%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : COM018+4 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n007.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 08:10:25 AM UTC 2026 % Result : Theorem 15.50s 15.78s % Output : Proof 15.50s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : COM018+4 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n007.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 : Mon Jun 1 20:27:56 EDT 2026 % 0.17/0.34 % CPUTime : % 0.30/0.50 %----Proving TF0_NAR, FOF, or CNF % 15.50/15.78 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 15.50/15.78 --- Run --no-e-matching --full-saturate-quant at 6... % 15.50/15.78 % SZS status Theorem % 15.50/15.78 % SZS output start Proof % 15.50/15.78 ( % 15.50/15.78 (declare-sort $$unsorted 0) % 15.50/15.78 (declare-const tptp.xv $$unsorted) % 15.50/15.78 (declare-const tptp.xu $$unsorted) % 15.50/15.78 (declare-const tptp.xa $$unsorted) % 15.50/15.78 (declare-const tptp.xw $$unsorted) % 15.50/15.78 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 15.50/15.78 (declare-const tptp.aRewritingSystem0 (-> $$unsorted Bool)) % 15.50/15.78 (declare-const tptp.sdtmndtplgtdt0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 15.50/15.78 (declare-const tptp.sdtmndtasgtdt0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 15.50/15.78 (declare-const tptp.aReductOfIn0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 15.50/15.78 (declare-const tptp.isLocallyConfluent0 (-> $$unsorted Bool)) % 15.50/15.78 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 15.50/15.78 (declare-const tptp.isConfluent0 (-> $$unsorted Bool)) % 15.50/15.78 (declare-const tptp.xR $$unsorted) % 15.50/15.78 (declare-const tptp.isTerminating0 (-> $$unsorted Bool)) % 15.50/15.78 (declare-const tptp.aNormalFormOfIn0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 15.50/15.78 (declare-const tptp.xc $$unsorted) % 15.50/15.78 (declare-const tptp.xb $$unsorted) % 15.50/15.78 (define @t1 () (@var "W0" $$unsorted)) % 15.50/15.78 (define @t2 () (tptp.aElement0 @t1)) % 15.50/15.78 (define @t3 () (@list @t1)) % 15.50/15.78 (define @t4 () (tptp.aRewritingSystem0 @t1)) % 15.50/15.78 (define @t5 () (@var "W2" $$unsorted)) % 15.50/15.78 (define @t6 () (tptp.aElement0 @t5)) % 15.50/15.78 (define @t7 () (@var "W1" $$unsorted)) % 15.50/15.78 (define @t8 () (tptp.aReductOfIn0 @t5 @t1 @t7)) % 15.50/15.78 (define @t9 () (@list @t5)) % 15.50/15.78 (define @t10 () (tptp.aRewritingSystem0 @t7)) % 15.50/15.78 (define @t11 () (and @t2 @t10)) % 15.50/15.78 (define @t12 () (@list @t1 @t7)) % 15.50/15.78 (define @t13 () (tptp.aElement0 @t7)) % 15.50/15.78 (define @t14 () (and @t2 @t13)) % 15.50/15.78 (define @t15 () (tptp.sdtmndtplgtdt0 @t1 @t7 @t5)) % 15.50/15.78 (define @t16 () (and @t2 @t10 @t6)) % 15.50/15.78 (define @t17 () (@list @t1 @t7 @t5)) % 15.50/15.78 (define @t18 () (@var "W3" $$unsorted)) % 15.50/15.78 (define @t19 () (tptp.aElement0 @t18)) % 15.50/15.78 (define @t20 () (@list @t18)) % 15.50/15.78 (define @t21 () (and @t2 @t10 @t6 @t19)) % 15.50/15.78 (define @t22 () (@list @t1 @t7 @t5 @t18)) % 15.50/15.78 (define @t23 () (= @t1 @t5)) % 15.50/15.78 (define @t24 () (tptp.sdtmndtasgtdt0 @t1 @t7 @t5)) % 15.50/15.78 (define @t25 () (@var "W4" $$unsorted)) % 15.50/15.78 (define @t26 () (tptp.aElement0 @t25)) % 15.50/15.78 (define @t27 () (@list @t25)) % 15.50/15.78 (define @t28 () (exists @t27 (and @t26 (tptp.sdtmndtasgtdt0 @t5 @t1 @t25) (tptp.sdtmndtasgtdt0 @t18 @t1 @t25)))) % 15.50/15.78 (define @t29 () (@list @t7 @t5 @t18)) % 15.50/15.78 (define @t30 () (tptp.isTerminating0 @t1)) % 15.50/15.78 (define @t31 () (tptp.aNormalFormOfIn0 @t5 @t7 @t1)) % 15.50/15.78 (define @t32 () (exists @t9 @t31)) % 15.50/15.78 (define @t33 () (=> @t13 @t32)) % 15.50/15.78 (define @t34 () (@list @t7)) % 15.50/15.78 (define @t35 () (forall @t34 @t33)) % 15.50/15.78 (define @t36 () (and @t4 @t30)) % 15.50/15.78 (define @t37 () (=> @t36 @t35)) % 15.50/15.78 (define @t38 () (forall @t3 @t37)) % 15.50/15.78 (define @t39 () (tptp.aRewritingSystem0 tptp.xR)) % 15.50/15.78 (define @t40 () (tptp.isTerminating0 tptp.xR)) % 15.50/15.78 (define @t41 () (tptp.sdtmndtplgtdt0 @t1 tptp.xR @t7)) % 15.50/15.78 (define @t42 () (tptp.aReductOfIn0 @t5 @t1 tptp.xR)) % 15.50/15.78 (define @t43 () (tptp.aReductOfIn0 @t7 @t1 tptp.xR)) % 15.50/15.78 (define @t44 () (tptp.sdtmndtplgtdt0 @t25 tptp.xR @t18)) % 15.50/15.78 (define @t45 () (exists @t20 (and @t19 (or (= @t7 @t18) (and (or (tptp.aReductOfIn0 @t18 @t7 tptp.xR) (exists @t27 (and @t26 (tptp.aReductOfIn0 @t25 @t7 tptp.xR) @t44))) (tptp.sdtmndtplgtdt0 @t7 tptp.xR @t18))) (tptp.sdtmndtasgtdt0 @t7 tptp.xR @t18) (or (= @t5 @t18) (and (or (tptp.aReductOfIn0 @t18 @t5 tptp.xR) (exists @t27 (and @t26 (tptp.aReductOfIn0 @t25 @t5 tptp.xR) @t44))) (tptp.sdtmndtplgtdt0 @t5 tptp.xR @t18))) (tptp.sdtmndtasgtdt0 @t5 tptp.xR @t18)))) % 15.50/15.78 (define @t46 () (tptp.aReductOfIn0 @t18 @t1 tptp.xR)) % 15.50/15.78 (define @t47 () (tptp.sdtmndtplgtdt0 @t1 tptp.xR tptp.xc)) % 15.50/15.78 (define @t48 () (tptp.aReductOfIn0 @t1 tptp.xa tptp.xR)) % 15.50/15.78 (define @t49 () (tptp.sdtmndtplgtdt0 @t1 tptp.xR tptp.xb)) % 15.50/15.78 (define @t50 () (tptp.aReductOfIn0 @t1 tptp.xu tptp.xR)) % 15.50/15.78 (define @t51 () (tptp.aReductOfIn0 @t1 tptp.xv tptp.xR)) % 15.50/15.78 (define @t52 () (tptp.sdtmndtplgtdt0 @t1 tptp.xR tptp.xw)) % 15.50/15.78 (define @t53 () (tptp.aElement0 tptp.xw)) % 15.50/15.78 (define @t54 () (tptp.aNormalFormOfIn0 @t1 tptp.xw tptp.xR)) % 15.50/15.78 (define @t55 () (exists @t34 @t43)) % 15.50/15.78 (define @t56 () (not @t55)) % 15.50/15.78 (define @t57 () (tptp.sdtmndtasgtdt0 tptp.xw tptp.xR @t1)) % 15.50/15.78 (define @t58 () (tptp.sdtmndtplgtdt0 tptp.xw tptp.xR @t1)) % 15.50/15.78 (define @t59 () (tptp.sdtmndtplgtdt0 @t7 tptp.xR @t1)) % 15.50/15.78 (define @t60 () (tptp.aReductOfIn0 @t7 tptp.xw tptp.xR)) % 15.50/15.78 (define @t61 () (and @t13 @t60 @t59)) % 15.50/15.78 (define @t62 () (exists @t34 @t61)) % 15.50/15.78 (define @t63 () (tptp.aReductOfIn0 @t1 tptp.xw tptp.xR)) % 15.50/15.78 (define @t64 () (or (= tptp.xw @t1) @t63 @t62 @t58 @t57)) % 15.50/15.78 (define @t65 () (and @t2 @t64 @t56)) % 15.50/15.78 (define @t66 () (or @t65 @t54)) % 15.50/15.78 (define @t67 () (exists @t3 @t66)) % 15.50/15.78 (define @t68 () (not @t67)) % 15.50/15.78 (define @t69 () (@var "BOUND_VARIABLE_8159" $$unsorted)) % 15.50/15.78 (define @t70 () (forall (@list @t69) (not (tptp.aNormalFormOfIn0 @t69 tptp.xw tptp.xR)))) % 15.50/15.78 (define @t71 () (@var "BOUND_VARIABLE_8135" $$unsorted)) % 15.50/15.78 (define @t72 () (not (forall @t34 (not (tptp.aReductOfIn0 @t7 @t71 tptp.xR))))) % 15.50/15.78 (define @t73 () (not (tptp.sdtmndtasgtdt0 tptp.xw tptp.xR @t71))) % 15.50/15.78 (define @t74 () (not (tptp.sdtmndtplgtdt0 tptp.xw tptp.xR @t71))) % 15.50/15.78 (define @t75 () (@var "BOUND_VARIABLE_8171" $$unsorted)) % 15.50/15.78 (define @t76 () (or (not (tptp.aElement0 @t75)) (not (tptp.aReductOfIn0 @t75 tptp.xw tptp.xR)) (not (tptp.sdtmndtplgtdt0 @t75 tptp.xR @t71)))) % 15.50/15.78 (define @t77 () (not (tptp.aReductOfIn0 @t71 tptp.xw tptp.xR))) % 15.50/15.78 (define @t78 () (not (= tptp.xw @t71))) % 15.50/15.78 (define @t79 () (and @t78 @t77 @t76 @t74 @t73)) % 15.50/15.78 (define @t80 () (not (tptp.aElement0 @t71))) % 15.50/15.78 (define @t81 () (or @t80 @t79 @t72)) % 15.50/15.78 (define @t82 () (forall (@list @t71 @t75) @t81)) % 15.50/15.78 (define @t83 () (@list @t75)) % 15.50/15.78 (define @t84 () (forall @t83 @t81)) % 15.50/15.78 (define @t85 () (@list @t71)) % 15.50/15.78 (define @t86 () (forall @t83 @t73)) % 15.50/15.78 (define @t87 () (forall @t83 @t74)) % 15.50/15.78 (define @t88 () (forall @t83 @t76)) % 15.50/15.78 (define @t89 () (@list @t7)) % 15.50/15.78 (define @t90 () (forall @t83 @t77)) % 15.50/15.78 (define @t91 () (forall @t83 @t78)) % 15.50/15.78 (define @t92 () (and @t91 @t90 @t88 @t87 @t86)) % 15.50/15.78 (define @t93 () (forall @t83 @t79)) % 15.50/15.78 (define @t94 () (or @t80 @t93 @t72)) % 15.50/15.78 (define @t95 () (not @t60)) % 15.50/15.78 (define @t96 () (not @t13)) % 15.50/15.78 (define @t97 () (forall @t34 (or @t96 @t95 (not (tptp.sdtmndtplgtdt0 @t7 tptp.xR @t71))))) % 15.50/15.78 (define @t98 () (not (= @t71 tptp.xw))) % 15.50/15.78 (define @t99 () (and @t98 @t77 @t97 @t74 @t73)) % 15.50/15.78 (define @t100 () (or @t80 @t99 @t72)) % 15.50/15.78 (define @t101 () (forall @t85 @t100)) % 15.50/15.78 (define @t102 () (not @t54)) % 15.50/15.78 (define @t103 () (forall @t3 @t102)) % 15.50/15.78 (define @t104 () (@list @t1)) % 15.50/15.78 (define @t105 () (@list @t69)) % 15.50/15.78 (define @t106 () (forall @t34 (not @t43))) % 15.50/15.78 (define @t107 () (not @t106)) % 15.50/15.78 (define @t108 () (not @t57)) % 15.50/15.78 (define @t109 () (not @t58)) % 15.50/15.78 (define @t110 () (not @t59)) % 15.50/15.78 (define @t111 () (or @t96 @t95 @t110)) % 15.50/15.78 (define @t112 () (forall @t34 @t111)) % 15.50/15.78 (define @t113 () (not @t63)) % 15.50/15.78 (define @t114 () (= @t1 tptp.xw)) % 15.50/15.78 (define @t115 () (not @t114)) % 15.50/15.78 (define @t116 () (not @t2)) % 15.50/15.78 (define @t117 () (or @t116 (and @t115 @t113 @t112 @t109 @t108) @t107)) % 15.50/15.78 (define @t118 () (forall @t3 @t117)) % 15.50/15.78 (define @t119 () (and @t118 @t103)) % 15.50/15.78 (define @t120 () (not @t112)) % 15.50/15.78 (define @t121 () (not @t120)) % 15.50/15.78 (define @t122 () (and @t115 @t113 @t121 @t109 @t108)) % 15.50/15.78 (define @t123 () (or @t114 @t63 @t120 @t58 @t57)) % 15.50/15.78 (define @t124 () (not @t123)) % 15.50/15.78 (define @t125 () (or @t116 @t124 @t107)) % 15.50/15.78 (define @t126 () (and @t2 @t123 @t106)) % 15.50/15.78 (define @t127 () (or @t126 @t54)) % 15.50/15.78 (define @t128 () (forall @t3 (not @t127))) % 15.50/15.78 (define @t129 () (not @t128)) % 15.50/15.78 (define @t130 () (forall @t34 (not @t61))) % 15.50/15.78 (define @t131 () (not @t130)) % 15.50/15.78 (define @t132 () (forall @t9 (not (tptp.aNormalFormOfIn0 @t5 tptp.xw tptp.xR)))) % 15.50/15.78 (define @t133 () (@var "BOUND_VARIABLE_7848" $$unsorted)) % 15.50/15.78 (define @t134 () (not (forall @t9 (not (tptp.aNormalFormOfIn0 @t5 @t133 @t1))))) % 15.50/15.78 (define @t135 () (not (tptp.aElement0 @t133))) % 15.50/15.78 (define @t136 () (not @t30)) % 15.50/15.78 (define @t137 () (not @t4)) % 15.50/15.78 (define @t138 () (or @t135 @t134)) % 15.50/15.78 (define @t139 () (or @t137 @t136 @t138)) % 15.50/15.78 (define @t140 () (forall (@list @t1 @t133) @t139)) % 15.50/15.78 (define @t141 () (@list @t133)) % 15.50/15.78 (define @t142 () (forall @t141 @t139)) % 15.50/15.78 (define @t143 () (forall @t141 @t138)) % 15.50/15.78 (define @t144 () (or @t137 @t136 @t143)) % 15.50/15.78 (define @t145 () (not (forall @t9 (not @t31)))) % 15.50/15.78 (define @t146 () (forall @t34 (or @t96 @t145))) % 15.50/15.78 (define @t147 () (or @t137 @t136 @t146)) % 15.50/15.78 (define @t148 () (not @t132)) % 15.50/15.78 (define @t149 () (not @t53)) % 15.50/15.78 (define @t150 () (not @t40)) % 15.50/15.78 (define @t151 () (not @t39)) % 15.50/15.78 (define @t152 () (or @t151 @t150 @t149 @t148)) % 15.50/15.78 (assume @p1 (forall @t3 (=> @t2 true))) % 15.50/15.78 (assume @p2 (forall @t3 (=> @t4 true))) % 15.50/15.78 (assume @p3 (forall @t12 (=> @t11 (forall @t9 (=> @t8 @t6))))) % 15.50/15.78 (assume @p4 (forall @t12 (=> @t14 (=> (tptp.iLess0 @t1 @t7) true)))) % 15.50/15.78 (assume @p5 (forall @t17 (=> @t16 (=> @t15 true)))) % 15.50/15.78 (assume @p6 (forall @t17 (=> @t16 (= @t15 (or @t8 (exists @t20 (and @t19 (tptp.aReductOfIn0 @t18 @t1 @t7) (tptp.sdtmndtplgtdt0 @t18 @t7 @t5)))))))) % 15.50/15.78 (assume @p7 (forall @t22 (=> @t21 (=> (and @t15 (tptp.sdtmndtplgtdt0 @t5 @t7 @t18)) (tptp.sdtmndtplgtdt0 @t1 @t7 @t18))))) % 15.50/15.78 (assume @p8 (forall @t17 (=> @t16 (= @t24 (or @t23 @t15))))) % 15.50/15.78 (assume @p9 (forall @t22 (=> @t21 (=> (and @t24 (tptp.sdtmndtasgtdt0 @t5 @t7 @t18)) (tptp.sdtmndtasgtdt0 @t1 @t7 @t18))))) % 15.50/15.78 (assume @p10 (forall @t3 (=> @t4 (= (tptp.isConfluent0 @t1) (forall @t29 (=> (and @t13 @t6 @t19 (tptp.sdtmndtasgtdt0 @t7 @t1 @t5) (tptp.sdtmndtasgtdt0 @t7 @t1 @t18)) @t28)))))) % 15.50/15.78 (assume @p11 (forall @t3 (=> @t4 (= (tptp.isLocallyConfluent0 @t1) (forall @t29 (=> (and @t13 @t6 @t19 (tptp.aReductOfIn0 @t5 @t7 @t1) (tptp.aReductOfIn0 @t18 @t7 @t1)) @t28)))))) % 15.50/15.78 (assume @p12 (forall @t3 (=> @t4 (= @t30 (forall (@list @t7 @t5) (=> (and @t13 @t6) (=> (tptp.sdtmndtplgtdt0 @t7 @t1 @t5) (tptp.iLess0 @t5 @t7)))))))) % 15.50/15.78 (assume @p13 (forall @t12 (=> @t11 (forall @t9 (= (tptp.aNormalFormOfIn0 @t5 @t1 @t7) (and @t6 @t24 (not (exists @t20 (tptp.aReductOfIn0 @t18 @t5 @t7))))))))) % 15.50/15.78 (assume @p14 @t38) % 15.50/15.78 (assume @p15 @t39) % 15.50/15.78 (assume @p16 (and (forall @t17 (=> (and @t2 @t13 @t6 @t43 @t42) @t45)) (tptp.isLocallyConfluent0 tptp.xR) (forall @t12 (=> @t14 (=> (or @t43 (exists @t9 (and @t6 @t42 (tptp.sdtmndtplgtdt0 @t5 tptp.xR @t7))) @t41) (tptp.iLess0 @t7 @t1)))) @t40)) % 15.50/15.78 (assume @p17 (and (tptp.aElement0 tptp.xa) (tptp.aElement0 tptp.xb) (tptp.aElement0 tptp.xc))) % 15.50/15.78 (assume @p18 (forall @t17 (=> (and @t2 @t13 @t6 (or (= @t1 @t7) @t43 (exists @t20 (and @t19 @t46 (tptp.sdtmndtplgtdt0 @t18 tptp.xR @t7))) @t41 (tptp.sdtmndtasgtdt0 @t1 tptp.xR @t7)) (or @t23 @t42 (exists @t20 (and @t19 @t46 (tptp.sdtmndtplgtdt0 @t18 tptp.xR @t5))) (tptp.sdtmndtplgtdt0 @t1 tptp.xR @t5) (tptp.sdtmndtasgtdt0 @t1 tptp.xR @t5))) (=> (tptp.iLess0 @t1 tptp.xa) @t45)))) % 15.50/15.78 (assume @p19 (and (or (tptp.aReductOfIn0 tptp.xb tptp.xa tptp.xR) (exists @t3 (and @t2 @t48 @t49))) (tptp.sdtmndtplgtdt0 tptp.xa tptp.xR tptp.xb) (or (tptp.aReductOfIn0 tptp.xc tptp.xa tptp.xR) (exists @t3 (and @t2 @t48 @t47))) (tptp.sdtmndtplgtdt0 tptp.xa tptp.xR tptp.xc))) % 15.50/15.78 (assume @p20 (and (tptp.aElement0 tptp.xu) (tptp.aReductOfIn0 tptp.xu tptp.xa tptp.xR) (or (= tptp.xu tptp.xb) (and (or (tptp.aReductOfIn0 tptp.xb tptp.xu tptp.xR) (exists @t3 (and @t2 @t50 @t49))) (tptp.sdtmndtplgtdt0 tptp.xu tptp.xR tptp.xb))) (tptp.sdtmndtasgtdt0 tptp.xu tptp.xR tptp.xb))) % 15.50/15.78 (assume @p21 (and (tptp.aElement0 tptp.xv) (tptp.aReductOfIn0 tptp.xv tptp.xa tptp.xR) (or (= tptp.xv tptp.xc) (and (or (tptp.aReductOfIn0 tptp.xc tptp.xv tptp.xR) (exists @t3 (and @t2 @t51 @t47))) (tptp.sdtmndtplgtdt0 tptp.xv tptp.xR tptp.xc))) (tptp.sdtmndtasgtdt0 tptp.xv tptp.xR tptp.xc))) % 15.50/15.78 (assume @p22 (and @t53 (or (= tptp.xu tptp.xw) (and (or (tptp.aReductOfIn0 tptp.xw tptp.xu tptp.xR) (exists @t3 (and @t2 @t50 @t52))) (tptp.sdtmndtplgtdt0 tptp.xu tptp.xR tptp.xw))) (tptp.sdtmndtasgtdt0 tptp.xu tptp.xR tptp.xw) (or (= tptp.xv tptp.xw) (and (or (tptp.aReductOfIn0 tptp.xw tptp.xv tptp.xR) (exists @t3 (and @t2 @t51 @t52))) (tptp.sdtmndtplgtdt0 tptp.xv tptp.xR tptp.xw))) (tptp.sdtmndtasgtdt0 tptp.xv tptp.xR tptp.xw))) % 15.50/15.78 (assume @p23 @t68) % 15.50/15.78 (assume @p24 true) % 15.50/15.78 (step @p25 :rule and_elim :premises (@p16) :args (3)) % 15.50/15.78 (step @p26 :rule and_elim :premises (@p22) :args (0)) % 15.50/15.78 (step @p27 :rule bool-double-not-elim :args ((and @t82 @t70))) % 15.50/15.78 (step @p28 :rule refl :args (@t70)) % 15.50/15.78 (step @p29 :rule quant-merge-prenex :args ((= (forall @t85 @t84) @t82))) % 15.50/15.78 (step @p30 :rule refl :args (@t72)) % 15.50/15.78 (step @p31 :rule quant-unused-vars :args ((= @t86 @t73))) % 15.50/15.78 (step @p32 :rule quant-unused-vars :args ((= @t87 @t74))) % 15.50/15.78 (step @p33 :rule alpha_equiv :args (@t88 (@list @t75) @t89)) % 15.50/15.78 (step @p34 :rule quant-unused-vars :args ((= @t90 @t77))) % 15.50/15.78 (step @p35 :rule quant-unused-vars :args ((= @t91 @t78))) % 15.50/15.78 (step @p36 :rule nary_cong :premises (@p35 @p34 @p33 @p32 @p31) :args (@t92)) % 15.50/15.78 (step @p37 :rule quant-miniscope-and :args ((= @t93 @t92))) % 15.50/15.78 (step @p38 :rule trans :premises (@p37 @p36)) % 15.50/15.78 (step @p39 :rule refl :args (@t80)) % 15.50/15.78 (step @p40 :rule nary_cong :premises (@p39 @p38 @p30) :args (@t94)) % 15.50/15.78 (step @p41 :rule quant-miniscope-or :args ((= @t84 @t94))) % 15.50/15.78 (step @p42 :rule trans :premises (@p41 @p40)) % 15.50/15.78 (step @p43 :rule symm :premises (@p42)) % 15.50/15.78 (step @p44 :rule cong :premises (@p43) :args ((forall @t85 (or @t80 (and @t78 @t77 @t97 @t74 @t73) @t72)))) % 15.50/15.78 (step @p45 :rule trans :premises (@p44 @p29)) % 15.50/15.78 (step @p46 :rule refl :args (@t72)) % 15.50/15.78 (step @p47 :rule refl :args (@t73)) % 15.50/15.78 (step @p48 :rule refl :args (@t74)) % 15.50/15.78 (step @p49 :rule refl :args (@t97)) % 15.50/15.78 (step @p50 :rule refl :args (@t77)) % 15.50/15.78 (step @p51 :rule eq-symm :args (@t71 tptp.xw)) % 15.50/15.78 (step @p52 :rule cong :premises (@p51) :args (@t98)) % 15.50/15.78 (step @p53 :rule nary_cong :premises (@p52 @p50 @p49 @p48 @p47) :args (@t99)) % 15.50/15.78 (step @p54 :rule refl :args (@t80)) % 15.50/15.78 (step @p55 :rule nary_cong :premises (@p54 @p53 @p46) :args (@t100)) % 15.50/15.78 (step @p56 :rule cong :premises (@p55) :args (@t101)) % 15.50/15.78 (step @p57 :rule trans :premises (@p56 @p45)) % 15.50/15.78 (step @p58 :rule nary_cong :premises (@p57 @p28) :args ((and @t101 @t70))) % 15.50/15.78 (step @p59 :rule alpha_equiv :args (@t103 @t104 @t105)) % 15.50/15.78 (step @p60 :rule alpha_equiv :args (@t118 @t104 (@list @t71))) % 15.50/15.78 (step @p61 :rule nary_cong :premises (@p60 @p59) :args (@t119)) % 15.50/15.78 (step @p62 :rule quant-miniscope-and :args ((= (forall @t3 (and @t117 @t102)) @t119))) % 15.50/15.78 (step @p63 :rule trans :premises (@p62 @p61)) % 15.50/15.78 (step @p64 :rule trans :premises (@p63 @p58)) % 15.50/15.78 (step @p65 :rule refl :args (@t102)) % 15.50/15.78 (step @p66 :rule refl :args (@t107)) % 15.50/15.78 (step @p67 :rule refl :args (@t108)) % 15.50/15.78 (step @p68 :rule refl :args (@t109)) % 15.50/15.78 (step @p69 :rule bool-double-not-elim :args (@t112)) % 15.50/15.78 (step @p70 :rule refl :args (@t113)) % 15.50/15.78 (step @p71 :rule refl :args (@t115)) % 15.50/15.78 (step @p72 :rule nary_cong :premises (@p71 @p70 @p69 @p68 @p67) :args (@t122)) % 15.50/15.78 (step @p73 :rule aci_norm :args ((= (and @t115 (and @t113 (and @t121 (and @t109 @t108)))) @t122))) % 15.50/15.78 (step @p74 :rule trans :premises (@p73 @p72)) % 15.50/15.78 (step @p75 :rule bool-or-de-morgan :args (@t58 @t57 false)) % 15.50/15.78 (step @p76 :rule refl :args (@t121)) % 15.50/15.78 (step @p77 :rule nary_cong :premises (@p76 @p75) :args ((and @t121 (not (or @t58 @t57))))) % 15.50/15.78 (step @p78 :rule bool-or-de-morgan :args (@t120 @t58 (or @t57))) % 15.50/15.78 (step @p79 :rule trans :premises (@p78 @p77)) % 15.50/15.78 (step @p80 :rule nary_cong :premises (@p70 @p79) :args ((and @t113 (not (or @t120 @t58 @t57))))) % 15.50/15.78 (step @p81 :rule bool-or-de-morgan :args (@t63 @t120 (or @t58 @t57))) % 15.50/15.78 (step @p82 :rule trans :premises (@p81 @p80)) % 15.50/15.78 (step @p83 :rule nary_cong :premises (@p71 @p82) :args ((and @t115 (not (or @t63 @t120 @t58 @t57))))) % 15.50/15.78 (step @p84 :rule bool-or-de-morgan :args (@t114 @t63 (or @t120 @t58 @t57))) % 15.50/15.78 (step @p85 :rule trans :premises (@p84 @p83)) % 15.50/15.78 (step @p86 :rule trans :premises (@p85 @p74)) % 15.50/15.78 (step @p87 :rule refl :args (@t116)) % 15.50/15.78 (step @p88 :rule nary_cong :premises (@p87 @p86 @p66) :args (@t125)) % 15.50/15.78 (step @p89 :rule aci_norm :args ((= (or @t116 (or @t124 @t107)) @t125))) % 15.50/15.78 (step @p90 :rule bool-and-de-morgan :args (@t123 @t106 true)) % 15.50/15.78 (step @p91 :rule nary_cong :premises (@p87 @p90) :args ((or @t116 (not (and @t123 @t106))))) % 15.50/15.78 (step @p92 :rule bool-and-de-morgan :args (@t2 @t123 (and @t106))) % 15.50/15.78 (step @p93 :rule trans :premises (@p92 @p91)) % 15.50/15.78 (step @p94 :rule trans :premises (@p93 @p89)) % 15.50/15.78 (step @p95 :rule trans :premises (@p94 @p88)) % 15.50/15.78 (step @p96 :rule nary_cong :premises (@p95 @p65) :args ((and (not @t126) @t102))) % 15.50/15.78 (step @p97 :rule bool-or-de-morgan :args (@t126 @t54 false)) % 15.50/15.78 (step @p98 :rule trans :premises (@p97 @p96)) % 15.50/15.78 (step @p99 :rule cong :premises (@p98) :args (@t128)) % 15.50/15.78 (step @p100 :rule trans :premises (@p99 @p64)) % 15.50/15.78 (step @p101 :rule cong :premises (@p100) :args (@t129)) % 15.50/15.78 (step @p102 :rule exists-elim :args ((= (exists @t3 @t127) @t129))) % 15.50/15.78 (step @p103 :rule trans :premises (@p102 @p101)) % 15.50/15.78 (step @p104 :rule refl :args (@t54)) % 15.50/15.78 (step @p105 :rule bool-double-not-elim :args (@t106)) % 15.50/15.78 (step @p106 :rule exists-elim :args ((= @t55 @t107))) % 15.50/15.78 (step @p107 :rule cong :premises (@p106) :args (@t56)) % 15.50/15.78 (step @p108 :rule trans :premises (@p107 @p105)) % 15.50/15.78 (step @p109 :rule refl :args (@t57)) % 15.50/15.78 (step @p110 :rule refl :args (@t58)) % 15.50/15.78 (step @p111 :rule aci_norm :args ((= (or @t96 (or @t95 @t110)) @t111))) % 15.50/15.78 (step @p112 :rule bool-and-de-morgan :args (@t60 @t59 true)) % 15.50/15.78 (step @p113 :rule refl :args (@t96)) % 15.50/15.78 (step @p114 :rule nary_cong :premises (@p113 @p112) :args ((or @t96 (not (and @t60 @t59))))) % 15.50/15.78 (step @p115 :rule bool-and-de-morgan :args (@t13 @t60 (and @t59))) % 15.50/15.78 (step @p116 :rule trans :premises (@p115 @p114)) % 15.50/15.78 (step @p117 :rule trans :premises (@p116 @p111)) % 15.50/15.78 (step @p118 :rule cong :premises (@p117) :args (@t130)) % 15.50/15.78 (step @p119 :rule cong :premises (@p118) :args (@t131)) % 15.50/15.78 (step @p120 :rule exists-elim :args ((= @t62 @t131))) % 15.50/15.78 (step @p121 :rule trans :premises (@p120 @p119)) % 15.50/15.78 (step @p122 :rule refl :args (@t63)) % 15.50/15.78 (step @p123 :rule eq-symm :args (tptp.xw @t1)) % 15.50/15.78 (step @p124 :rule nary_cong :premises (@p123 @p122 @p121 @p110 @p109) :args (@t64)) % 15.50/15.78 (step @p125 :rule refl :args (@t2)) % 15.50/15.78 (step @p126 :rule nary_cong :premises (@p125 @p124 @p108) :args (@t65)) % 15.50/15.78 (step @p127 :rule nary_cong :premises (@p126 @p104) :args (@t66)) % 15.50/15.78 (step @p128 :rule cong :premises (@p127) :args (@t67)) % 15.50/15.78 (step @p129 :rule trans :premises (@p128 @p103)) % 15.50/15.78 (step @p130 :rule cong :premises (@p129) :args (@t68)) % 15.50/15.78 (step @p131 :rule trans :premises (@p130 @p27)) % 15.50/15.78 (step @p132 :rule eq_resolve :premises (@p23 @p131)) % 15.50/15.78 (step @p133 :rule and_elim :premises (@p132) :args (1)) % 15.50/15.78 (step @p134 :rule alpha_equiv :args (@t70 @t105 (@list @t5))) % 15.50/15.78 (step @p135 :rule equiv_elim1 :premises (@p134)) % 15.50/15.78 (step @p136 :rule chain_m_resolution :premises (@p135 @p133) :args (@t132 (@list false) (@list @t70))) % 15.50/15.78 (step @p137 :rule aci_norm :args ((= @t139 (or @t137 @t136 @t135 @t134)))) % 15.50/15.78 (step @p138 :rule cong :premises (@p137) :args (@t140)) % 15.50/15.78 (step @p139 :rule quant-merge-prenex :args ((= (forall @t3 @t142) @t140))) % 15.50/15.78 (step @p140 :rule alpha_equiv :args (@t143 (@list @t133) @t89)) % 15.50/15.78 (step @p141 :rule refl :args (@t136)) % 15.50/15.78 (step @p142 :rule refl :args (@t137)) % 15.50/15.78 (step @p143 :rule nary_cong :premises (@p142 @p141 @p140) :args (@t144)) % 15.50/15.78 (step @p144 :rule quant-miniscope-or :args ((= @t142 @t144))) % 15.50/15.78 (step @p145 :rule trans :premises (@p144 @p143)) % 15.50/15.78 (step @p146 :rule symm :premises (@p145)) % 15.50/15.78 (step @p147 :rule cong :premises (@p146) :args ((forall @t3 @t147))) % 15.50/15.78 (step @p148 :rule trans :premises (@p147 @p139)) % 15.50/15.78 (step @p149 :rule trans :premises (@p148 @p138)) % 15.50/15.78 (step @p150 :rule aci_norm :args ((= (or (or @t137 @t136) @t146) @t147))) % 15.50/15.78 (step @p151 :rule refl :args (@t146)) % 15.50/15.78 (step @p152 :rule bool-and-de-morgan :args (@t4 @t30 true)) % 15.50/15.78 (step @p153 :rule nary_cong :premises (@p152 @p151) :args ((or (not @t36) @t146))) % 15.50/15.78 (step @p154 :rule trans :premises (@p153 @p150)) % 15.50/15.78 (step @p155 :rule bool-impl-elim :args (@t36 @t146)) % 15.50/15.78 (step @p156 :rule trans :premises (@p155 @p154)) % 15.50/15.78 (step @p157 :rule cong :premises (@p156) :args ((forall @t3 (=> @t36 @t146)))) % 15.50/15.78 (step @p158 :rule trans :premises (@p157 @p149)) % 15.50/15.78 (step @p159 :rule bool-impl-elim :args (@t13 @t145)) % 15.50/15.78 (step @p160 :rule cong :premises (@p159) :args ((forall @t34 (=> @t13 @t145)))) % 15.50/15.78 (step @p161 :rule exists-elim :args ((= @t32 @t145))) % 15.50/15.78 (step @p162 :rule refl :args (@t13)) % 15.50/15.78 (step @p163 :rule cong :premises (@p162 @p161) :args (@t33)) % 15.50/15.78 (step @p164 :rule cong :premises (@p163) :args (@t35)) % 15.50/15.78 (step @p165 :rule trans :premises (@p164 @p160)) % 15.50/15.78 (step @p166 :rule refl :args (@t36)) % 15.50/15.78 (step @p167 :rule cong :premises (@p166 @p165) :args (@t37)) % 15.50/15.78 (step @p168 :rule cong :premises (@p167) :args (@t38)) % 15.50/15.78 (step @p169 :rule trans :premises (@p168 @p158)) % 15.50/15.78 (step @p170 :rule eq_resolve :premises (@p14 @p169)) % 15.50/15.78 (step @p171 :rule instantiate :premises (@p170) :args ((@list tptp.xR tptp.xw))) % 15.50/15.78 (step @p172 :rule cnf_or_pos :args (@t152)) % 15.50/15.78 (step @p173 :rule reordering :premises (@p172) :args ((or @t151 @t150 @t149 @t148 (not @t152)))) % 15.50/15.78 (step @p174 false :rule chain_m_resolution :premises (@p173 @p171 @p136 @p26 @p25 @p15) :args (false (@list false false false false false) (@list @t152 @t132 @t53 @t40 @t39))) % 15.50/15.78 ) % 15.50/15.78 % SZS output end Proof % 15.50/15.78 % cvc5 exiting %------------------------------------------------------------------------------