18.35 (step @p35 :rule bool-and-de-morgan :args (@t6 @t20 true)) % 18.13/18.35 (step @p36 :rule refl :args (@t88)) % 18.13/18.35 (step @p37 :rule nary_cong :premises (@p36 @p35) :args ((or @t88 (not (and @t6 @t20))))) % 18.13/18.35 (step @p38 :rule bool-and-de-morgan :args (@t10 @t6 (and @t20))) % 18.13/18.35 (step @p39 :rule trans :premises (@p38 @p37)) % 18.13/18.35 (step @p40 :rule refl :args (@t89)) % 18.13/18.35 (step @p41 :rule nary_cong :premises (@p40 @p39) :args ((or @t89 (not (and @t10 @t6 @t20))))) % 18.13/18.35 (step @p42 :rule bool-and-de-morgan :args (@t2 @t10 (and @t6 @t20))) % 18.13/18.35 (step @p43 :rule trans :premises (@p42 @p41)) % 18.13/18.35 (step @p44 :rule trans :premises (@p43 @p34)) % 18.13/18.35 (step @p45 :rule nary_cong :premises (@p44 @p33) :args ((or (not @t28) @t34))) % 18.13/18.35 (step @p46 :rule trans :premises (@p45 @p26)) % 18.13/18.35 (step @p47 :rule bool-impl-elim :args (@t28 @t34)) % 18.13/18.35 (step @p48 :rule trans :premises (@p47 @p46)) % 18.13/18.35 (step @p49 :rule cong :premises (@p48) :args (@t35)) % 18.13/18.35 (step @p50 :rule eq_resolve :premises (@p9 @p49)) % 18.13/18.35 (step @p51 :rule aci_norm :args ((= (or @t101 (or @t97 @t96)) (or @t89 @t100 @t87 @t99 @t98 @t97 @t96)))) % 18.13/18.35 (step @p52 :rule bool-impl-elim :args (@t66 @t96)) % 18.13/18.35 (step @p53 :rule aci_norm :args ((= (or @t89 (or @t100 (or @t87 (or @t99 @t98)))) @t101))) % 18.13/18.35 (step @p54 :rule bool-and-de-morgan :args (@t69 @t68 true)) % 18.13/18.35 (step @p55 :rule refl :args (@t87)) % 18.13/18.35 (step @p56 :rule nary_cong :premises (@p55 @p54) :args ((or @t87 (not (and @t69 @t68))))) % 18.13/18.35 (step @p57 :rule bool-and-de-morgan :args (@t6 @t69 (and @t68))) % 18.13/18.35 (step @p58 :rule trans :premises (@p57 @p56)) % 18.13/18.35 (step @p59 :rule refl :args (@t100)) % 18.13/18.35 (step @p60 :rule nary_cong :premises (@p59 @p58) :args ((or @t100 (not (and @t6 @t69 @t68))))) % 18.13/18.35 (step @p61 :rule bool-and-de-morgan :args (@t13 @t6 (and @t69 @t68))) % 18.13/18.35 (step @p62 :rule trans :premises (@p61 @p60)) % 18.13/18.35 (step @p63 :rule nary_cong :premises (@p40 @p62) :args ((or @t89 (not (and @t13 @t6 @t69 @t68))))) % 18.13/18.35 (step @p64 :rule bool-and-de-morgan :args (@t2 @t13 (and @t6 @t69 @t68))) % 18.13/18.35 (step @p65 :rule trans :premises (@p64 @p63)) % 18.13/18.35 (step @p66 :rule trans :premises (@p65 @p53)) % 18.13/18.35 (step @p67 :rule nary_cong :premises (@p66 @p52) :args ((or (not @t70) @t102))) % 18.13/18.35 (step @p68 :rule trans :premises (@p67 @p51)) % 18.13/18.35 (step @p69 :rule bool-impl-elim :args (@t70 @t102)) % 18.13/18.35 (step @p70 :rule trans :premises (@p69 @p68)) % 18.13/18.35 (step @p71 :rule cong :premises (@p70) :args ((forall @t16 (=> @t70 @t102)))) % 18.13/18.35 (step @p72 :rule aci_norm :args ((= (or @t86 (or @t94 @t93)) @t95))) % 18.13/18.35 (step @p73 :rule bool-and-de-morgan :args (@t63 @t62 true)) % 18.13/18.35 (step @p74 :rule refl :args (@t86)) % 18.13/18.35 (step @p75 :rule nary_cong :premises (@p74 @p73) :args ((or @t86 (not (and @t63 @t62))))) % 18.13/18.35 (step @p76 :rule bool-and-de-morgan :args (@t20 @t63 (and @t62))) % 18.13/18.35 (step @p77 :rule trans :premises (@p76 @p75)) % 18.13/18.35 (step @p78 :rule trans :premises (@p77 @p72)) % 18.13/18.35 (step @p79 :rule cong :premises (@p78) :args (@t103)) % 18.13/18.35 (step @p80 :rule cong :premises (@p79) :args (@t104)) % 18.13/18.35 (step @p81 :rule exists-elim :args ((= @t65 @t104))) % 18.13/18.35 (step @p82 :rule trans :premises (@p81 @p80)) % 18.13/18.35 (step @p83 :rule refl :args (@t66)) % 18.13/18.35 (step @p84 :rule cong :premises (@p83 @p82) :args (@t67)) % 18.13/18.35 (step @p85 :rule refl :args (@t70)) % 18.13/18.35 (step @p86 :rule cong :premises (@p85 @p84) :args (@t71)) % 18.13/18.35 (step @p87 :rule cong :premises (@p86) :args (@t72)) % 18.13/18.35 (step @p88 :rule trans :premises (@p87 @p71)) % 18.13/18.35 (step @p89 :rule eq_resolve :premises (@p18 @p88)) % 18.13/18.35 (step @p90 :rule instantiate :premises (@p89) :args ((@list tptp.xu tptp.xb tptp.xd))) % 18.13/18.35 (step @p91 :rule bool-impl-elim :args (@t4 @t107)) % 18.13/18.35 (step @p92 :rule cong :premises (@p91) :args ((forall @t3 (=> @t4 @t107)))) % 18.13/18.35 (step @p93 :rule aci_norm :args ((= (or (or @t100 @t87) (or @t105 @t39)) @t106))) % 18.13/18.35 (step @p94 :rule bool-impl-elim :args (@t40 @t39)) % 18.13/18.35 (step @p95 :rule bool-and-de-morgan :args (@t13 @t6 true)) % 18.13/18.35 (step @p96 :rule nary_cong :premises (@p95 @p94) :args ((or (not @t42) @t41))) % 18.13/18.35 (step @p97 :rule trans :premises (@p96 @p93)) % 18.13/18.35 (step @p98 :rule bool-impl-elim :args (@t42 @t41)) % 18.13/18.35 (step @p99 :rule trans :premises (@p98 @p97)) % 18.13/18.35 (step @p100 :rule cong :premises (@p99) :args (@t44)) % 18.13/18.35 (step @p101 :rule refl :args (@t45)) % 18.13/18.35 (step @p102 :rule cong :premises (@p101 @p100) :args (@t46)) % 18.13/18.35 (step @p103 :rule refl :args (@t4)) % 18.13/18.35 (step @p104 :rule cong :premises (@p103 @p102) :args (@t47)) % 18.13/18.35 (step @p105 :rule cong :premises (@p104) :args (@t48)) % 18.13/18.35 (step @p106 :rule trans :premises (@p105 @p92)) % 18.13/18.35 (step @p107 :rule eq_resolve :premises (@p12 @p106)) % 18.13/18.35 (step @p108 :rule instantiate :premises (@p107) :args ((@list tptp.xR))) % 18.13/18.35 (step @p109 :rule cnf_or_pos :args (@t111)) % 18.13/18.35 (step @p110 :rule reordering :premises (@p109) :args ((or @t110 @t109 (not @t111)))) % 18.13/18.35 (step @p111 :rule chain_m_resolution :premises (@p110 @p15 @p108) :args (@t109 @t112 (@list @t58 @t111))) % 18.13/18.35 (step @p112 :rule and_elim :premises (@p16) :args (1)) % 18.13/18.35 (step @p113 :rule cnf_equiv_pos1 :args (@t109)) % 18.13/18.35 (step @p114 :rule reordering :premises (@p113) :args ((or (not @t59) @t108 (not @t109)))) % 18.13/18.35 (step @p115 :rule chain_m_resolution :premises (@p114 @p112 @p111) :args (@t108 @t112 (@list @t59 @t109))) % 18.13/18.35 (step @p116 :rule instantiate :premises (@p115) :args ((@list tptp.xa tptp.xu))) % 18.13/18.35 (step @p117 :rule aci_norm :args ((= (or @t117 @t116) (or @t89 @t88 @t87 @t116)))) % 18.13/18.35 (step @p118 :rule refl :args (@t116)) % 18.13/18.35 (step @p119 :rule aci_norm :args ((= (or @t89 (or @t88 @t87)) @t117))) % 18.13/18.35 (step @p120 :rule bool-and-de-morgan :args (@t10 @t6 true)) % 18.13/18.35 (step @p121 :rule nary_cong :premises (@p40 @p120) :args ((or @t89 (not (and @t10 @t6))))) % 18.13/18.35 (step @p122 :rule bool-and-de-morgan :args (@t2 @t10 (and @t6))) % 18.13/18.35 (step @p123 :rule trans :premises (@p122 @p121)) % 18.13/18.35 (step @p124 :rule trans :premises (@p123 @p119)) % 18.13/18.35 (step @p125 :rule nary_cong :premises (@p124 @p118) :args ((or (not @t15) @t116))) % 18.13/18.35 (step @p126 :rule trans :premises (@p125 @p117)) % 18.13/18.35 (step @p127 :rule bool-impl-elim :args (@t15 @t116)) % 18.13/18.35 (step @p128 :rule trans :premises (@p127 @p126)) % 18.13/18.35 (step @p129 :rule cong :premises (@p128) :args ((forall @t16 (=> @t15 @t116)))) % 18.13/18.35 (step @p130 :rule aci_norm :args ((= (or @t86 (or @t114 @t113)) @t115))) % 18.13/18.35 (step @p131 :rule bool-and-de-morgan :args (@t19 @t18 true)) % 18.13/18.35 (step @p132 :rule nary_cong :premises (@p74 @p131) :args ((or @t86 (not (and @t19 @t18))))) % 18.13/18.35 (step @p133 :rule bool-and-de-morgan :args (@t20 @t19 (and @t18))) % 18.13/18.35 (step @p134 :rule trans :premises (@p133 @p132)) % 18.13/18.35 (step @p135 :rule trans :premises (@p134 @p130)) % 18.13/18.35 (step @p136 :rule cong :premises (@p135) :args (@t118)) % 18.13/18.35 (step @p137 :rule cong :premises (@p136) :args (@t119)) % 18.13/18.35 (step @p138 :rule exists-elim :args ((= @t23 @t119))) % 18.13/18.35 (step @p139 :rule trans :premises (@p138 @p137)) % 18.13/18.35 (step @p140 :rule refl :args (@t8)) % 18.13/18.35 (step @p141 :rule nary_cong :premises (@p140 @p139) :args (@t24)) % 18.13/18.35 (step @p142 :rule refl :args (@t14)) % 18.13/18.35 (step @p143 :rule cong :premises (@p142 @p141) :args (@t25)) % 18.13/18.35 (step @p144 :rule refl :args (@t15)) % 18.13/18.35 (step @p145 :rule cong :premises (@p144 @p143) :args (@t26)) % 18.13/18.35 (step @p146 :rule cong :premises (@p145) :args (@t27)) % 18.13/18.35 (step @p147 :rule trans :premises (@p146 @p129)) % 18.13/18.35 (step @p148 :rule eq_resolve :premises (@p6 @p147)) % 18.13/18.35 (step @p149 :rule instantiate :premises (@p148) :args ((@list tptp.xa tptp.xR tptp.xu))) % 18.13/18.35 (step @p150 :rule and_elim :premises (@p20) :args (0)) % 18.13/18.35 (step @p151 :rule and_elim :premises (@p17) :args (0)) % 18.13/18.35 (step @p152 :rule cnf_or_pos :args (@t125)) % 18.13/18.35 (step @p153 :rule reordering :premises (@p152) :args ((or @t110 @t124 @t123 @t122 (not @t125)))) % 18.13/18.35 (step @p154 :rule chain_m_resolution :premises (@p153 @p15 @p151 @p150 @p149) :args (@t122 @t126 (@list @t58 @t61 @t75 @t125))) % 18.13/18.35 (step @p155 :rule and_elim :premises (@p20) :args (1)) % 18.13/18.35 (step @p156 :rule cnf_or_neg :args (@t120 0)) % 18.13/18.35 (step @p157 :rule reordering :premises (@p156) :args ((or (not @t74) @t120))) % 18.13/18.35 (step @p158 :rule chain_m_resolution :premises (@p157 @p155) :args (@t120 @t127 (@list @t74))) % 18.13/18.35 (step @p159 :rule cnf_equiv_pos2 :args (@t122)) % 18.13/18.35 (step @p160 :rule reordering :premises (@p159) :args ((or @t121 (not @t120) (not @t122)))) % 18.13/18.35 (step @p161 :rule chain_m_resolution :premises (@p160 @p158 @p154) :args (@t121 @t112 (@list @t120 @t122))) % 18.13/18.35 (step @p162 :rule cnf_or_pos :args (@t130)) % 18.13/18.35 (step @p163 :rule reordering :premises (@p162) :args ((or @t124 @t123 @t129 @t128 (not @t130)))) % 18.13/18.35 (step @p164 :rule chain_m_resolution :premises (@p163 @p151 @p150 @p161 @p116) :args (@t128 @t126 (@list @t61 @t75 @t121 @t130))) % 18.13/18.35 (step @p165 :rule bool-double-not-elim :args (@t134)) % 18.13/18.35 (step @p166 :rule aci_norm :args ((= (or @t89 (or @t132 @t131)) @t133))) % 18.13/18.35 (step @p167 :rule bool-and-de-morgan :args (@t80 @t79 true)) % 18.13/18.35 (step @p168 :rule nary_cong :premises (@p40 @p167) :args ((or @t89 (not (and @t80 @t79))))) % 18.13/18.35 (step @p169 :rule bool-and-de-morgan :args (@t2 @t80 (and @t79))) % 18.13/18.35 (step @p170 :rule trans :premises (@p169 @p168)) % 18.13/18.35 (step @p171 :rule trans :premises (@p170 @p166)) % 18.13/18.35 (step @p172 :rule cong :premises (@p171) :args (@t135)) % 18.13/18.35 (step @p173 :rule cong :premises (@p172) :args (@t136)) % 18.13/18.35 (step @p174 :rule exists-elim :args ((= @t82 @t136))) % 18.13/18.35 (step @p175 :rule trans :premises (@p174 @p173)) % 18.13/18.35 (step @p176 :rule cong :premises (@p175) :args (@t83)) % 18.13/18.35 (step @p177 :rule trans :premises (@p176 @p165)) % 18.13/18.35 (step @p178 :rule eq_resolve :premises (@p24 @p177)) % 18.13/18.35 (step @p179 :rule alpha_equiv :args (@t134 (@list @t1) (@list @t17))) % 18.13/18.35 (step @p180 :rule equiv_elim1 :premises (@p179)) % 18.13/18.35 (step @p181 :rule chain_m_resolution :premises (@p180 @p178) :args (@t137 @t127 (@list @t134))) % 18.13/18.35 (step @p182 :rule quant-merge-prenex :args ((= (forall @t12 @t142) (forall (@list @t1 @t7 @t138) @t140)))) % 18.13/18.35 (step @p183 :rule alpha_equiv :args (@t143 (@list @t138) (@list @t5))) % 18.13/18.35 (step @p184 :rule nary_cong :premises (@p40 @p36 @p183) :args (@t144)) % 18.13/18.35 (step @p185 :rule quant-miniscope-or :args ((= @t142 @t144))) % 18.13/18.35 (step @p186 :rule trans :premises (@p185 @p184)) % 18.13/18.35 (step @p187 :rule symm :premises (@p186)) % 18.13/18.35 (step @p188 :rule cong :premises (@p187) :args ((forall @t12 @t147))) % 18.13/18.35 (step @p189 :rule trans :premises (@p188 @p182)) % 18.13/18.35 (step @p190 :rule aci_norm :args ((= (or (or @t89 @t88) @t146) @t147))) % 18.13/18.35 (step @p191 :rule refl :args (@t146)) % 18.13/18.35 (step @p192 :rule bool-and-de-morgan :args (@t2 @t10 true)) % 18.13/18.35 (step @p193 :rule nary_cong :premises (@p192 @p191) :args ((or (not @t11) @t146))) % 18.13/18.35 (step @p194 :rule trans :premises (@p193 @p190)) % 18.13/18.35 (step @p195 :rule bool-impl-elim :args (@t11 @t146)) % 18.13/18.35 (step @p196 :rule trans :premises (@p195 @p194)) % 18.13/18.35 (step @p197 :rule cong :premises (@p196) :args ((forall @t12 (=> @t11 @t146)))) % 18.13/18.35 (step @p198 :rule trans :premises (@p197 @p189)) % 18.13/18.35 (step @p199 :rule bool-double-not-elim :args (@t145)) % 18.13/18.35 (step @p200 :rule exists-elim :args ((= @t50 (not @t145)))) % 18.13/18.35 (step @p201 :rule cong :premises (@p200) :args (@t51)) % 18.13/18.35 (step @p202 :rule trans :premises (@p201 @p199)) % 18.13/18.35 (step @p203 :rule refl :args (@t30)) % 18.13/18.35 (step @p204 :rule refl :args (@t6)) % 18.13/18.35 (step @p205 :rule nary_cong :premises (@p204 @p203 @p202) :args (@t52)) % 18.13/18.35 (step @p206 :rule refl :args (@t53)) % 18.13/18.35 (step @p207 :rule cong :premises (@p206 @p205) :args (@t54)) % 18.13/18.35 (step @p208 :rule cong :premises (@p207) :args (@t55)) % 18.13/18.35 (step @p209 :rule refl :args (@t11)) % 18.13/18.35 (step @p210 :rule cong :premises (@p209 @p208) :args (@t56)) % 18.13/18.35 (step @p211 :rule cong :premises (@p210) :args (@t57)) % 18.13/18.35 (step @p212 :rule trans :premises (@p211 @p198)) % 18.13/18.35 (step @p213 :rule eq_resolve :premises (@p13 @p212)) % 18.13/18.35 (step @p214 :rule instantiate :premises (@p213) :args ((@list tptp.xw tptp.xR tptp.xd))) % 18.13/18.35 (step @p215 :rule and_elim :premises (@p22) :args (0)) % 18.13/18.35 (step @p216 :rule cnf_or_pos :args (@t153)) % 18.13/18.35 (step @p217 :rule reordering :premises (@p216) :args ((or @t110 @t152 @t151 (not @t153)))) % 18.13/18.35 (step @p218 :rule chain_m_resolution :premises (@p217 @p15 @p215 @p214) :args (@t151 (@list false false false) (@list @t58 @t77 @t153))) % 18.13/18.35 (step @p219 :rule cnf_equiv_pos1 :args (@t151)) % 18.13/18.35 (step @p220 :rule reordering :premises (@p219) :args ((or (not @t78) @t150 (not @t151)))) % 18.13/18.35 (step @p221 :rule chain_m_resolution :premises (@p220 @p23 @p218) :args (@t150 @t112 (@list @t78 @t151))) % 18.13/18.35 (step @p222 :rule cnf_and_pos :args (@t150 0)) % 18.13/18.35 (step @p223 :rule reordering :premises (@p222) :args ((or @t149 @t154))) % 18.13/18.35 (step @p224 :rule chain_m_resolution :premises (@p223 @p221) :args (@t149 @t127 @t155)) % 18.13/18.35 (step @p225 :rule and_elim :premises (@p20) :args (2)) % 18.13/18.35 (step @p226 :rule and_elim :premises (@p17) :args (1)) % 18.13/18.35 (step @p227 :rule cnf_or_pos :args (@t163)) % 18.13/18.35 (step @p228 :rule reordering :premises (@p227) :args ((or @t162 @t123 @t160 @t161 @t156 @t157 @t159 (not @t163)))) % 18.13/18.35 (step @p229 :rule chain_m_resolution :premises (@p228 @p226 @p150 @p225 @p224 @p181 @p164 @p90) :args (@t159 (@list false false false false false false false) (@list @t60 @t75 @t73 @t149 @t137 @t128 @t163))) % 18.13/18.35 (step @p230 :rule cnf_and_pos :args (@t150 1)) % 18.13/18.35 (step @p231 :rule reordering :premises (@p230) :args ((or @t148 @t154))) % 18.13/18.35 (step @p232 :rule chain_m_resolution :premises (@p231 @p221) :args (@t148 @t127 @t155)) % 18.13/18.35 (step @p233 :rule and_elim :premises (@p22) :args (1)) % 18.13/18.35 (step @p234 :rule cnf_or_pos :args (@t166)) % 18.13/18.35 (step @p235 :rule reordering :premises (@p234) :args ((or @t110 @t123 @t152 @t165 @t161 @t164 @t158 @t167))) % 18.13/18.35 (step @p236 :rule chain_m_resolution :premises (@p235 @p15 @p150 @p215 @p233 @p224 @p232 @p229) :args (@t167 (@list false false false false false false true) (@list @t58 @t75 @t77 @t76 @t149 @t148 @t158))) % 18.13/18.35 (assume-push @p243 @t168) % 18.13/18.35 (step @p238 :rule instantiate :premises (@p50) :args ((@list tptp.xu tptp.xR tptp.xw tptp.xd))) % 18.13/18.35 (step-pop @p244 :rule scope :premises (@p238)) % 18.13/18.35 (step @p239 :rule process_scope :premises (@p244) :args (@t166)) % 18.13/18.35 (step @p241 :rule implies_elim :premises (@p239)) % 18.13/18.35 (step @p242 false :rule chain_m_resolution :premises (@p241 @p236 @p50) :args (false (@list true false) (@list @t166 @t168))) % 18.13/18.35 ) % 18.13/18.35 % SZS output end Proof % 18.13/18.35 % cvc5 exiting %------------------------------------------------------------------------------