%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWC208+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 : 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 08:58:27 AM UTC 2026 % Result : Theorem 0.45s 0.65s % Output : Proof 0.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWC208+1 : TPTP v9.2.1. Released v2.4.0. % 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.18/0.34 % Computer : n007.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 19:23:56 EDT 2026 % 0.18/0.34 % CPUTime : % 0.28/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.45/0.65 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.45/0.65 % SZS status Theorem % 0.45/0.65 % SZS output start Proof % 0.45/0.65 ( % 0.45/0.65 (declare-sort $$unsorted 0) % 0.45/0.65 (declare-const tptp.tl (-> $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.hd (-> $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.duplicatefreeP (-> $$unsorted Bool)) % 0.45/0.65 (declare-const tptp.strictorderedP (-> $$unsorted Bool)) % 0.45/0.65 (declare-const tptp.geq (-> $$unsorted $$unsorted Bool)) % 0.45/0.65 (declare-const tptp.strictorderP (-> $$unsorted Bool)) % 0.45/0.65 (declare-const tptp.equalelemsP (-> $$unsorted Bool)) % 0.45/0.65 (declare-const tptp.totalorderP (-> $$unsorted Bool)) % 0.45/0.65 (declare-const tptp.neq (-> $$unsorted $$unsorted Bool)) % 0.45/0.65 (declare-const tptp.totalorderedP (-> $$unsorted Bool)) % 0.45/0.65 (declare-const tptp.singletonP (-> $$unsorted Bool)) % 0.45/0.65 (declare-const tptp.cons (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.app (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.nil $$unsorted) % 0.45/0.65 (declare-const tptp.memberP (-> $$unsorted $$unsorted Bool)) % 0.45/0.65 (declare-const tptp.lt (-> $$unsorted $$unsorted Bool)) % 0.45/0.65 (declare-const tptp.frontsegP (-> $$unsorted $$unsorted Bool)) % 0.45/0.65 (declare-const tptp.rearsegP (-> $$unsorted $$unsorted Bool)) % 0.45/0.65 (declare-const tptp.gt (-> $$unsorted $$unsorted Bool)) % 0.45/0.65 (declare-const tptp.ssList (-> $$unsorted Bool)) % 0.45/0.65 (declare-const tptp.segmentP (-> $$unsorted $$unsorted Bool)) % 0.45/0.65 (declare-const tptp.cyclefreeP (-> $$unsorted Bool)) % 0.45/0.65 (declare-const tptp.ssItem (-> $$unsorted Bool)) % 0.45/0.65 (declare-const tptp.leq (-> $$unsorted $$unsorted Bool)) % 0.45/0.65 (define @t1 () (@var "V" $$unsorted)) % 0.45/0.65 (define @t2 () (@var "U" $$unsorted)) % 0.45/0.65 (define @t3 () (= @t2 @t1)) % 0.45/0.65 (define @t4 () (not @t3)) % 0.45/0.65 (define @t5 () (= (tptp.neq @t2 @t1) @t4)) % 0.45/0.65 (define @t6 () (tptp.ssItem @t1)) % 0.45/0.65 (define @t7 () (@list @t1)) % 0.45/0.65 (define @t8 () (tptp.ssItem @t2)) % 0.45/0.65 (define @t9 () (@list @t2)) % 0.45/0.65 (define @t10 () (@var "X" $$unsorted)) % 0.45/0.65 (define @t11 () (tptp.cons @t1 @t10)) % 0.45/0.65 (define @t12 () (@var "W" $$unsorted)) % 0.45/0.65 (define @t13 () (tptp.ssList @t10)) % 0.45/0.65 (define @t14 () (@list @t10)) % 0.45/0.65 (define @t15 () (tptp.ssList @t12)) % 0.45/0.65 (define @t16 () (@list @t12)) % 0.45/0.65 (define @t17 () (tptp.ssList @t2)) % 0.45/0.65 (define @t18 () (tptp.cons @t1 tptp.nil)) % 0.45/0.65 (define @t19 () (tptp.app @t1 @t12)) % 0.45/0.65 (define @t20 () (tptp.frontsegP @t2 @t1)) % 0.45/0.65 (define @t21 () (tptp.ssList @t1)) % 0.45/0.65 (define @t22 () (tptp.app @t12 @t1)) % 0.45/0.65 (define @t23 () (tptp.rearsegP @t2 @t1)) % 0.45/0.65 (define @t24 () (tptp.segmentP @t2 @t1)) % 0.45/0.65 (define @t25 () (tptp.leq @t12 @t1)) % 0.45/0.65 (define @t26 () (tptp.leq @t1 @t12)) % 0.45/0.65 (define @t27 () (@var "Z" $$unsorted)) % 0.45/0.65 (define @t28 () (@var "Y" $$unsorted)) % 0.45/0.65 (define @t29 () (= (tptp.app (tptp.app @t10 (tptp.cons @t1 @t28)) (tptp.cons @t12 @t27)) @t2)) % 0.45/0.65 (define @t30 () (tptp.ssList @t27)) % 0.45/0.65 (define @t31 () (@list @t27)) % 0.45/0.65 (define @t32 () (tptp.ssList @t28)) % 0.45/0.65 (define @t33 () (@list @t28)) % 0.45/0.65 (define @t34 () (tptp.ssItem @t12)) % 0.45/0.65 (define @t35 () (tptp.lt @t1 @t12)) % 0.45/0.65 (define @t36 () (= @t1 @t12)) % 0.45/0.65 (define @t37 () (tptp.cons @t1 @t2)) % 0.45/0.65 (define @t38 () (= @t1 @t2)) % 0.45/0.65 (define @t39 () (tptp.cons @t12 @t1)) % 0.45/0.65 (define @t40 () (= tptp.nil @t2)) % 0.45/0.65 (define @t41 () (tptp.hd @t2)) % 0.45/0.65 (define @t42 () (not @t40)) % 0.45/0.65 (define @t43 () (tptp.tl @t2)) % 0.45/0.65 (define @t44 () (tptp.app @t2 @t1)) % 0.45/0.65 (define @t45 () (tptp.app @t1 @t2)) % 0.45/0.65 (define @t46 () (tptp.leq @t1 @t2)) % 0.45/0.65 (define @t47 () (tptp.leq @t2 @t1)) % 0.45/0.65 (define @t48 () (tptp.geq @t2 @t1)) % 0.45/0.65 (define @t49 () (tptp.lt @t1 @t2)) % 0.45/0.65 (define @t50 () (tptp.lt @t2 @t1)) % 0.45/0.65 (define @t51 () (tptp.lt @t2 @t12)) % 0.45/0.65 (define @t52 () (tptp.gt @t2 @t1)) % 0.45/0.65 (define @t53 () (tptp.memberP @t12 @t2)) % 0.45/0.65 (define @t54 () (tptp.frontsegP @t1 @t12)) % 0.45/0.65 (define @t55 () (tptp.frontsegP @t1 @t2)) % 0.45/0.65 (define @t56 () (tptp.app @t12 @t2)) % 0.45/0.65 (define @t57 () (tptp.cons @t2 tptp.nil)) % 0.45/0.65 (define @t58 () (tptp.hd @t1)) % 0.45/0.65 (define @t59 () (= tptp.nil @t1)) % 0.45/0.65 (define @t60 () (not @t59)) % 0.45/0.65 (define @t61 () (tptp.cons @t2 @t1)) % 0.45/0.65 (define @t62 () (= @t12 @t2)) % 0.45/0.65 (define @t63 () (not (tptp.neq @t12 tptp.nil))) % 0.45/0.65 (define @t64 () (or @t63 (not (tptp.frontsegP @t10 @t12)))) % 0.45/0.65 (define @t65 () (not (= tptp.nil @t12))) % 0.45/0.65 (define @t66 () (not (= tptp.nil @t10))) % 0.45/0.65 (define @t67 () (or @t66 @t65)) % 0.45/0.65 (define @t68 () (and @t67 @t64)) % 0.45/0.65 (define @t69 () (tptp.neq @t2 tptp.nil)) % 0.45/0.65 (define @t70 () (not (tptp.neq @t1 tptp.nil))) % 0.45/0.65 (define @t71 () (not (= @t2 @t12))) % 0.45/0.65 (define @t72 () (not (= @t1 @t10))) % 0.45/0.65 (define @t73 () (or @t72 @t71 @t70 @t69 @t68)) % 0.45/0.65 (define @t74 () (=> @t13 @t73)) % 0.45/0.65 (define @t75 () (forall @t14 @t74)) % 0.45/0.65 (define @t76 () (=> @t15 @t75)) % 0.45/0.65 (define @t77 () (forall @t16 @t76)) % 0.45/0.65 (define @t78 () (=> @t21 @t77)) % 0.45/0.65 (define @t79 () (forall @t7 @t78)) % 0.45/0.65 (define @t80 () (=> @t17 @t79)) % 0.45/0.65 (define @t81 () (forall @t9 @t80)) % 0.45/0.65 (define @t82 () (not @t81)) % 0.45/0.65 (define @t83 () (@var "BOUND_VARIABLE_10975" $$unsorted)) % 0.45/0.65 (define @t84 () (not @t69)) % 0.45/0.65 (define @t85 () (or @t84 (not (tptp.frontsegP @t83 @t2)))) % 0.45/0.65 (define @t86 () (not (= @t2 tptp.nil))) % 0.45/0.65 (define @t87 () (not (= @t83 tptp.nil))) % 0.45/0.65 (define @t88 () (or @t87 @t86)) % 0.45/0.65 (define @t89 () (and @t88 @t85)) % 0.45/0.65 (define @t90 () (not (tptp.neq @t83 tptp.nil))) % 0.45/0.65 (define @t91 () (not (tptp.ssList @t83))) % 0.45/0.65 (define @t92 () (not @t17)) % 0.45/0.65 (define @t93 () (or @t92 @t69 @t91 @t90 @t89)) % 0.45/0.65 (define @t94 () (or @t91 @t90 @t89)) % 0.45/0.65 (define @t95 () (or @t92 @t69 @t94)) % 0.45/0.65 (define @t96 () (@list @t2 @t83)) % 0.45/0.65 (define @t97 () (forall @t96 @t95)) % 0.45/0.65 (define @t98 () (@list @t83)) % 0.45/0.65 (define @t99 () (forall @t98 @t95)) % 0.45/0.65 (define @t100 () (forall @t98 @t94)) % 0.45/0.65 (define @t101 () (or @t92 @t69 @t100)) % 0.45/0.65 (define @t102 () (not (= @t1 tptp.nil))) % 0.45/0.65 (define @t103 () (and (or @t102 @t86) (or @t84 (not @t55)))) % 0.45/0.65 (define @t104 () (not @t21)) % 0.45/0.65 (define @t105 () (or @t104 @t70 @t103)) % 0.45/0.65 (define @t106 () (forall @t7 @t105)) % 0.45/0.65 (define @t107 () (or @t92 @t69 @t106)) % 0.45/0.65 (define @t108 () (or @t69 @t92 @t106)) % 0.45/0.65 (define @t109 () (or @t69 @t92 @t105)) % 0.45/0.65 (define @t110 () (or @t104 @t70 @t69 @t92 @t103)) % 0.45/0.65 (define @t111 () (or @t70 @t69 @t104 @t92 @t103)) % 0.45/0.65 (define @t112 () (or @t92 @t103)) % 0.45/0.65 (define @t113 () (not (= @t2 @t2))) % 0.45/0.65 (define @t114 () (or @t92 @t113 @t103)) % 0.45/0.65 (define @t115 () (not (= @t12 tptp.nil))) % 0.45/0.65 (define @t116 () (and (or @t102 @t115) (or @t63 (not @t54)))) % 0.45/0.65 (define @t117 () (not @t15)) % 0.45/0.65 (define @t118 () (or @t71 @t117 @t71 @t116)) % 0.45/0.65 (define @t119 () (or @t117 @t71 @t116)) % 0.45/0.65 (define @t120 () (forall @t16 @t119)) % 0.45/0.65 (define @t121 () (or @t70 @t69 @t104 @t120)) % 0.45/0.65 (define @t122 () (or @t70 @t69 @t104 @t119)) % 0.45/0.65 (define @t123 () (or @t117 @t71 @t70 @t69 @t104 @t116)) % 0.45/0.65 (define @t124 () (or @t71 @t70 @t69 @t104 @t116)) % 0.45/0.65 (define @t125 () (or @t104 @t116)) % 0.45/0.65 (define @t126 () (not (= @t1 @t1))) % 0.45/0.65 (define @t127 () (or @t104 @t126 @t116)) % 0.45/0.65 (define @t128 () (and (or (not (= @t10 tptp.nil)) @t115) @t64)) % 0.45/0.65 (define @t129 () (not @t13)) % 0.45/0.65 (define @t130 () (or @t72 @t129 @t72 @t128)) % 0.45/0.65 (define @t131 () (or @t129 @t72 @t128)) % 0.45/0.65 (define @t132 () (forall @t14 @t131)) % 0.45/0.65 (define @t133 () (or @t71 @t70 @t69 @t132)) % 0.45/0.65 (define @t134 () (or @t71 @t70 @t69 @t131)) % 0.45/0.65 (define @t135 () (or @t129 @t72 @t71 @t70 @t69 @t128)) % 0.45/0.65 (define @t136 () (or @t72 @t71 @t70 @t69 @t128)) % 0.45/0.65 (define @t137 () (forall @t96 (or @t92 @t69 @t91 @t90 (and (or (not (= tptp.nil @t83)) @t86) @t85)))) % 0.45/0.65 (define @t138 () (@quantifiers_skolemize @t137 0)) % 0.45/0.65 (define @t139 () (@quantifiers_skolemize @t137 1)) % 0.45/0.65 (define @t140 () (tptp.neq @t138 tptp.nil)) % 0.45/0.65 (define @t141 () (not @t140)) % 0.45/0.65 (define @t142 () (or @t141 (not (tptp.frontsegP @t139 @t138)))) % 0.45/0.65 (define @t143 () (= tptp.nil @t138)) % 0.45/0.65 (define @t144 () (not @t143)) % 0.45/0.65 (define @t145 () (= tptp.nil @t139)) % 0.45/0.65 (define @t146 () (not @t145)) % 0.45/0.65 (define @t147 () (or @t146 @t144)) % 0.45/0.65 (define @t148 () (and @t147 @t142)) % 0.45/0.65 (define @t149 () (tptp.neq @t139 tptp.nil)) % 0.45/0.65 (define @t150 () (not @t149)) % 0.45/0.65 (define @t151 () (not (tptp.ssList @t139))) % 0.45/0.65 (define @t152 () (not (tptp.ssList @t138))) % 0.45/0.65 (define @t153 () (or @t152 @t140 @t151 @t150 @t148)) % 0.45/0.65 (define @t154 () (not @t153)) % 0.45/0.65 (define @t155 () (not @t137)) % 0.45/0.65 (define @t156 () (not (= @t138 tptp.nil))) % 0.45/0.65 (define @t157 () (or @t146 @t156)) % 0.45/0.65 (define @t158 () (and @t157 @t142)) % 0.45/0.65 (define @t159 () (or @t152 @t140 @t151 @t150 @t158)) % 0.45/0.65 (define @t160 () (not @t159)) % 0.45/0.65 (define @t161 () (@list true)) % 0.45/0.65 (define @t162 () (@list @t153)) % 0.45/0.65 (define @t163 () (@list @t147)) % 0.45/0.65 (assume @p1 (forall @t9 (=> @t8 (forall @t7 (=> @t6 @t5))))) % 0.45/0.65 (assume @p2 (exists @t9 (and @t8 (exists @t7 (and @t6 @t4))))) % 0.45/0.65 (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))))))))))) % 0.45/0.65 (assume @p4 (forall @t9 (=> @t17 (= (tptp.singletonP @t2) (exists @t7 (and @t6 (= @t18 @t2))))))) % 0.45/0.65 (assume @p5 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t20 (exists @t16 (and @t15 (= @t19 @t2))))))))) % 0.45/0.65 (assume @p6 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t23 (exists @t16 (and @t15 (= @t22 @t2))))))))) % 0.45/0.65 (assume @p7 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t24 (exists @t16 (and @t15 (exists @t14 (and @t13 (= (tptp.app @t22 @t10) @t2))))))))))) % 0.45/0.65 (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))))))))))))))))) % 0.45/0.65 (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)))))))))))))))) % 0.45/0.65 (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))))))))))))))))) % 0.45/0.65 (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))))))))))))))) % 0.45/0.65 (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))))))))))))))) % 0.45/0.65 (assume @p13 (forall @t9 (=> @t17 (= (tptp.duplicatefreeP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t34 (forall @t14 (=> @t13 (forall @t33 (=> @t32 (forall @t31 (=> @t30 (=> @t29 (not @t36)))))))))))))))) % 0.45/0.65 (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))))))))))))) % 0.45/0.65 (assume @p15 (forall @t9 (=> @t17 (forall @t7 (=> @t21 @t5))))) % 0.45/0.65 (assume @p16 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (tptp.ssList @t37)))))) % 0.45/0.65 (assume @p17 (tptp.ssList tptp.nil)) % 0.45/0.65 (assume @p18 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= @t37 @t2))))))) % 0.45/0.65 (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 (= @t12 @t10) @t38))))))))))) % 0.45/0.65 (assume @p20 (forall @t9 (=> @t17 (or @t40 (exists @t7 (and @t21 (exists @t16 (and @t34 (= @t39 @t2))))))))) % 0.45/0.65 (assume @p21 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= tptp.nil @t37))))))) % 0.45/0.65 (assume @p22 (forall @t9 (=> @t17 (=> @t42 (tptp.ssItem @t41))))) % 0.45/0.65 (assume @p23 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.hd @t37) @t1)))))) % 0.45/0.65 (assume @p24 (forall @t9 (=> @t17 (=> @t42 (tptp.ssList @t43))))) % 0.45/0.65 (assume @p25 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.tl @t37) @t2)))))) % 0.45/0.65 (assume @p26 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (tptp.ssList @t44)))))) % 0.45/0.65 (assume @p27 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t34 (= (tptp.cons @t12 @t45) (tptp.app @t39 @t2))))))))) % 0.45/0.65 (assume @p28 (forall @t9 (=> @t17 (= (tptp.app tptp.nil @t2) @t2)))) % 0.45/0.65 (assume @p29 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> (and @t47 @t46) @t3)))))) % 0.45/0.65 (assume @p30 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t47 @t26) (tptp.leq @t2 @t12))))))))) % 0.45/0.65 (assume @p31 (forall @t9 (=> @t8 (tptp.leq @t2 @t2)))) % 0.45/0.65 (assume @p32 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t48 @t46)))))) % 0.45/0.65 (assume @p33 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t50 (not @t49))))))) % 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@t57)))) % 0.45/0.65 (assume @p74 (tptp.equalelemsP tptp.nil)) % 0.45/0.65 (assume @p75 (forall @t9 (=> @t17 (=> @t42 (exists @t7 (and @t6 (= @t41 @t1))))))) % 0.45/0.65 (assume @p76 (forall @t9 (=> @t17 (=> @t42 (exists @t7 (and @t21 (= @t43 @t1))))))) % 0.45/0.65 (assume @p77 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t60 @t42 (= @t58 @t41) (= (tptp.tl @t1) @t43)) @t38)))))) % 0.45/0.65 (assume @p78 (forall @t9 (=> @t17 (=> @t42 (= (tptp.cons @t41 @t43) @t2))))) % 0.45/0.65 (assume @p79 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (= @t22 @t44) @t62)))))))) % 0.45/0.65 (assume @p80 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (= @t19 @t45) @t62)))))))) % 0.45/0.65 (assume @p81 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= @t37 (tptp.app @t18 @t2))))))) % 0.45/0.65 (assume @p82 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (= (tptp.app @t44 @t12) (tptp.app @t2 @t19))))))))) % 0.45/0.65 (assume @p83 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= (= tptp.nil @t44) (and @t59 @t40))))))) % 0.45/0.65 (assume @p84 (forall @t9 (=> @t17 (= (tptp.app @t2 tptp.nil) @t2)))) % 0.45/0.65 (assume @p85 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> @t42 (= (tptp.hd @t44) @t41))))))) % 0.45/0.65 (assume @p86 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> @t42 (= (tptp.tl @t44) (tptp.app @t43 @t1)))))))) % 0.45/0.65 (assume @p87 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> (and @t48 (tptp.geq @t1 @t2)) @t3)))))) % 0.45/0.65 (assume @p88 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t48 (tptp.geq @t1 @t12)) (tptp.geq @t2 @t12))))))))) % 0.45/0.65 (assume @p89 (forall @t9 (=> @t8 (tptp.geq @t2 @t2)))) % 0.45/0.65 (assume @p90 (forall @t9 (=> @t8 (not (tptp.lt @t2 @t2))))) % 0.45/0.65 (assume @p91 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t47 @t35) @t51)))))))) % 0.45/0.65 (assume @p92 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t47 (or @t3 @t50))))))) % 0.45/0.65 (assume @p93 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t50 (and @t4 @t47))))))) % 0.45/0.65 (assume @p94 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t52 (not (tptp.gt @t1 @t2)))))))) % 0.45/0.65 (assume @p95 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t52 (tptp.gt @t1 @t12)) (tptp.gt @t2 @t12))))))))) % 0.45/0.65 (assume @p96 @t82) % 0.45/0.65 (assume @p97 true) % 0.45/0.65 (step @p98 :rule evaluate :args ((= true false))) % 0.45/0.65 (step @p99 :rule refl :args (@t85)) % 0.45/0.65 (step @p100 :rule refl :args (@t86)) % 0.45/0.65 (step @p101 :rule eq-symm :args (@t83 tptp.nil)) % 0.45/0.65 (step @p102 :rule cong :premises (@p101) :args (@t87)) % 0.45/0.65 (step @p103 :rule nary_cong :premises (@p102 @p100) :args (@t88)) % 0.45/0.65 (step @p104 :rule nary_cong :premises (@p103 @p99) :args (@t89)) % 0.45/0.65 (step @p105 :rule refl :args (@t90)) % 0.45/0.65 (step @p106 :rule refl :args (@t91)) % 0.45/0.65 (step @p107 :rule refl :args (@t69)) % 0.45/0.65 (step @p108 :rule refl :args (@t92)) % 0.45/0.65 (step @p109 :rule nary_cong :premises (@p108 @p107 @p106 @p105 @p104) :args (@t93)) % 0.45/0.65 (step @p110 :rule aci_norm :args ((= @t95 @t93))) % 0.45/0.65 (step @p111 :rule trans :premises (@p110 @p109)) % 0.45/0.65 (step @p112 :rule cong :premises (@p111) :args (@t97)) % 0.45/0.65 (step @p113 :rule quant-merge-prenex :args ((= (forall @t9 @t99) @t97))) % 0.45/0.65 (step @p114 :rule alpha_equiv :args (@t100 (@list @t83) (@list @t1))) % 0.45/0.65 (step @p115 :rule refl :args (@t69)) % 0.45/0.65 (step @p116 :rule refl :args (@t92)) % 0.45/0.65 (step @p117 :rule nary_cong :premises (@p116 @p115 @p114) :args (@t101)) % 0.45/0.65 (step @p118 :rule quant-miniscope-or :args ((= @t99 @t101))) % 0.45/0.65 (step @p119 :rule trans :premises (@p118 @p117)) % 0.45/0.65 (step @p120 :rule symm :premises (@p119)) % 0.45/0.65 (step @p121 :rule cong :premises (@p120) :args ((forall @t9 @t107))) % 0.45/0.65 (step @p122 :rule trans :premises (@p121 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0.45/0.65 (step @p152 :rule cong :premises (@p151) :args (@t71)) % 0.45/0.65 (step @p153 :rule nary_cong :premises (@p152 @p150 @p149 @p148) :args (@t118)) % 0.45/0.65 (step @p154 :rule aci_norm :args ((= @t119 @t118))) % 0.45/0.65 (step @p155 :rule trans :premises (@p154 @p153)) % 0.45/0.65 (step @p156 :rule cong :premises (@p155) :args (@t120)) % 0.45/0.65 (step @p157 :rule trans :premises (@p156 @p147)) % 0.45/0.65 (step @p158 :rule trans :premises (@p157 @p146)) % 0.45/0.65 (step @p159 :rule refl :args (@t104)) % 0.45/0.65 (step @p160 :rule refl :args (@t70)) % 0.45/0.65 (step @p161 :rule nary_cong :premises (@p160 @p107 @p159 @p158) :args (@t121)) % 0.45/0.65 (step @p162 :rule trans :premises (@p161 @p138)) % 0.45/0.65 (step @p163 :rule quant-miniscope-or :args ((= (forall @t16 @t122) @t121))) % 0.45/0.65 (step @p164 :rule aci_norm :args ((= @t123 @t122))) % 0.45/0.65 (step @p165 :rule cong :premises (@p164) :args ((forall @t16 @t123))) % 0.45/0.65 (step @p166 :rule trans 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@p181 :rule quant-var-elim-eq :args ((= (forall @t14 (or (not (= @t10 @t1)) @t129 @t72 @t128)) @t127))) % 0.45/0.65 (step @p182 :rule refl :args (@t128)) % 0.45/0.65 (step @p183 :rule refl :args (@t72)) % 0.45/0.65 (step @p184 :rule refl :args (@t129)) % 0.45/0.65 (step @p185 :rule eq-symm :args (@t1 @t10)) % 0.45/0.65 (step @p186 :rule cong :premises (@p185) :args (@t72)) % 0.45/0.65 (step @p187 :rule nary_cong :premises (@p186 @p184 @p183 @p182) :args (@t130)) % 0.45/0.65 (step @p188 :rule aci_norm :args ((= @t131 @t130))) % 0.45/0.65 (step @p189 :rule trans :premises (@p188 @p187)) % 0.45/0.65 (step @p190 :rule cong :premises (@p189) :args (@t132)) % 0.45/0.65 (step @p191 :rule trans :premises (@p190 @p181)) % 0.45/0.65 (step @p192 :rule trans :premises (@p191 @p180)) % 0.45/0.65 (step @p193 :rule refl :args (@t71)) % 0.45/0.65 (step @p194 :rule nary_cong :premises (@p193 @p160 @p107 @p192) :args (@t133)) % 0.45/0.65 (step @p195 :rule trans :premises (@p194 @p173)) % 0.45/0.65 (step @p196 :rule quant-miniscope-or :args ((= (forall @t14 @t134) @t133))) % 0.45/0.65 (step @p197 :rule aci_norm :args ((= @t135 @t134))) % 0.45/0.65 (step @p198 :rule cong :premises (@p197) :args ((forall @t14 @t135))) % 0.45/0.65 (step @p199 :rule trans :premises (@p198 @p196)) % 0.45/0.65 (step @p200 :rule trans :premises (@p199 @p195)) % 0.45/0.65 (step @p201 :rule aci_norm :args ((= (or @t129 @t136) @t135))) % 0.45/0.65 (step @p202 :rule bool-impl-elim :args (@t13 @t136)) % 0.45/0.65 (step @p203 :rule trans :premises (@p202 @p201)) % 0.45/0.65 (step @p204 :rule cong :premises (@p203) :args ((forall @t14 (=> @t13 @t136)))) % 0.45/0.65 (step @p205 :rule trans :premises (@p204 @p200)) % 0.45/0.65 (step @p206 :rule refl :args (@t64)) % 0.45/0.65 (step @p207 :rule eq-symm :args (tptp.nil @t12)) % 0.45/0.65 (step @p208 :rule cong :premises (@p207) :args (@t65)) % 0.45/0.65 (step @p209 :rule eq-symm :args (tptp.nil @t10)) % 0.45/0.65 (step @p210 :rule cong :premises (@p209) :args (@t66)) % 0.45/0.65 (step @p211 :rule nary_cong :premises (@p210 @p208) :args (@t67)) % 0.45/0.65 (step @p212 :rule nary_cong :premises (@p211 @p206) :args (@t68)) % 0.45/0.65 (step @p213 :rule refl :args (@t72)) % 0.45/0.65 (step @p214 :rule nary_cong :premises (@p213 @p193 @p160 @p107 @p212) :args (@t73)) % 0.45/0.65 (step @p215 :rule refl :args (@t13)) % 0.45/0.65 (step @p216 :rule cong :premises (@p215 @p214) :args (@t74)) % 0.45/0.65 (step @p217 :rule cong :premises (@p216) :args (@t75)) % 0.45/0.65 (step @p218 :rule trans :premises (@p217 @p205)) % 0.45/0.65 (step @p219 :rule refl :args (@t15)) % 0.45/0.65 (step @p220 :rule cong :premises (@p219 @p218) :args (@t76)) % 0.45/0.65 (step @p221 :rule cong :premises (@p220) :args (@t77)) % 0.45/0.65 (step @p222 :rule trans :premises (@p221 @p172)) % 0.45/0.65 (step @p223 :rule refl :args (@t21)) % 0.45/0.65 (step @p224 :rule cong :premises (@p223 @p222) :args (@t78)) % 0.45/0.65 (step @p225 :rule cong :premises (@p224) :args (@t79)) % 0.45/0.65 (step @p226 :rule trans :premises (@p225 @p137)) % 0.45/0.65 (step @p227 :rule refl :args (@t17)) % 0.45/0.65 (step @p228 :rule cong :premises (@p227 @p226) :args (@t80)) % 0.45/0.65 (step @p229 :rule cong :premises (@p228) :args (@t81)) % 0.45/0.65 (step @p230 :rule trans :premises (@p229 @p128)) % 0.45/0.65 (step @p231 :rule cong :premises (@p230) :args (@t82)) % 0.45/0.65 (step @p232 :rule eq_resolve :premises (@p96 @p231)) % 0.45/0.65 (step @p233 :rule refl :args (@t154)) % 0.45/0.65 (step @p234 :rule bool-double-not-elim :args (@t137)) % 0.45/0.65 (step @p235 :rule nary_cong :premises (@p234 @p233) :args ((or (not @t155) @t154))) % 0.45/0.65 (step @p236 :rule refl :args (@t142)) % 0.45/0.65 (step @p237 :rule eq-symm :args (@t138 tptp.nil)) % 0.45/0.65 (step @p238 :rule cong :premises (@p237) :args (@t156)) % 0.45/0.65 (step @p239 :rule refl :args (@t146)) % 0.45/0.65 (step @p240 :rule nary_cong :premises (@p239 @p238) :args (@t157)) % 0.45/0.65 (step @p241 :rule nary_cong :premises (@p240 @p236) :args (@t158)) % 0.45/0.65 (step @p242 :rule refl :args (@t150)) % 0.45/0.65 (step @p243 :rule refl :args (@t151)) % 0.45/0.65 (step @p244 :rule refl :args (@t140)) % 0.45/0.65 (step @p245 :rule refl :args (@t152)) % 0.45/0.65 (step @p246 :rule nary_cong :premises (@p245 @p244 @p243 @p242 @p241) :args (@t159)) % 0.45/0.65 (step @p247 :rule cong :premises (@p246) :args (@t160)) % 0.45/0.65 (step @p248 :rule refl :args (@t155)) % 0.45/0.65 (step @p249 :rule cong :premises (@p248 @p247) :args ((=> @t155 @t160))) % 0.45/0.65 (assume-push @p300 @t155) % 0.45/0.65 (step @p251 :rule skolemize :premises (@p232)) % 0.45/0.65 (step-pop @p301 :rule scope :premises (@p251)) % 0.45/0.65 (step @p252 :rule process_scope :premises (@p301) :args (@t160)) % 0.45/0.65 (step @p254 :rule eq_resolve :premises (@p252 @p249)) % 0.45/0.65 (step @p255 :rule implies_elim :premises (@p254)) % 0.45/0.65 (step @p256 :rule eq_resolve :premises (@p255 @p235)) % 0.45/0.65 (step @p257 :rule chain_m_resolution :premises (@p256 @p232) :args (@t154 @t161 (@list @t137))) % 0.45/0.65 (step @p258 :rule cnf_or_neg :args (@t153 1)) % 0.45/0.65 (step @p259 :rule reordering :premises (@p258) :args ((or @t141 @t153))) % 0.45/0.65 (step @p260 :rule chain_m_resolution :premises (@p259 @p257) :args (@t141 @t161 @t162)) % 0.45/0.65 (step @p261 :rule false_intro :premises (@p260)) % 0.45/0.65 (step @p262 :rule refl :args (tptp.nil)) % 0.45/0.65 (step @p263 :rule bool-double-not-elim :args (@t140)) % 0.45/0.65 (step @p264 :rule nary_cong :premises (@p236 @p263) :args ((or @t142 (not @t141)))) % 0.45/0.65 (step @p265 :rule cnf_or_neg :args (@t142 0)) % 0.45/0.65 (step @p266 :rule eq_resolve :premises (@p265 @p264)) % 0.45/0.65 (step @p267 :rule reordering :premises (@p266) :args ((or @t140 @t142))) % 0.45/0.65 (step @p268 :rule chain_m_resolution :premises (@p267 @p260) :args (@t142 @t161 (@list @t140))) % 0.45/0.65 (step @p269 :rule cnf_or_neg :args (@t153 4)) % 0.45/0.65 (step @p270 :rule chain_m_resolution :premises (@p269 @p257) :args ((not @t148) @t161 @t162)) % 0.45/0.65 (step @p271 :rule cnf_and_neg :args (@t148)) % 0.45/0.65 (step @p272 :rule chain_m_resolution :premises (@p271 @p270 @p268) :args ((not @t147) (@list true false) (@list @t148 @t142))) % 0.45/0.65 (step @p273 :rule bool-double-not-elim :args (@t143)) % 0.45/0.65 (step @p274 :rule refl :args (@t147)) % 0.45/0.65 (step @p275 :rule nary_cong :premises (@p274 @p273) :args ((or @t147 (not @t144)))) % 0.45/0.65 (step @p276 :rule cnf_or_neg :args (@t147 1)) % 0.45/0.65 (step @p277 :rule eq_resolve :premises (@p276 @p275)) % 0.45/0.65 (step @p278 :rule reordering :premises (@p277) :args ((or @t143 @t147))) % 0.45/0.65 (step @p279 :rule chain_m_resolution :premises (@p278 @p272) :args (@t143 @t161 @t163)) % 0.45/0.65 (step @p280 :rule bool-double-not-elim :args (@t145)) % 0.45/0.65 (step @p281 :rule nary_cong :premises (@p274 @p280) :args ((or @t147 (not @t146)))) % 0.45/0.65 (step @p282 :rule cnf_or_neg :args (@t147 0)) % 0.45/0.65 (step @p283 :rule eq_resolve :premises (@p282 @p281)) % 0.45/0.65 (step @p284 :rule reordering :premises (@p283) :args ((or @t145 @t147))) % 0.45/0.65 (step @p285 :rule chain_m_resolution :premises (@p284 @p272) :args (@t145 @t161 @t163)) % 0.45/0.65 (step @p286 :rule symm :premises (@p285)) % 0.45/0.65 (step @p287 :rule trans :premises (@p286 @p279)) % 0.45/0.65 (step @p288 :rule cong :premises (@p287 @p262) :args (@t149)) % 0.45/0.65 (step @p289 :rule bool-double-not-elim :args (@t149)) % 0.45/0.65 (step @p290 :rule refl :args (@t153)) % 0.45/0.65 (step @p291 :rule nary_cong :premises (@p290 @p289) :args ((or @t153 (not @t150)))) % 0.45/0.65 (step @p292 :rule cnf_or_neg :args (@t153 3)) % 0.45/0.65 (step @p293 :rule eq_resolve :premises (@p292 @p291)) % 0.45/0.65 (step @p294 :rule reordering :premises (@p293) :args ((or @t149 @t153))) % 0.45/0.65 (step @p295 :rule chain_m_resolution :premises (@p294 @p257) :args (@t149 @t161 @t162)) % 0.45/0.65 (step @p296 :rule true_intro :premises (@p295)) % 0.45/0.65 (step @p297 :rule symm :premises (@p296)) % 0.45/0.65 (step @p298 :rule trans :premises (@p297 @p288 @p261)) % 0.45/0.65 (step @p299 false :rule eq_resolve :premises (@p298 @p98)) % 0.45/0.65 ) % 0.45/0.65 % SZS output end Proof % 0.45/0.65 % cvc5 exiting %------------------------------------------------------------------------------