%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWC019+1 : TPTP v9.2.1. Released v2.4.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n002.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 08:57:43 AM UTC 2026 % Result : Theorem 0.38s 0.88s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWC019+1 : TPTP v9.2.1. Released v2.4.0. % 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.18/0.34 % Computer : n002.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 : Tue Jun 2 19:10:03 EDT 2026 % 0.18/0.35 % CPUTime : % 0.27/0.52 %----Proving TF0_NAR, FOF, or CNF % 0.38/0.88 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.38/0.88 % SZS status Theorem % 0.38/0.88 % SZS output start Proof % 0.38/0.88 ( % 0.38/0.88 (declare-sort $$unsorted 0) % 0.38/0.88 (declare-const tptp.tl (-> $$unsorted $$unsorted)) % 0.38/0.88 (declare-const tptp.hd (-> $$unsorted $$unsorted)) % 0.38/0.88 (declare-const tptp.duplicatefreeP (-> $$unsorted Bool)) % 0.38/0.88 (declare-const tptp.strictorderedP (-> $$unsorted Bool)) % 0.38/0.88 (declare-const tptp.geq (-> $$unsorted $$unsorted Bool)) % 0.38/0.88 (declare-const tptp.strictorderP (-> $$unsorted Bool)) % 0.38/0.88 (declare-const tptp.equalelemsP (-> $$unsorted Bool)) % 0.38/0.88 (declare-const tptp.totalorderP (-> $$unsorted Bool)) % 0.38/0.88 (declare-const tptp.neq (-> $$unsorted $$unsorted Bool)) % 0.38/0.88 (declare-const tptp.totalorderedP (-> $$unsorted Bool)) % 0.38/0.88 (declare-const tptp.singletonP (-> $$unsorted Bool)) % 0.38/0.88 (declare-const tptp.cons (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.88 (declare-const tptp.app (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.88 (declare-const tptp.nil $$unsorted) % 0.38/0.88 (declare-const tptp.memberP (-> $$unsorted $$unsorted Bool)) % 0.38/0.88 (declare-const tptp.lt (-> $$unsorted $$unsorted Bool)) % 0.38/0.88 (declare-const tptp.frontsegP (-> $$unsorted $$unsorted Bool)) % 0.38/0.88 (declare-const tptp.rearsegP (-> $$unsorted $$unsorted Bool)) % 0.38/0.88 (declare-const tptp.gt (-> $$unsorted $$unsorted Bool)) % 0.38/0.88 (declare-const tptp.ssList (-> $$unsorted Bool)) % 0.38/0.88 (declare-const tptp.segmentP (-> $$unsorted $$unsorted Bool)) % 0.38/0.88 (declare-const tptp.cyclefreeP (-> $$unsorted Bool)) % 0.38/0.88 (declare-const tptp.ssItem (-> $$unsorted Bool)) % 0.38/0.88 (declare-const tptp.leq (-> $$unsorted $$unsorted Bool)) % 0.38/0.88 (define @t1 () (@var "V" $$unsorted)) % 0.38/0.88 (define @t2 () (@var "U" $$unsorted)) % 0.38/0.88 (define @t3 () (= @t2 @t1)) % 0.38/0.88 (define @t4 () (not @t3)) % 0.38/0.88 (define @t5 () (= (tptp.neq @t2 @t1) @t4)) % 0.38/0.88 (define @t6 () (tptp.ssItem @t1)) % 0.38/0.88 (define @t7 () (@list @t1)) % 0.38/0.88 (define @t8 () (tptp.ssItem @t2)) % 0.38/0.88 (define @t9 () (@list @t2)) % 0.38/0.88 (define @t10 () (@var "X" $$unsorted)) % 0.38/0.88 (define @t11 () (tptp.cons @t1 @t10)) % 0.38/0.88 (define @t12 () (@var "W" $$unsorted)) % 0.38/0.88 (define @t13 () (tptp.ssList @t10)) % 0.38/0.88 (define @t14 () (@list @t10)) % 0.38/0.88 (define @t15 () (tptp.ssList @t12)) % 0.38/0.88 (define @t16 () (@list @t12)) % 0.38/0.89 (define @t17 () (tptp.ssList @t2)) % 0.38/0.89 (define @t18 () (tptp.cons @t1 tptp.nil)) % 0.38/0.89 (define @t19 () (tptp.app @t1 @t12)) % 0.38/0.89 (define @t20 () (tptp.frontsegP @t2 @t1)) % 0.38/0.89 (define @t21 () (tptp.ssList @t1)) % 0.38/0.89 (define @t22 () (tptp.app @t12 @t1)) % 0.38/0.89 (define @t23 () (tptp.rearsegP @t2 @t1)) % 0.38/0.89 (define @t24 () (tptp.segmentP @t2 @t1)) % 0.38/0.89 (define @t25 () (tptp.leq @t12 @t1)) % 0.38/0.89 (define @t26 () (tptp.leq @t1 @t12)) % 0.38/0.89 (define @t27 () (@var "Z" $$unsorted)) % 0.38/0.89 (define @t28 () (@var "Y" $$unsorted)) % 0.38/0.89 (define @t29 () (= (tptp.app (tptp.app @t10 (tptp.cons @t1 @t28)) (tptp.cons @t12 @t27)) @t2)) % 0.38/0.89 (define @t30 () (tptp.ssList @t27)) % 0.38/0.89 (define @t31 () (@list @t27)) % 0.38/0.89 (define @t32 () (tptp.ssList @t28)) % 0.38/0.89 (define @t33 () (@list @t28)) % 0.38/0.89 (define @t34 () (tptp.ssItem @t12)) % 0.38/0.89 (define @t35 () (tptp.lt @t1 @t12)) % 0.38/0.89 (define @t36 () (= @t1 @t12)) % 0.38/0.89 (define @t37 () (not @t36)) % 0.38/0.89 (define @t38 () (forall @t7 (=> @t21 @t5))) % 0.38/0.89 (define @t39 () (=> @t17 @t38)) % 0.38/0.89 (define @t40 () (forall @t9 @t39)) % 0.38/0.89 (define @t41 () (tptp.cons @t1 @t2)) % 0.38/0.89 (define @t42 () (tptp.ssList tptp.nil)) % 0.38/0.89 (define @t43 () (= @t1 @t2)) % 0.38/0.89 (define @t44 () (= @t12 @t10)) % 0.38/0.89 (define @t45 () (tptp.cons @t12 @t1)) % 0.38/0.89 (define @t46 () (= tptp.nil @t2)) % 0.38/0.89 (define @t47 () (tptp.hd @t2)) % 0.38/0.89 (define @t48 () (not @t46)) % 0.38/0.89 (define @t49 () (tptp.tl @t2)) % 0.38/0.89 (define @t50 () (tptp.app @t2 @t1)) % 0.38/0.89 (define @t51 () (tptp.app @t1 @t2)) % 0.38/0.89 (define @t52 () (tptp.leq @t1 @t2)) % 0.38/0.89 (define @t53 () (tptp.leq @t2 @t1)) % 0.38/0.89 (define @t54 () (tptp.geq @t2 @t1)) % 0.38/0.89 (define @t55 () (tptp.lt @t1 @t2)) % 0.38/0.89 (define @t56 () (tptp.lt @t2 @t1)) % 0.38/0.89 (define @t57 () (tptp.lt @t2 @t12)) % 0.38/0.89 (define @t58 () (tptp.gt @t2 @t1)) % 0.38/0.89 (define @t59 () (tptp.memberP @t12 @t2)) % 0.38/0.89 (define @t60 () (tptp.frontsegP @t2 @t2)) % 0.38/0.89 (define @t61 () (forall @t9 (=> @t17 @t60))) % 0.38/0.89 (define @t62 () (tptp.app @t12 @t2)) % 0.38/0.89 (define @t63 () (tptp.cons @t2 tptp.nil)) % 0.38/0.89 (define @t64 () (tptp.hd @t1)) % 0.38/0.89 (define @t65 () (= tptp.nil @t1)) % 0.38/0.89 (define @t66 () (not @t65)) % 0.38/0.89 (define @t67 () (tptp.cons @t2 @t1)) % 0.38/0.89 (define @t68 () (= @t12 @t2)) % 0.38/0.89 (define @t69 () (and @t65 @t46)) % 0.38/0.89 (define @t70 () (tptp.frontsegP @t2 @t28)) % 0.38/0.89 (define @t71 () (tptp.frontsegP @t1 @t28)) % 0.38/0.89 (define @t72 () (tptp.neq @t28 tptp.nil)) % 0.38/0.89 (define @t73 () (and @t32 @t72 @t71 @t70)) % 0.38/0.89 (define @t74 () (exists @t33 @t73)) % 0.38/0.89 (define @t75 () (not (= @t10 @t12))) % 0.38/0.89 (define @t76 () (not (= @t2 @t12))) % 0.38/0.89 (define @t77 () (not (= @t1 @t10))) % 0.38/0.89 (define @t78 () (or @t77 @t76 @t75 @t74 @t69)) % 0.38/0.89 (define @t79 () (=> @t13 @t78)) % 0.38/0.89 (define @t80 () (forall @t14 @t79)) % 0.38/0.89 (define @t81 () (=> @t15 @t80)) % 0.38/0.89 (define @t82 () (forall @t16 @t81)) % 0.38/0.89 (define @t83 () (=> @t21 @t82)) % 0.38/0.89 (define @t84 () (forall @t7 @t83)) % 0.38/0.89 (define @t85 () (=> @t17 @t84)) % 0.38/0.89 (define @t86 () (forall @t9 @t85)) % 0.38/0.89 (define @t87 () (not @t86)) % 0.38/0.89 (define @t88 () (= @t2 tptp.nil)) % 0.38/0.89 (define @t89 () (not @t70)) % 0.38/0.89 (define @t90 () (not @t72)) % 0.38/0.89 (define @t91 () (not @t32)) % 0.38/0.89 (define @t92 () (or @t91 @t90 @t89)) % 0.38/0.89 (define @t93 () (not (forall @t33 @t92))) % 0.38/0.89 (define @t94 () (not @t17)) % 0.38/0.89 (define @t95 () (or @t94 @t93 @t88)) % 0.38/0.89 (define @t96 () (not (= @t2 @t2))) % 0.38/0.89 (define @t97 () (and @t88 @t88)) % 0.38/0.89 (define @t98 () (or @t91 @t90 @t89 @t89)) % 0.38/0.89 (define @t99 () (forall @t33 @t98)) % 0.38/0.89 (define @t100 () (not @t99)) % 0.38/0.89 (define @t101 () (or @t94 @t100 @t97 @t96)) % 0.38/0.89 (define @t102 () (and (= @t1 tptp.nil) @t88)) % 0.38/0.89 (define @t103 () (not @t71)) % 0.38/0.89 (define @t104 () (or @t91 @t90 @t103 @t89)) % 0.38/0.89 (define @t105 () (not (forall @t33 @t104))) % 0.38/0.89 (define @t106 () (not @t21)) % 0.38/0.89 (define @t107 () (not @t43)) % 0.38/0.89 (define @t108 () (or @t4 @t106 @t105 @t102 @t4)) % 0.38/0.89 (define @t109 () (or @t106 @t105 @t102 @t4)) % 0.38/0.89 (define @t110 () (forall @t7 @t109)) % 0.38/0.89 (define @t111 () (or @t94 @t110)) % 0.38/0.89 (define @t112 () (or @t94 @t109)) % 0.38/0.89 (define @t113 () (or @t106 @t105 @t102 @t94 @t4)) % 0.38/0.89 (define @t114 () (or @t105 @t102 @t106 @t94 @t4)) % 0.38/0.89 (define @t115 () (or @t94 @t4)) % 0.38/0.89 (define @t116 () (or @t94 @t96 @t107)) % 0.38/0.89 (define @t117 () (not @t15)) % 0.38/0.89 (define @t118 () (or @t76 @t117 @t76 @t37)) % 0.38/0.89 (define @t119 () (or @t117 @t76 @t37)) % 0.38/0.89 (define @t120 () (forall @t16 @t119)) % 0.38/0.89 (define @t121 () (or @t105 @t102 @t106 @t120)) % 0.38/0.89 (define @t122 () (or @t105 @t102 @t106 @t119)) % 0.38/0.89 (define @t123 () (or @t117 @t76 @t105 @t102 @t106 @t37)) % 0.38/0.89 (define @t124 () (or @t76 @t105 @t102 @t106 @t37)) % 0.38/0.89 (define @t125 () (or @t106 @t37)) % 0.38/0.89 (define @t126 () (not (= @t12 @t1))) % 0.38/0.89 (define @t127 () (not (= @t1 @t1))) % 0.38/0.89 (define @t128 () (or @t106 @t127 @t126)) % 0.38/0.89 (define @t129 () (not @t44)) % 0.38/0.89 (define @t130 () (not @t13)) % 0.38/0.89 (define @t131 () (or @t77 @t130 @t77 @t129)) % 0.38/0.89 (define @t132 () (or @t130 @t77 @t129)) % 0.38/0.89 (define @t133 () (forall @t14 @t132)) % 0.38/0.89 (define @t134 () (or @t76 @t105 @t102 @t133)) % 0.38/0.89 (define @t135 () (or @t76 @t105 @t102 @t132)) % 0.38/0.89 (define @t136 () (or @t130 @t77 @t76 @t129 @t105 @t102)) % 0.38/0.89 (define @t137 () (or @t77 @t76 @t129 @t105 @t102)) % 0.38/0.89 (define @t138 () (forall @t33 (not @t73))) % 0.38/0.89 (define @t139 () (not @t138)) % 0.38/0.89 (define @t140 () (forall @t9 @t95)) % 0.38/0.89 (define @t141 () (@quantifiers_skolemize @t140 0)) % 0.38/0.89 (define @t142 () (= tptp.nil @t141)) % 0.38/0.89 (define @t143 () (forall @t33 (or @t91 @t90 (not (tptp.frontsegP @t141 @t28))))) % 0.38/0.89 (define @t144 () (not @t143)) % 0.38/0.89 (define @t145 () (tptp.ssList @t141)) % 0.38/0.89 (define @t146 () (not @t145)) % 0.38/0.89 (define @t147 () (or @t146 @t144 @t142)) % 0.38/0.89 (define @t148 () (not @t147)) % 0.38/0.89 (define @t149 () (not @t140)) % 0.38/0.89 (define @t150 () (= @t141 tptp.nil)) % 0.38/0.89 (define @t151 () (or @t146 @t144 @t150)) % 0.38/0.89 (define @t152 () (not @t151)) % 0.38/0.89 (define @t153 () (@list true)) % 0.38/0.89 (define @t154 () (@list @t147)) % 0.38/0.89 (define @t155 () (@list @t141)) % 0.38/0.89 (define @t156 () (tptp.frontsegP @t141 @t141)) % 0.38/0.89 (define @t157 () (or @t146 @t156)) % 0.38/0.89 (define @t158 () (not @t156)) % 0.38/0.89 (define @t159 () (tptp.neq @t141 tptp.nil)) % 0.38/0.89 (define @t160 () (not @t159)) % 0.38/0.89 (define @t161 () (or @t146 @t160 @t158)) % 0.38/0.89 (define @t162 () (not @t142)) % 0.38/0.89 (define @t163 () (= @t162 @t159)) % 0.38/0.89 (define @t164 () (not @t163)) % 0.38/0.89 (define @t165 () (@var "BOUND_VARIABLE_9094" $$unsorted)) % 0.38/0.89 (define @t166 () (= (tptp.neq @t2 @t165) (not (= @t2 @t165)))) % 0.38/0.89 (define @t167 () (not (tptp.ssList @t165))) % 0.38/0.89 (define @t168 () (or @t94 @t167 @t166)) % 0.38/0.89 (define @t169 () (or @t167 @t166)) % 0.38/0.89 (define @t170 () (or @t94 @t169)) % 0.38/0.89 (define @t171 () (@list @t2 @t165)) % 0.38/0.89 (define @t172 () (forall @t171 @t170)) % 0.38/0.89 (define @t173 () (@list @t165)) % 0.38/0.89 (define @t174 () (forall @t173 @t170)) % 0.38/0.89 (define @t175 () (forall @t173 @t169)) % 0.38/0.89 (define @t176 () (or @t94 @t175)) % 0.38/0.89 (define @t177 () (forall @t7 (or @t106 @t5))) % 0.38/0.89 (define @t178 () (not @t150)) % 0.38/0.89 (define @t179 () (= @t159 @t178)) % 0.38/0.89 (define @t180 () (not @t42)) % 0.38/0.89 (define @t181 () (or @t146 @t180 @t179)) % 0.38/0.89 (define @t182 () (forall @t171 @t168)) % 0.38/0.89 (define @t183 () (or @t146 @t180 @t163)) % 0.38/0.89 (assume @p1 (forall @t9 (=> @t8 (forall @t7 (=> @t6 @t5))))) % 0.38/0.89 (assume @p2 (exists @t9 (and @t8 (exists @t7 (and @t6 @t4))))) % 0.38/0.89 (assume @p3 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.memberP @t2 @t1) (exists @t16 (and @t15 (exists @t14 (and @t13 (= (tptp.app @t12 @t11) @t2))))))))))) % 0.38/0.89 (assume @p4 (forall @t9 (=> @t17 (= (tptp.singletonP @t2) (exists @t7 (and @t6 (= @t18 @t2))))))) % 0.38/0.89 (assume @p5 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t20 (exists @t16 (and @t15 (= @t19 @t2))))))))) % 0.38/0.89 (assume @p6 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t23 (exists @t16 (and @t15 (= @t22 @t2))))))))) % 0.38/0.89 (assume @p7 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t24 (exists @t16 (and @t15 (exists @t14 (and @t13 (= (tptp.app @t22 @t10) @t2))))))))))) % 0.38/0.89 (assume @p8 (forall @t9 (=> @t17 (= (tptp.cyclefreeP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t34 (forall @t14 (=> @t13 (forall @t33 (=> @t32 (forall @t31 (=> @t30 (=> @t29 (not (and @t26 @t25))))))))))))))))) % 0.38/0.89 (assume @p9 (forall @t9 (=> @t17 (= (tptp.totalorderP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t34 (forall @t14 (=> @t13 (forall @t33 (=> @t32 (forall @t31 (=> @t30 (=> @t29 (or @t26 @t25)))))))))))))))) % 0.38/0.89 (assume @p10 (forall @t9 (=> @t17 (= (tptp.strictorderP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t34 (forall @t14 (=> @t13 (forall @t33 (=> @t32 (forall @t31 (=> @t30 (=> @t29 (or @t35 (tptp.lt @t12 @t1))))))))))))))))) % 0.38/0.89 (assume @p11 (forall @t9 (=> @t17 (= (tptp.totalorderedP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t34 (forall @t14 (=> @t13 (forall @t33 (=> @t32 (forall @t31 (=> @t30 (=> @t29 @t26))))))))))))))) % 0.38/0.89 (assume @p12 (forall @t9 (=> @t17 (= (tptp.strictorderedP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t34 (forall @t14 (=> @t13 (forall @t33 (=> @t32 (forall @t31 (=> @t30 (=> @t29 @t35))))))))))))))) % 0.38/0.89 (assume @p13 (forall @t9 (=> @t17 (= (tptp.duplicatefreeP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t34 (forall @t14 (=> @t13 (forall @t33 (=> @t32 (forall @t31 (=> @t30 (=> @t29 @t37))))))))))))))) % 0.38/0.89 (assume @p14 (forall @t9 (=> @t17 (= (tptp.equalelemsP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t34 (forall @t14 (=> @t13 (forall @t33 (=> @t32 (=> (= (tptp.app @t10 (tptp.cons @t1 (tptp.cons @t12 @t28))) @t2) @t36))))))))))))) % 0.38/0.89 (assume @p15 @t40) % 0.38/0.89 (assume @p16 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (tptp.ssList @t41)))))) % 0.38/0.89 (assume @p17 @t42) % 0.38/0.89 (assume @p18 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= @t41 @t2))))))) % 0.38/0.89 (assume @p19 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t34 (forall @t14 (=> (tptp.ssItem @t10) (=> (= (tptp.cons @t12 @t2) (tptp.cons @t10 @t1)) (and @t44 @t43))))))))))) % 0.38/0.89 (assume @p20 (forall @t9 (=> @t17 (or @t46 (exists @t7 (and @t21 (exists @t16 (and @t34 (= @t45 @t2))))))))) % 0.38/0.89 (assume @p21 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= tptp.nil @t41))))))) % 0.38/0.89 (assume @p22 (forall @t9 (=> @t17 (=> @t48 (tptp.ssItem @t47))))) % 0.38/0.89 (assume @p23 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.hd @t41) @t1)))))) % 0.38/0.89 (assume @p24 (forall @t9 (=> @t17 (=> @t48 (tptp.ssList @t49))))) % 0.38/0.89 (assume @p25 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.tl @t41) @t2)))))) % 0.38/0.89 (assume @p26 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (tptp.ssList @t50)))))) % 0.38/0.89 (assume @p27 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t34 (= (tptp.cons @t12 @t51) (tptp.app @t45 @t2))))))))) % 0.38/0.89 (assume @p28 (forall @t9 (=> @t17 (= (tptp.app tptp.nil @t2) @t2)))) % 0.38/0.89 (assume @p29 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> (and @t53 @t52) @t3)))))) % 0.38/0.89 (assume @p30 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t53 @t26) (tptp.leq @t2 @t12))))))))) % 0.38/0.89 (assume @p31 (forall @t9 (=> @t8 (tptp.leq @t2 @t2)))) % 0.38/0.89 (assume @p32 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t54 @t52)))))) % 0.38/0.89 (assume @p33 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t56 (not @t55))))))) % 0.38/0.89 (assume @p34 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t56 @t35) @t57)))))))) % 0.38/0.89 (assume @p35 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t58 @t55)))))) % 0.38/0.89 (assume @p36 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (= (tptp.memberP @t19 @t2) (or 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tptp.nil)) % 0.38/0.89 (assume @p67 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (= (tptp.totalorderedP @t67) (or @t65 (and @t66 (tptp.totalorderedP @t1) (tptp.leq @t2 @t64))))))))) % 0.38/0.89 (assume @p68 (forall @t9 (=> @t8 (tptp.strictorderedP @t63)))) % 0.38/0.89 (assume @p69 (tptp.strictorderedP tptp.nil)) % 0.38/0.89 (assume @p70 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (= (tptp.strictorderedP @t67) (or @t65 (and @t66 (tptp.strictorderedP @t1) (tptp.lt @t2 @t64))))))))) % 0.38/0.89 (assume @p71 (forall @t9 (=> @t8 (tptp.duplicatefreeP @t63)))) % 0.38/0.89 (assume @p72 (tptp.duplicatefreeP tptp.nil)) % 0.38/0.89 (assume @p73 (forall @t9 (=> @t8 (tptp.equalelemsP @t63)))) % 0.38/0.89 (assume @p74 (tptp.equalelemsP tptp.nil)) % 0.38/0.89 (assume @p75 (forall @t9 (=> @t17 (=> @t48 (exists @t7 (and @t6 (= @t47 @t1))))))) % 0.38/0.89 (assume @p76 (forall @t9 (=> @t17 (=> @t48 (exists @t7 (and @t21 (= @t49 @t1))))))) % 0.38/0.89 (assume @p77 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> 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(step @p141 :rule eq-symm :args (@t1 @t2)) % 0.38/0.89 (step @p142 :rule cong :premises (@p141) :args (@t107)) % 0.38/0.89 (step @p143 :rule nary_cong :premises (@p111 @p106 @p142) :args (@t116)) % 0.38/0.89 (step @p144 :rule trans :premises (@p143 @p140)) % 0.38/0.89 (step @p145 :rule quant-var-elim-eq :args ((= (forall @t16 (or (not @t68) @t117 @t76 @t37)) @t116))) % 0.38/0.89 (step @p146 :rule refl :args (@t37)) % 0.38/0.89 (step @p147 :rule refl :args (@t76)) % 0.38/0.89 (step @p148 :rule refl :args (@t117)) % 0.38/0.89 (step @p149 :rule eq-symm :args (@t2 @t12)) % 0.38/0.89 (step @p150 :rule cong :premises (@p149) :args (@t76)) % 0.38/0.89 (step @p151 :rule nary_cong :premises (@p150 @p148 @p147 @p146) :args (@t118)) % 0.38/0.89 (step @p152 :rule aci_norm :args ((= @t119 @t118))) % 0.38/0.89 (step @p153 :rule trans :premises (@p152 @p151)) % 0.38/0.89 (step @p154 :rule cong :premises (@p153) :args (@t120)) % 0.38/0.89 (step @p155 :rule trans :premises (@p154 @p145)) % 0.38/0.89 (step @p156 :rule trans :premises (@p155 @p144)) % 0.38/0.89 (step @p157 :rule refl :args (@t106)) % 0.38/0.89 (step @p158 :rule refl :args (@t102)) % 0.38/0.89 (step @p159 :rule refl :args (@t105)) % 0.38/0.89 (step @p160 :rule nary_cong :premises (@p159 @p158 @p157 @p156) :args (@t121)) % 0.38/0.89 (step @p161 :rule trans :premises (@p160 @p139)) % 0.38/0.89 (step @p162 :rule quant-miniscope-or :args ((= (forall @t16 @t122) @t121))) % 0.38/0.89 (step @p163 :rule aci_norm :args ((= @t123 @t122))) % 0.38/0.89 (step @p164 :rule cong :premises (@p163) :args ((forall @t16 @t123))) % 0.38/0.89 (step @p165 :rule trans :premises (@p164 @p162)) % 0.38/0.89 (step @p166 :rule trans :premises (@p165 @p161)) % 0.38/0.89 (step @p167 :rule aci_norm :args ((= (or @t117 @t124) @t123))) % 0.38/0.89 (step @p168 :rule bool-impl-elim :args (@t15 @t124)) % 0.38/0.89 (step @p169 :rule trans :premises (@p168 @p167)) % 0.38/0.89 (step @p170 :rule cong :premises (@p169) :args ((forall @t16 (=> @t15 @t124)))) 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@t10)) % 0.38/0.89 (step @p186 :rule cong :premises (@p185) :args (@t77)) % 0.38/0.89 (step @p187 :rule nary_cong :premises (@p186 @p184 @p183 @p182) :args (@t131)) % 0.38/0.89 (step @p188 :rule aci_norm :args ((= @t132 @t131))) % 0.38/0.89 (step @p189 :rule trans :premises (@p188 @p187)) % 0.38/0.89 (step @p190 :rule cong :premises (@p189) :args (@t133)) % 0.38/0.89 (step @p191 :rule trans :premises (@p190 @p181)) % 0.38/0.89 (step @p192 :rule trans :premises (@p191 @p180)) % 0.38/0.89 (step @p193 :rule refl :args (@t76)) % 0.38/0.89 (step @p194 :rule nary_cong :premises (@p193 @p159 @p158 @p192) :args (@t134)) % 0.38/0.89 (step @p195 :rule trans :premises (@p194 @p172)) % 0.38/0.89 (step @p196 :rule quant-miniscope-or :args ((= (forall @t14 @t135) @t134))) % 0.38/0.89 (step @p197 :rule aci_norm :args ((= @t136 @t135))) % 0.38/0.89 (step @p198 :rule cong :premises (@p197) :args ((forall @t14 @t136))) % 0.38/0.89 (step @p199 :rule trans :premises (@p198 @p196)) % 0.38/0.89 (step @p200 :rule trans :premises (@p199 @p195)) % 0.38/0.89 (step @p201 :rule aci_norm :args ((= (or @t130 @t137) @t136))) % 0.38/0.89 (step @p202 :rule bool-impl-elim :args (@t13 @t137)) % 0.38/0.89 (step @p203 :rule trans :premises (@p202 @p201)) % 0.38/0.89 (step @p204 :rule cong :premises (@p203) :args ((forall @t14 (=> @t13 @t137)))) % 0.38/0.89 (step @p205 :rule trans :premises (@p204 @p200)) % 0.38/0.89 (step @p206 :rule eq-symm :args (tptp.nil @t2)) % 0.38/0.89 (step @p207 :rule eq-symm :args (tptp.nil @t1)) % 0.38/0.89 (step @p208 :rule nary_cong :premises (@p207 @p206) :args (@t69)) % 0.38/0.89 (step @p209 :rule aci_norm :args ((= (or @t91 (or @t90 (or @t103 @t89))) @t104))) % 0.38/0.89 (step @p210 :rule bool-and-de-morgan :args (@t71 @t70 true)) % 0.38/0.89 (step @p211 :rule refl :args (@t90)) % 0.38/0.89 (step @p212 :rule nary_cong :premises (@p211 @p210) :args ((or @t90 (not (and @t71 @t70))))) % 0.38/0.89 (step @p213 :rule bool-and-de-morgan :args (@t72 @t71 (and @t70))) % 0.38/0.89 (step @p214 :rule trans :premises (@p213 @p212)) % 0.38/0.89 (step @p215 :rule refl :args (@t91)) % 0.38/0.89 (step @p216 :rule nary_cong :premises (@p215 @p214) :args ((or @t91 (not (and @t72 @t71 @t70))))) % 0.38/0.89 (step @p217 :rule bool-and-de-morgan :args (@t32 @t72 (and @t71 @t70))) % 0.38/0.89 (step @p218 :rule trans :premises (@p217 @p216)) % 0.38/0.89 (step @p219 :rule trans :premises (@p218 @p209)) % 0.38/0.89 (step @p220 :rule cong :premises (@p219) :args (@t138)) % 0.38/0.89 (step @p221 :rule cong :premises (@p220) :args (@t139)) % 0.38/0.89 (step @p222 :rule exists-elim :args ((= @t74 @t139))) % 0.38/0.89 (step @p223 :rule trans :premises (@p222 @p221)) % 0.38/0.89 (step @p224 :rule eq-symm :args (@t10 @t12)) % 0.38/0.89 (step @p225 :rule cong :premises (@p224) :args (@t75)) % 0.38/0.89 (step @p226 :rule refl :args (@t77)) % 0.38/0.89 (step @p227 :rule nary_cong :premises (@p226 @p193 @p225 @p223 @p208) :args (@t78)) % 0.38/0.89 (step @p228 :rule refl :args (@t13)) % 0.38/0.89 (step @p229 :rule cong :premises (@p228 @p227) :args (@t79)) % 0.38/0.89 (step @p230 :rule cong :premises (@p229) :args (@t80)) % 0.38/0.89 (step @p231 :rule trans :premises (@p230 @p205)) % 0.38/0.89 (step @p232 :rule refl :args (@t15)) % 0.38/0.89 (step @p233 :rule cong :premises (@p232 @p231) :args (@t81)) % 0.38/0.89 (step @p234 :rule cong :premises (@p233) :args (@t82)) % 0.38/0.89 (step @p235 :rule trans :premises (@p234 @p171)) % 0.38/0.89 (step @p236 :rule refl :args (@t21)) % 0.38/0.89 (step @p237 :rule cong :premises (@p236 @p235) :args (@t83)) % 0.38/0.89 (step @p238 :rule cong :premises (@p237) :args (@t84)) % 0.38/0.89 (step @p239 :rule trans :premises (@p238 @p138)) % 0.38/0.89 (step @p240 :rule refl :args (@t17)) % 0.38/0.89 (step @p241 :rule cong :premises (@p240 @p239) :args (@t85)) % 0.38/0.89 (step @p242 :rule cong :premises (@p241) :args (@t86)) % 0.38/0.89 (step @p243 :rule trans :premises (@p242 @p101)) % 0.38/0.89 (step @p244 :rule cong :premises (@p243) :args (@t87)) % 0.38/0.89 (step @p245 :rule eq_resolve :premises (@p96 @p244)) % 0.38/0.89 (step @p246 :rule refl :args (@t148)) % 0.38/0.89 (step @p247 :rule bool-double-not-elim :args (@t140)) % 0.38/0.89 (step @p248 :rule nary_cong :premises (@p247 @p246) :args ((or (not @t149) @t148))) % 0.38/0.89 (step @p249 :rule eq-symm :args (@t141 tptp.nil)) % 0.38/0.89 (step @p250 :rule refl :args (@t144)) % 0.38/0.89 (step @p251 :rule refl :args (@t146)) % 0.38/0.89 (step @p252 :rule nary_cong :premises (@p251 @p250 @p249) :args (@t151)) % 0.38/0.89 (step @p253 :rule cong :premises (@p252) :args (@t152)) % 0.38/0.89 (step @p254 :rule refl :args (@t149)) % 0.38/0.89 (step @p255 :rule cong :premises (@p254 @p253) :args ((=> @t149 @t152))) % 0.38/0.89 (assume-push @p337 @t149) % 0.38/0.89 (step @p257 :rule skolemize :premises (@p245)) % 0.38/0.89 (step-pop @p338 :rule scope :premises (@p257)) % 0.38/0.89 (step @p258 :rule process_scope :premises (@p338) :args (@t152)) % 0.38/0.89 (step @p260 :rule eq_resolve :premises (@p258 @p255)) % 0.38/0.89 (step @p261 :rule implies_elim :premises (@p260)) % 0.38/0.89 (step @p262 :rule eq_resolve :premises (@p261 @p248)) % 0.38/0.89 (step @p263 :rule chain_m_resolution :premises (@p262 @p245) :args (@t148 @t153 (@list @t140))) % 0.38/0.89 (step @p264 :rule bool-double-not-elim :args (@t145)) % 0.38/0.89 (step @p265 :rule refl :args (@t147)) % 0.38/0.89 (step @p266 :rule nary_cong :premises (@p265 @p264) :args ((or @t147 (not @t146)))) % 0.38/0.89 (step @p267 :rule cnf_or_neg :args (@t147 0)) % 0.38/0.89 (step @p268 :rule eq_resolve :premises (@p267 @p266)) % 0.38/0.89 (step @p269 :rule reordering :premises (@p268) :args ((or @t145 @t147))) % 0.38/0.89 (step @p270 :rule chain_m_resolution :premises (@p269 @p263) :args (@t145 @t153 @t154)) % 0.38/0.89 (step @p271 :rule bool-double-not-elim :args (@t143)) % 0.38/0.89 (step @p272 :rule nary_cong :premises (@p265 @p271) :args ((or @t147 (not @t144)))) % 0.38/0.89 (step @p273 :rule cnf_or_neg :args (@t147 1)) % 0.38/0.89 (step @p274 :rule eq_resolve :premises (@p273 @p272)) % 0.38/0.89 (step @p275 :rule reordering :premises (@p274) :args ((or @t143 @t147))) % 0.38/0.89 (step @p276 :rule chain_m_resolution :premises (@p275 @p263) :args (@t143 @t153 @t154)) % 0.38/0.89 (step @p277 :rule instantiate :premises (@p276) :args (@t155)) % 0.38/0.89 (step @p278 :rule bool-impl-elim :args (@t17 @t60)) % 0.38/0.89 (step @p279 :rule cong :premises (@p278) :args (@t61)) % 0.38/0.89 (step @p280 :rule eq_resolve :premises (@p42 @p279)) % 0.38/0.89 (step @p281 :rule instantiate :premises (@p280) :args (@t155)) % 0.38/0.89 (step @p282 :rule cnf_or_pos :args (@t157)) % 0.38/0.89 (step @p283 :rule reordering :premises (@p282) :args ((or @t146 @t156 (not @t157)))) % 0.38/0.89 (step @p284 :rule chain_m_resolution :premises (@p283 @p270 @p281) :args (@t156 (@list false false) (@list @t145 @t157))) % 0.38/0.89 (step @p285 :rule cnf_or_pos :args (@t161)) % 0.38/0.89 (step @p286 :rule reordering :premises (@p285) :args ((or @t146 @t158 @t160 (not @t161)))) % 0.38/0.89 (step @p287 :rule chain_m_resolution :premises (@p286 @p270 @p284 @p277) :args (@t160 (@list false false false) (@list @t145 @t156 @t161))) % 0.38/0.89 (step @p288 :rule cnf_or_neg :args (@t147 2)) % 0.38/0.89 (step @p289 :rule chain_m_resolution :premises (@p288 @p263) :args (@t162 @t153 @t154)) % 0.38/0.89 (step @p290 :rule refl :args (@t159)) % 0.38/0.89 (step @p291 :rule bool-double-not-elim :args (@t142)) % 0.38/0.89 (step @p292 :rule refl :args (@t164)) % 0.38/0.89 (step @p293 :rule nary_cong :premises (@p292 @p291 @p290) :args ((or @t164 (not @t162) @t159))) % 0.38/0.89 (step @p294 :rule cnf_equiv_pos1 :args (@t163)) % 0.38/0.89 (step @p295 :rule eq_resolve :premises (@p294 @p293)) % 0.38/0.89 (step @p296 :rule reordering :premises (@p295) :args ((or @t142 @t159 @t164))) % 0.38/0.89 (step @p297 :rule chain_m_resolution :premises (@p296 @p289 @p287) :args (@t164 (@list true true) (@list @t142 @t159))) % 0.38/0.89 (step @p298 :rule aci_norm :args ((= @t170 @t168))) % 0.38/0.89 (step @p299 :rule cong :premises (@p298) :args (@t172)) % 0.38/0.89 (step @p300 :rule quant-merge-prenex :args ((= (forall @t9 @t174) @t172))) % 0.38/0.89 (step @p301 :rule alpha_equiv :args (@t175 (@list @t165) (@list @t1))) % 0.38/0.89 (step @p302 :rule refl :args (@t94)) % 0.38/0.89 (step @p303 :rule nary_cong :premises (@p302 @p301) :args (@t176)) % 0.38/0.89 (step @p304 :rule quant-miniscope-or :args ((= @t174 @t176))) % 0.38/0.89 (step @p305 :rule trans :premises (@p304 @p303)) % 0.38/0.89 (step @p306 :rule symm :premises (@p305)) % 0.38/0.89 (step @p307 :rule cong :premises (@p306) :args ((forall @t9 (or @t94 @t177)))) % 0.38/0.89 (step @p308 :rule trans :premises (@p307 @p300)) % 0.38/0.89 (step @p309 :rule trans :premises (@p308 @p299)) % 0.38/0.89 (step @p310 :rule bool-impl-elim :args (@t17 @t177)) % 0.38/0.89 (step @p311 :rule cong :premises (@p310) :args ((forall @t9 (=> @t17 @t177)))) % 0.38/0.89 (step @p312 :rule trans :premises (@p311 @p309)) % 0.38/0.89 (step @p313 :rule bool-impl-elim :args (@t21 @t5)) % 0.38/0.89 (step @p314 :rule cong :premises (@p313) :args (@t38)) % 0.38/0.89 (step @p315 :rule cong :premises (@p240 @p314) :args (@t39)) % 0.38/0.89 (step @p316 :rule cong :premises (@p315) :args (@t40)) % 0.38/0.89 (step @p317 :rule trans :premises (@p316 @p312)) % 0.38/0.89 (step @p318 :rule eq_resolve :premises (@p15 @p317)) % 0.38/0.89 (step @p319 :rule eq-symm :args (@t159 @t162)) % 0.38/0.89 (step @p320 :rule cong :premises (@p249) :args (@t178)) % 0.38/0.89 (step @p321 :rule cong :premises (@p290 @p320) :args (@t179)) % 0.38/0.89 (step @p322 :rule trans :premises (@p321 @p319)) % 0.38/0.89 (step @p323 :rule refl :args (@t180)) % 0.38/0.89 (step @p324 :rule nary_cong :premises (@p251 @p323 @p322) :args (@t181)) % 0.38/0.89 (step @p325 :rule refl :args (@t182)) % 0.38/0.89 (step @p326 :rule cong :premises (@p325 @p324) :args ((=> @t182 @t181))) % 0.38/0.89 (assume-push @p339 @t182) % 0.38/0.89 (step @p328 :rule instantiate :premises (@p318) :args ((@list @t141 tptp.nil))) % 0.38/0.89 (step-pop @p340 :rule scope :premises (@p328)) % 0.38/0.89 (step @p329 :rule process_scope :premises (@p340) :args (@t181)) % 0.38/0.89 (step @p331 :rule eq_resolve :premises (@p329 @p326)) % 0.38/0.89 (step @p332 :rule implies_elim :premises (@p331)) % 0.38/0.89 (step @p333 :rule chain_m_resolution :premises (@p332 @p318) :args (@t183 (@list false) (@list @t182))) % 0.38/0.89 (step @p334 :rule cnf_or_pos :args (@t183)) % 0.38/0.89 (step @p335 :rule reordering :premises (@p334) :args ((or @t180 @t146 @t163 (not @t183)))) % 0.38/0.89 (step @p336 false :rule chain_m_resolution :premises (@p335 @p333 @p297 @p270 @p17) :args (false (@list false true false false) (@list @t183 @t163 @t145 @t42))) % 0.38/0.89 ) % 0.38/0.89 % SZS output end Proof % 0.38/0.89 % cvc5 exiting %------------------------------------------------------------------------------