%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWC205+1 : TPTP v9.2.1. Released v2.4.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n010.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 0.44s 0.69s % Output : Proof 0.44s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWC205+1 : TPTP v9.2.1. Released v2.4.0. % 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n010.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 19:24:25 EDT 2026 % 0.17/0.34 % CPUTime : % 0.30/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.44/0.69 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.44/0.69 % SZS status Theorem % 0.44/0.69 % SZS output start Proof % 0.44/0.69 ( % 0.44/0.69 (declare-sort $$unsorted 0) % 0.44/0.69 (declare-const tptp.tl (-> $$unsorted $$unsorted)) % 0.44/0.69 (declare-const tptp.hd (-> $$unsorted $$unsorted)) % 0.44/0.69 (declare-const tptp.duplicatefreeP (-> $$unsorted Bool)) % 0.44/0.69 (declare-const tptp.strictorderedP (-> $$unsorted Bool)) % 0.44/0.69 (declare-const tptp.geq (-> $$unsorted $$unsorted Bool)) % 0.44/0.69 (declare-const tptp.strictorderP (-> $$unsorted Bool)) % 0.44/0.69 (declare-const tptp.equalelemsP (-> $$unsorted Bool)) % 0.44/0.69 (declare-const tptp.totalorderP (-> $$unsorted Bool)) % 0.44/0.69 (declare-const tptp.neq (-> $$unsorted $$unsorted Bool)) % 0.44/0.69 (declare-const tptp.totalorderedP (-> $$unsorted Bool)) % 0.44/0.69 (declare-const tptp.singletonP (-> $$unsorted Bool)) % 0.44/0.69 (declare-const tptp.cons (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.69 (declare-const tptp.app (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.69 (declare-const tptp.nil $$unsorted) % 0.44/0.69 (declare-const tptp.memberP (-> $$unsorted $$unsorted Bool)) % 0.44/0.69 (declare-const tptp.lt (-> $$unsorted $$unsorted Bool)) % 0.44/0.69 (declare-const tptp.frontsegP (-> $$unsorted $$unsorted Bool)) % 0.44/0.69 (declare-const tptp.rearsegP (-> $$unsorted $$unsorted Bool)) % 0.44/0.69 (declare-const tptp.gt (-> $$unsorted $$unsorted Bool)) % 0.44/0.69 (declare-const tptp.ssList (-> $$unsorted Bool)) % 0.44/0.69 (declare-const tptp.segmentP (-> $$unsorted $$unsorted Bool)) % 0.44/0.69 (declare-const tptp.cyclefreeP (-> $$unsorted Bool)) % 0.44/0.69 (declare-const tptp.ssItem (-> $$unsorted Bool)) % 0.44/0.69 (declare-const tptp.leq (-> $$unsorted $$unsorted Bool)) % 0.44/0.69 (define @t1 () (@var "V" $$unsorted)) % 0.44/0.69 (define @t2 () (@var "U" $$unsorted)) % 0.44/0.69 (define @t3 () (= @t2 @t1)) % 0.44/0.69 (define @t4 () (not @t3)) % 0.44/0.69 (define @t5 () (= (tptp.neq @t2 @t1) @t4)) % 0.44/0.69 (define @t6 () (tptp.ssItem @t1)) % 0.44/0.69 (define @t7 () (@list @t1)) % 0.44/0.69 (define @t8 () (tptp.ssItem @t2)) % 0.44/0.69 (define @t9 () (@list @t2)) % 0.44/0.69 (define @t10 () (@var "X" $$unsorted)) % 0.44/0.69 (define @t11 () (tptp.cons @t1 @t10)) % 0.44/0.69 (define @t12 () (@var "W" $$unsorted)) % 0.44/0.69 (define @t13 () (tptp.ssList @t10)) % 0.44/0.69 (define @t14 () (@list @t10)) % 0.44/0.69 (define @t15 () (tptp.ssList @t12)) % 0.44/0.69 (define @t16 () (@list @t12)) % 0.44/0.69 (define @t17 () (tptp.ssList @t2)) % 0.44/0.69 (define @t18 () (tptp.cons @t1 tptp.nil)) % 0.44/0.69 (define @t19 () (tptp.app @t1 @t12)) % 0.44/0.69 (define @t20 () (tptp.frontsegP @t2 @t1)) % 0.44/0.69 (define @t21 () (tptp.ssList @t1)) % 0.44/0.69 (define @t22 () (tptp.app @t12 @t1)) % 0.44/0.69 (define @t23 () (tptp.rearsegP @t2 @t1)) % 0.44/0.69 (define @t24 () (tptp.segmentP @t2 @t1)) % 0.44/0.69 (define @t25 () (tptp.leq @t12 @t1)) % 0.44/0.69 (define @t26 () (tptp.leq @t1 @t12)) % 0.44/0.69 (define @t27 () (@var "Z" $$unsorted)) % 0.44/0.69 (define @t28 () (@var "Y" $$unsorted)) % 0.44/0.69 (define @t29 () (= (tptp.app (tptp.app @t10 (tptp.cons @t1 @t28)) (tptp.cons @t12 @t27)) @t2)) % 0.44/0.69 (define @t30 () (tptp.ssList @t27)) % 0.44/0.69 (define @t31 () (@list @t27)) % 0.44/0.69 (define @t32 () (tptp.ssList @t28)) % 0.44/0.69 (define @t33 () (@list @t28)) % 0.44/0.69 (define @t34 () (tptp.ssItem @t12)) % 0.44/0.69 (define @t35 () (tptp.lt @t1 @t12)) % 0.44/0.69 (define @t36 () (= @t1 @t12)) % 0.44/0.69 (define @t37 () (forall @t7 (=> @t21 @t5))) % 0.44/0.69 (define @t38 () (=> @t17 @t37)) % 0.44/0.69 (define @t39 () (forall @t9 @t38)) % 0.44/0.69 (define @t40 () (tptp.cons @t1 @t2)) % 0.44/0.69 (define @t41 () (tptp.ssList tptp.nil)) % 0.44/0.69 (define @t42 () (= @t1 @t2)) % 0.44/0.69 (define @t43 () (tptp.cons @t12 @t1)) % 0.44/0.69 (define @t44 () (= tptp.nil @t2)) % 0.44/0.69 (define @t45 () (tptp.hd @t2)) % 0.44/0.69 (define @t46 () (not @t44)) % 0.44/0.69 (define @t47 () (tptp.tl @t2)) % 0.44/0.69 (define @t48 () (tptp.app @t2 @t1)) % 0.44/0.69 (define @t49 () (tptp.app @t1 @t2)) % 0.44/0.69 (define @t50 () (tptp.leq @t1 @t2)) % 0.44/0.69 (define @t51 () (tptp.leq @t2 @t1)) % 0.44/0.69 (define @t52 () (tptp.geq @t2 @t1)) % 0.44/0.69 (define @t53 () (tptp.lt @t1 @t2)) % 0.44/0.69 (define @t54 () (tptp.lt @t2 @t1)) % 0.44/0.69 (define @t55 () (tptp.lt @t2 @t12)) % 0.44/0.69 (define @t56 () (tptp.gt @t2 @t1)) % 0.44/0.69 (define @t57 () (tptp.memberP @t12 @t2)) % 0.44/0.69 (define @t58 () (tptp.app @t12 @t2)) % 0.44/0.69 (define @t59 () (tptp.cons @t2 tptp.nil)) % 0.44/0.69 (define @t60 () (tptp.hd @t1)) % 0.44/0.69 (define @t61 () (= tptp.nil @t1)) % 0.44/0.69 (define @t62 () (not @t61)) % 0.44/0.69 (define @t63 () (tptp.cons @t2 @t1)) % 0.44/0.69 (define @t64 () (= @t12 @t2)) % 0.44/0.69 (define @t65 () (= tptp.nil @t10)) % 0.44/0.69 (define @t66 () (= tptp.nil @t12)) % 0.44/0.69 (define @t67 () (not @t66)) % 0.44/0.69 (define @t68 () (and @t67 @t65)) % 0.44/0.69 (define @t69 () (not @t65)) % 0.44/0.69 (define @t70 () (and @t69 @t66)) % 0.44/0.69 (define @t71 () (tptp.neq @t2 tptp.nil)) % 0.44/0.69 (define @t72 () (not (tptp.neq @t1 tptp.nil))) % 0.44/0.69 (define @t73 () (not (= @t2 @t12))) % 0.44/0.69 (define @t74 () (not (= @t1 @t10))) % 0.44/0.69 (define @t75 () (or @t74 @t73 @t72 @t71 @t70 @t68)) % 0.44/0.69 (define @t76 () (=> @t13 @t75)) % 0.44/0.69 (define @t77 () (forall @t14 @t76)) % 0.44/0.69 (define @t78 () (=> @t15 @t77)) % 0.44/0.69 (define @t79 () (forall @t16 @t78)) % 0.44/0.69 (define @t80 () (=> @t21 @t79)) % 0.44/0.69 (define @t81 () (forall @t7 @t80)) % 0.44/0.69 (define @t82 () (=> @t17 @t81)) % 0.44/0.69 (define @t83 () (forall @t9 @t82)) % 0.44/0.69 (define @t84 () (not @t83)) % 0.44/0.69 (define @t85 () (@var "BOUND_VARIABLE_10967" $$unsorted)) % 0.44/0.69 (define @t86 () (= @t2 tptp.nil)) % 0.44/0.69 (define @t87 () (not @t86)) % 0.44/0.69 (define @t88 () (= @t85 tptp.nil)) % 0.44/0.69 (define @t89 () (and @t87 @t88)) % 0.44/0.69 (define @t90 () (not @t88)) % 0.44/0.69 (define @t91 () (and @t90 @t86)) % 0.44/0.69 (define @t92 () (not (tptp.neq @t85 tptp.nil))) % 0.44/0.69 (define @t93 () (not (tptp.ssList @t85))) % 0.44/0.69 (define @t94 () (not @t17)) % 0.44/0.69 (define @t95 () (or @t94 @t71 @t93 @t92 @t91 @t89)) % 0.44/0.69 (define @t96 () (or @t93 @t92 @t91 @t89)) % 0.44/0.69 (define @t97 () (or @t94 @t71 @t96)) % 0.44/0.69 (define @t98 () (@list @t2 @t85)) % 0.44/0.69 (define @t99 () (forall @t98 @t97)) % 0.44/0.69 (define @t100 () (@list @t85)) % 0.44/0.69 (define @t101 () (forall @t100 @t97)) % 0.44/0.69 (define @t102 () (forall @t100 @t96)) % 0.44/0.69 (define @t103 () (@list @t1)) % 0.44/0.69 (define @t104 () (or @t94 @t71 @t102)) % 0.44/0.69 (define @t105 () (= @t1 tptp.nil)) % 0.44/0.69 (define @t106 () (and @t87 @t105)) % 0.44/0.69 (define @t107 () (not @t105)) % 0.44/0.69 (define @t108 () (and @t107 @t86)) % 0.44/0.69 (define @t109 () (not @t21)) % 0.44/0.69 (define @t110 () (or @t109 @t72 @t108 @t106)) % 0.44/0.69 (define @t111 () (forall @t7 @t110)) % 0.44/0.69 (define @t112 () (or @t94 @t71 @t111)) % 0.44/0.69 (define @t113 () (or @t71 @t94 @t111)) % 0.44/0.69 (define @t114 () (or @t71 @t94 @t110)) % 0.44/0.69 (define @t115 () (or @t109 @t72 @t71 @t94 @t108 @t106)) % 0.44/0.69 (define @t116 () (or @t72 @t71 @t109 @t94 @t108 @t106)) % 0.44/0.69 (define @t117 () (or @t94 @t108 @t106)) % 0.44/0.69 (define @t118 () (not (= @t2 @t2))) % 0.44/0.69 (define @t119 () (or @t94 @t118 @t108 @t106)) % 0.44/0.69 (define @t120 () (= @t12 tptp.nil)) % 0.44/0.69 (define @t121 () (not @t120)) % 0.44/0.69 (define @t122 () (and @t121 @t105)) % 0.44/0.69 (define @t123 () (and @t107 @t120)) % 0.44/0.69 (define @t124 () (not @t15)) % 0.44/0.69 (define @t125 () (or @t73 @t124 @t73 @t123 @t122)) % 0.44/0.69 (define @t126 () (or @t124 @t73 @t123 @t122)) % 0.44/0.69 (define @t127 () (forall @t16 @t126)) % 0.44/0.69 (define @t128 () (or @t72 @t71 @t109 @t127)) % 0.44/0.69 (define @t129 () (or @t72 @t71 @t109 @t126)) % 0.44/0.69 (define @t130 () (or @t124 @t73 @t72 @t71 @t109 @t123 @t122)) % 0.44/0.69 (define @t131 () (or @t73 @t72 @t71 @t109 @t123 @t122)) % 0.44/0.69 (define @t132 () (or @t109 @t123 @t122)) % 0.44/0.69 (define @t133 () (not (= @t1 @t1))) % 0.44/0.69 (define @t134 () (or @t109 @t133 @t123 @t122)) % 0.44/0.69 (define @t135 () (= @t10 tptp.nil)) % 0.44/0.69 (define @t136 () (and @t121 @t135)) % 0.44/0.69 (define @t137 () (and (not @t135) @t120)) % 0.44/0.69 (define @t138 () (not @t13)) % 0.44/0.69 (define @t139 () (or @t74 @t138 @t74 @t137 @t136)) % 0.44/0.69 (define @t140 () (or @t138 @t74 @t137 @t136)) % 0.44/0.69 (define @t141 () (forall @t14 @t140)) % 0.44/0.69 (define @t142 () (or @t73 @t72 @t71 @t141)) % 0.44/0.69 (define @t143 () (or @t73 @t72 @t71 @t140)) % 0.44/0.69 (define @t144 () (or @t138 @t74 @t73 @t72 @t71 @t137 @t136)) % 0.44/0.69 (define @t145 () (or @t74 @t73 @t72 @t71 @t137 @t136)) % 0.44/0.69 (define @t146 () (= tptp.nil @t85)) % 0.44/0.69 (define @t147 () (forall @t98 (or @t94 @t71 @t93 @t92 (and (not @t146) @t86) (and @t87 @t146)))) % 0.44/0.69 (define @t148 () (@quantifiers_skolemize @t147 1)) % 0.44/0.69 (define @t149 () (= tptp.nil @t148)) % 0.44/0.69 (define @t150 () (@quantifiers_skolemize @t147 0)) % 0.44/0.69 (define @t151 () (= tptp.nil @t150)) % 0.44/0.69 (define @t152 () (not @t151)) % 0.44/0.69 (define @t153 () (not @t149)) % 0.44/0.69 (define @t154 () (and @t153 @t151)) % 0.44/0.69 (define @t155 () (tptp.neq @t148 tptp.nil)) % 0.44/0.69 (define @t156 () (not @t155)) % 0.44/0.69 (define @t157 () (not (tptp.ssList @t148))) % 0.44/0.69 (define @t158 () (tptp.neq @t150 tptp.nil)) % 0.44/0.69 (define @t159 () (tptp.ssList @t150)) % 0.44/0.69 (define @t160 () (not @t159)) % 0.44/0.69 (define @t161 () (or @t160 @t158 @t157 @t156 @t154 (and @t152 @t149))) % 0.44/0.69 (define @t162 () (not @t161)) % 0.44/0.69 (define @t163 () (not @t147)) % 0.44/0.69 (define @t164 () (= @t150 tptp.nil)) % 0.44/0.69 (define @t165 () (not @t164)) % 0.44/0.69 (define @t166 () (and @t165 @t149)) % 0.44/0.69 (define @t167 () (and @t153 @t164)) % 0.44/0.69 (define @t168 () (or @t160 @t158 @t157 @t156 @t167 @t166)) % 0.44/0.69 (define @t169 () (not @t168)) % 0.44/0.69 (define @t170 () (@list true)) % 0.44/0.69 (define @t171 () (@list @t161)) % 0.44/0.69 (define @t172 () (@var "BOUND_VARIABLE_9096" $$unsorted)) % 0.44/0.69 (define @t173 () (= (tptp.neq @t2 @t172) (not (= @t2 @t172)))) % 0.44/0.69 (define @t174 () (not (tptp.ssList @t172))) % 0.44/0.69 (define @t175 () (or @t94 @t174 @t173)) % 0.44/0.69 (define @t176 () (or @t174 @t173)) % 0.44/0.69 (define @t177 () (or @t94 @t176)) % 0.44/0.69 (define @t178 () (@list @t2 @t172)) % 0.44/0.69 (define @t179 () (forall @t178 @t177)) % 0.44/0.69 (define @t180 () (@list @t172)) % 0.44/0.69 (define @t181 () (forall @t180 @t177)) % 0.44/0.69 (define @t182 () (forall @t180 @t176)) % 0.44/0.69 (define @t183 () (or @t94 @t182)) % 0.44/0.69 (define @t184 () (forall @t7 (or @t109 @t5))) % 0.44/0.69 (define @t185 () (= @t158 @t165)) % 0.44/0.69 (define @t186 () (not @t41)) % 0.44/0.69 (define @t187 () (or @t160 @t186 @t185)) % 0.44/0.69 (define @t188 () (forall @t178 @t175)) % 0.44/0.69 (define @t189 () (= @t158 @t152)) % 0.44/0.69 (define @t190 () (or @t160 @t186 @t189)) % 0.44/0.69 (define @t191 () (not @t189)) % 0.44/0.69 (define @t192 () (@list true false)) % 0.44/0.69 (assume @p1 (forall @t9 (=> @t8 (forall @t7 (=> @t6 @t5))))) % 0.44/0.69 (assume @p2 (exists @t9 (and @t8 (exists @t7 (and @t6 @t4))))) % 0.44/0.69 (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))))))))))) % 0.44/0.69 (assume @p4 (forall @t9 (=> @t17 (= (tptp.singletonP @t2) (exists @t7 (and @t6 (= @t18 @t2))))))) % 0.44/0.69 (assume @p5 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t20 (exists @t16 (and @t15 (= @t19 @t2))))))))) % 0.44/0.69 (assume @p6 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t23 (exists @t16 (and @t15 (= @t22 @t2))))))))) % 0.44/0.69 (assume @p7 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t24 (exists @t16 (and @t15 (exists @t14 (and @t13 (= (tptp.app @t22 @t10) @t2))))))))))) % 0.44/0.69 (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))))))))))))))))) % 0.44/0.69 (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)))))))))))))))) % 0.44/0.69 (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))))))))))))))))) % 0.44/0.69 (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))))))))))))))) % 0.44/0.69 (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))))))))))))))) % 0.44/0.69 (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)))))))))))))))) % 0.44/0.69 (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))))))))))))) % 0.44/0.69 (assume @p15 @t39) % 0.44/0.69 (assume @p16 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (tptp.ssList @t40)))))) % 0.44/0.69 (assume @p17 @t41) % 0.44/0.69 (assume @p18 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= @t40 @t2))))))) % 0.44/0.69 (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) @t42))))))))))) % 0.44/0.69 (assume @p20 (forall @t9 (=> @t17 (or @t44 (exists @t7 (and @t21 (exists @t16 (and @t34 (= @t43 @t2))))))))) % 0.44/0.69 (assume @p21 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= tptp.nil @t40))))))) % 0.44/0.69 (assume @p22 (forall @t9 (=> @t17 (=> @t46 (tptp.ssItem @t45))))) % 0.44/0.69 (assume @p23 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.hd @t40) @t1)))))) % 0.44/0.69 (assume @p24 (forall @t9 (=> @t17 (=> @t46 (tptp.ssList @t47))))) % 0.44/0.69 (assume @p25 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.tl @t40) @t2)))))) % 0.44/0.69 (assume @p26 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (tptp.ssList @t48)))))) % 0.44/0.69 (assume @p27 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t34 (= (tptp.cons @t12 @t49) (tptp.app @t43 @t2))))))))) % 0.44/0.69 (assume @p28 (forall @t9 (=> @t17 (= (tptp.app tptp.nil @t2) @t2)))) % 0.44/0.69 (assume @p29 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> (and @t51 @t50) @t3)))))) % 0.44/0.69 (assume @p30 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t51 @t26) (tptp.leq @t2 @t12))))))))) % 0.44/0.69 (assume @p31 (forall @t9 (=> @t8 (tptp.leq @t2 @t2)))) % 0.44/0.69 (assume @p32 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t52 @t50)))))) % 0.44/0.69 (assume @p33 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t54 (not @t53))))))) % 0.44/0.69 (assume @p34 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t54 @t35) @t55)))))))) % 0.44/0.69 (assume @p35 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t56 @t53)))))) % 0.44/0.69 (assume @p36 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (= (tptp.memberP @t19 @t2) (or (tptp.memberP @t1 @t2) @t57))))))))) % 0.44/0.69 (assume @p37 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t15 (= (tptp.memberP (tptp.cons @t1 @t12) @t2) (or @t3 @t57))))))))) % 0.44/0.69 (assume @p38 (forall @t9 (=> @t8 (not (tptp.memberP tptp.nil @t2))))) % 0.44/0.69 (assume @p39 (not (tptp.singletonP tptp.nil))) % 0.44/0.69 (assume @p40 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t20 (tptp.frontsegP @t1 @t12)) (tptp.frontsegP @t2 @t12))))))))) % 0.44/0.69 (assume @p41 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t20 (tptp.frontsegP @t1 @t2)) @t3)))))) % 0.44/0.69 (assume @p42 (forall @t9 (=> @t17 (tptp.frontsegP @t2 @t2)))) % 0.44/0.69 (assume @p43 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> @t20 (tptp.frontsegP (tptp.app @t2 @t12) @t1))))))))) % 0.44/0.69 (assume @p44 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t15 (forall @t14 (=> @t13 (= (tptp.frontsegP (tptp.cons @t2 @t12) @t11) (and @t3 (tptp.frontsegP @t12 @t10)))))))))))) % 0.44/0.69 (assume @p45 (forall @t9 (=> @t17 (tptp.frontsegP @t2 tptp.nil)))) % 0.44/0.69 (assume @p46 (forall @t9 (=> @t17 (= (tptp.frontsegP tptp.nil @t2) @t44)))) % 0.44/0.69 (assume @p47 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t23 (tptp.rearsegP @t1 @t12)) (tptp.rearsegP @t2 @t12))))))))) % 0.44/0.69 (assume @p48 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t23 (tptp.rearsegP @t1 @t2)) @t3)))))) % 0.44/0.69 (assume @p49 (forall @t9 (=> @t17 (tptp.rearsegP @t2 @t2)))) % 0.44/0.69 (assume @p50 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> @t23 (tptp.rearsegP @t58 @t1))))))))) % 0.44/0.69 (assume @p51 (forall @t9 (=> @t17 (tptp.rearsegP @t2 tptp.nil)))) % 0.44/0.69 (assume @p52 (forall @t9 (=> @t17 (= (tptp.rearsegP tptp.nil @t2) @t44)))) % 0.44/0.69 (assume @p53 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t24 (tptp.segmentP @t1 @t12)) (tptp.segmentP @t2 @t12))))))))) % 0.44/0.69 (assume @p54 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t24 (tptp.segmentP @t1 @t2)) @t3)))))) % 0.44/0.69 (assume @p55 (forall @t9 (=> @t17 (tptp.segmentP @t2 @t2)))) % 0.44/0.69 (assume @p56 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (forall @t14 (=> @t13 (=> @t24 (tptp.segmentP (tptp.app @t58 @t10) @t1))))))))))) % 0.44/0.69 (assume @p57 (forall @t9 (=> @t17 (tptp.segmentP @t2 tptp.nil)))) % 0.44/0.69 (assume @p58 (forall @t9 (=> @t17 (= (tptp.segmentP tptp.nil @t2) @t44)))) % 0.44/0.69 (assume @p59 (forall @t9 (=> @t8 (tptp.cyclefreeP @t59)))) % 0.44/0.69 (assume @p60 (tptp.cyclefreeP tptp.nil)) % 0.44/0.69 (assume @p61 (forall @t9 (=> @t8 (tptp.totalorderP @t59)))) % 0.44/0.69 (assume @p62 (tptp.totalorderP tptp.nil)) % 0.44/0.69 (assume @p63 (forall @t9 (=> @t8 (tptp.strictorderP @t59)))) % 0.44/0.69 (assume @p64 (tptp.strictorderP tptp.nil)) % 0.44/0.69 (assume @p65 (forall @t9 (=> @t8 (tptp.totalorderedP @t59)))) % 0.44/0.69 (assume @p66 (tptp.totalorderedP tptp.nil)) % 0.44/0.69 (assume @p67 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (= (tptp.totalorderedP @t63) (or @t61 (and @t62 (tptp.totalorderedP @t1) (tptp.leq @t2 @t60))))))))) % 0.44/0.69 (assume @p68 (forall @t9 (=> @t8 (tptp.strictorderedP @t59)))) % 0.44/0.69 (assume @p69 (tptp.strictorderedP tptp.nil)) % 0.44/0.69 (assume @p70 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (= (tptp.strictorderedP @t63) (or @t61 (and @t62 (tptp.strictorderedP @t1) (tptp.lt @t2 @t60))))))))) % 0.44/0.69 (assume @p71 (forall @t9 (=> @t8 (tptp.duplicatefreeP @t59)))) % 0.44/0.69 (assume @p72 (tptp.duplicatefreeP tptp.nil)) % 0.44/0.69 (assume @p73 (forall @t9 (=> @t8 (tptp.equalelemsP @t59)))) % 0.44/0.69 (assume @p74 (tptp.equalelemsP tptp.nil)) % 0.44/0.69 (assume @p75 (forall @t9 (=> @t17 (=> @t46 (exists @t7 (and @t6 (= @t45 @t1))))))) % 0.44/0.69 (assume @p76 (forall @t9 (=> @t17 (=> @t46 (exists @t7 (and @t21 (= @t47 @t1))))))) % 0.44/0.69 (assume @p77 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t62 @t46 (= @t60 @t45) (= (tptp.tl @t1) @t47)) @t42)))))) % 0.44/0.69 (assume @p78 (forall @t9 (=> @t17 (=> @t46 (= (tptp.cons @t45 @t47) @t2))))) % 0.44/0.69 (assume @p79 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (= @t22 @t48) @t64)))))))) % 0.44/0.69 (assume @p80 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (= @t19 @t49) @t64)))))))) % 0.44/0.69 (assume @p81 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= @t40 (tptp.app @t18 @t2))))))) % 0.44/0.69 (assume @p82 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (= (tptp.app @t48 @t12) (tptp.app @t2 @t19))))))))) % 0.44/0.69 (assume @p83 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= (= tptp.nil @t48) (and @t61 @t44))))))) % 0.44/0.69 (assume @p84 (forall @t9 (=> @t17 (= (tptp.app @t2 tptp.nil) @t2)))) % 0.44/0.69 (assume @p85 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> @t46 (= (tptp.hd @t48) @t45))))))) % 0.44/0.69 (assume @p86 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> @t46 (= (tptp.tl @t48) (tptp.app @t47 @t1)))))))) % 0.44/0.69 (assume @p87 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> (and @t52 (tptp.geq @t1 @t2)) @t3)))))) % 0.44/0.69 (assume @p88 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t52 (tptp.geq @t1 @t12)) (tptp.geq @t2 @t12))))))))) % 0.44/0.69 (assume @p89 (forall @t9 (=> @t8 (tptp.geq @t2 @t2)))) % 0.44/0.69 (assume @p90 (forall @t9 (=> @t8 (not (tptp.lt @t2 @t2))))) % 0.44/0.69 (assume @p91 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t51 @t35) @t55)))))))) % 0.44/0.69 (assume @p92 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t51 (or @t3 @t54))))))) % 0.44/0.69 (assume @p93 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t54 (and @t4 @t51))))))) % 0.44/0.69 (assume @p94 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t56 (not (tptp.gt @t1 @t2)))))))) % 0.44/0.69 (assume @p95 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t56 (tptp.gt @t1 @t12)) (tptp.gt @t2 @t12))))))))) % 0.44/0.69 (assume @p96 @t84) % 0.44/0.69 (assume @p97 true) % 0.44/0.69 (step @p98 :rule evaluate :args ((= false true))) % 0.44/0.69 (step @p99 :rule eq-symm :args (@t85 tptp.nil)) % 0.44/0.69 (step @p100 :rule refl :args (@t87)) % 0.44/0.69 (step @p101 :rule nary_cong :premises (@p100 @p99) :args (@t89)) % 0.44/0.69 (step @p102 :rule refl :args (@t86)) % 0.44/0.69 (step @p103 :rule cong :premises (@p99) :args (@t90)) % 0.44/0.69 (step @p104 :rule nary_cong :premises (@p103 @p102) :args (@t91)) % 0.44/0.69 (step @p105 :rule refl :args (@t92)) % 0.44/0.69 (step @p106 :rule refl :args (@t93)) % 0.44/0.69 (step @p107 :rule refl :args (@t71)) % 0.44/0.69 (step @p108 :rule refl :args (@t94)) % 0.44/0.69 (step @p109 :rule nary_cong :premises (@p108 @p107 @p106 @p105 @p104 @p101) :args (@t95)) % 0.44/0.69 (step @p110 :rule aci_norm :args ((= @t97 @t95))) % 0.44/0.69 (step @p111 :rule trans :premises (@p110 @p109)) % 0.44/0.69 (step @p112 :rule cong :premises (@p111) :args (@t99)) % 0.44/0.69 (step @p113 :rule quant-merge-prenex :args ((= (forall @t9 @t101) @t99))) % 0.44/0.69 (step @p114 :rule alpha_equiv :args (@t102 (@list @t85) @t103)) % 0.44/0.69 (step @p115 :rule refl :args (@t71)) % 0.44/0.69 (step @p116 :rule refl :args (@t94)) % 0.44/0.69 (step @p117 :rule nary_cong :premises (@p116 @p115 @p114) :args (@t104)) % 0.44/0.69 (step @p118 :rule quant-miniscope-or :args ((= @t101 @t104))) % 0.44/0.69 (step @p119 :rule trans :premises (@p118 @p117)) % 0.44/0.69 (step @p120 :rule symm :premises (@p119)) % 0.44/0.69 (step @p121 :rule cong :premises (@p120) :args ((forall @t9 @t112))) % 0.44/0.69 (step @p122 :rule trans :premises (@p121 @p113)) % 0.44/0.69 (step @p123 :rule trans :premises (@p122 @p112)) % 0.44/0.69 (step @p124 :rule aci_norm :args ((= (or @t94 @t113) @t112))) % 0.44/0.69 (step @p125 :rule bool-impl-elim :args (@t17 @t113)) % 0.44/0.69 (step @p126 :rule trans :premises (@p125 @p124)) % 0.44/0.69 (step @p127 :rule cong :premises (@p126) :args ((forall @t9 (=> @t17 @t113)))) % 0.44/0.69 (step @p128 :rule trans :premises (@p127 @p123)) % 0.44/0.69 (step @p129 :rule quant-miniscope-or :args ((= (forall @t7 @t114) @t113))) % 0.44/0.69 (step @p130 :rule aci_norm :args ((= @t115 @t114))) % 0.44/0.69 (step @p131 :rule cong :premises (@p130) :args ((forall @t7 @t115))) % 0.44/0.69 (step @p132 :rule trans :premises (@p131 @p129)) % 0.44/0.69 (step @p133 :rule aci_norm :args ((= (or @t109 @t116) @t115))) % 0.44/0.69 (step @p134 :rule bool-impl-elim :args (@t21 @t116)) % 0.44/0.69 (step @p135 :rule trans :premises (@p134 @p133)) % 0.44/0.69 (step @p136 :rule cong :premises (@p135) :args ((forall @t7 (=> @t21 @t116)))) % 0.44/0.69 (step @p137 :rule trans :premises (@p136 @p132)) % 0.44/0.69 (step @p138 :rule aci_norm :args ((= (or @t72 @t71 @t109 @t117) @t116))) % 0.44/0.69 (step @p139 :rule aci_norm :args ((= (or @t94 false @t108 @t106) @t117))) % 0.44/0.69 (step @p140 :rule refl :args (@t106)) % 0.44/0.69 (step @p141 :rule refl :args (@t108)) % 0.44/0.69 (step @p142 :rule evaluate :args ((not true))) % 0.44/0.69 (step @p143 :rule eq-refl :args (@t2)) % 0.44/0.69 (step @p144 :rule cong :premises (@p143) :args (@t118)) % 0.44/0.69 (step @p145 :rule trans :premises (@p144 @p142)) % 0.44/0.69 (step @p146 :rule nary_cong :premises (@p108 @p145 @p141 @p140) :args (@t119)) % 0.44/0.69 (step @p147 :rule trans :premises (@p146 @p139)) % 0.44/0.69 (step @p148 :rule quant-var-elim-eq :args ((= (forall @t16 (or (not @t64) @t124 @t73 @t123 @t122)) @t119))) % 0.44/0.69 (step @p149 :rule refl :args (@t122)) % 0.44/0.69 (step @p150 :rule refl :args (@t123)) % 0.44/0.69 (step @p151 :rule refl :args (@t73)) % 0.44/0.69 (step @p152 :rule refl :args (@t124)) % 0.44/0.69 (step @p153 :rule eq-symm :args (@t2 @t12)) % 0.44/0.69 (step @p154 :rule cong :premises (@p153) :args (@t73)) % 0.44/0.69 (step @p155 :rule nary_cong :premises (@p154 @p152 @p151 @p150 @p149) :args (@t125)) % 0.44/0.69 (step @p156 :rule aci_norm :args ((= @t126 @t125))) % 0.44/0.69 (step @p157 :rule trans :premises (@p156 @p155)) % 0.44/0.69 (step @p158 :rule cong :premises (@p157) :args (@t127)) % 0.44/0.69 (step @p159 :rule trans :premises (@p158 @p148)) % 0.44/0.69 (step @p160 :rule trans :premises (@p159 @p147)) % 0.44/0.69 (step @p161 :rule refl :args (@t109)) % 0.44/0.69 (step @p162 :rule refl :args (@t72)) % 0.44/0.69 (step @p163 :rule nary_cong :premises (@p162 @p107 @p161 @p160) :args (@t128)) % 0.44/0.69 (step @p164 :rule trans :premises (@p163 @p138)) % 0.44/0.69 (step @p165 :rule quant-miniscope-or :args ((= (forall @t16 @t129) @t128))) % 0.44/0.69 (step @p166 :rule aci_norm :args ((= @t130 @t129))) % 0.44/0.69 (step @p167 :rule cong :premises (@p166) :args ((forall @t16 @t130))) % 0.44/0.69 (step @p168 :rule trans :premises (@p167 @p165)) % 0.44/0.69 (step @p169 :rule trans :premises (@p168 @p164)) % 0.44/0.69 (step @p170 :rule aci_norm :args ((= (or @t124 @t131) @t130))) % 0.44/0.69 (step @p171 :rule bool-impl-elim :args (@t15 @t131)) % 0.44/0.69 (step @p172 :rule trans :premises (@p171 @p170)) % 0.44/0.69 (step @p173 :rule cong :premises (@p172) :args ((forall @t16 (=> @t15 @t131)))) % 0.44/0.69 (step @p174 :rule trans :premises (@p173 @p169)) % 0.44/0.69 (step @p175 :rule aci_norm :args ((= (or @t73 @t72 @t71 @t132) @t131))) % 0.44/0.69 (step @p176 :rule aci_norm :args ((= (or @t109 false @t123 @t122) @t132))) % 0.44/0.69 (step @p177 :rule refl :args (@t122)) % 0.44/0.69 (step @p178 :rule refl :args (@t123)) % 0.44/0.69 (step @p179 :rule eq-refl :args (@t1)) % 0.44/0.69 (step @p180 :rule cong :premises (@p179) :args (@t133)) % 0.44/0.69 (step @p181 :rule trans :premises (@p180 @p142)) % 0.44/0.69 (step @p182 :rule nary_cong :premises (@p161 @p181 @p178 @p177) :args (@t134)) % 0.44/0.69 (step @p183 :rule trans :premises (@p182 @p176)) % 0.44/0.69 (step @p184 :rule quant-var-elim-eq :args ((= (forall @t14 (or (not (= @t10 @t1)) @t138 @t74 @t137 @t136)) @t134))) % 0.44/0.69 (step @p185 :rule refl :args (@t136)) % 0.44/0.69 (step @p186 :rule refl :args (@t137)) % 0.44/0.69 (step @p187 :rule refl :args (@t74)) % 0.44/0.69 (step @p188 :rule refl :args (@t138)) % 0.44/0.69 (step @p189 :rule eq-symm :args (@t1 @t10)) % 0.44/0.69 (step @p190 :rule cong :premises (@p189) :args (@t74)) % 0.44/0.69 (step @p191 :rule nary_cong :premises (@p190 @p188 @p187 @p186 @p185) :args (@t139)) % 0.44/0.69 (step @p192 :rule aci_norm :args ((= @t140 @t139))) % 0.44/0.69 (step @p193 :rule trans :premises (@p192 @p191)) % 0.44/0.69 (step @p194 :rule cong :premises (@p193) :args (@t141)) % 0.44/0.69 (step @p195 :rule trans :premises (@p194 @p184)) % 0.44/0.69 (step @p196 :rule trans :premises (@p195 @p183)) % 0.44/0.69 (step @p197 :rule refl :args (@t73)) % 0.44/0.69 (step @p198 :rule nary_cong :premises (@p197 @p162 @p107 @p196) :args (@t142)) % 0.44/0.69 (step @p199 :rule trans :premises (@p198 @p175)) % 0.44/0.69 (step @p200 :rule quant-miniscope-or :args ((= (forall @t14 @t143) @t142))) % 0.44/0.69 (step @p201 :rule aci_norm :args ((= @t144 @t143))) % 0.44/0.69 (step @p202 :rule cong :premises (@p201) :args ((forall @t14 @t144))) % 0.44/0.69 (step @p203 :rule trans :premises (@p202 @p200)) % 0.44/0.69 (step @p204 :rule trans :premises (@p203 @p199)) % 0.44/0.69 (step @p205 :rule aci_norm :args ((= (or @t138 @t145) @t144))) % 0.44/0.69 (step @p206 :rule bool-impl-elim :args (@t13 @t145)) % 0.44/0.69 (step @p207 :rule trans :premises (@p206 @p205)) % 0.44/0.69 (step @p208 :rule cong :premises (@p207) :args ((forall @t14 (=> @t13 @t145)))) % 0.44/0.69 (step @p209 :rule trans :premises (@p208 @p204)) % 0.44/0.69 (step @p210 :rule eq-symm :args (tptp.nil @t10)) % 0.44/0.69 (step @p211 :rule eq-symm :args (tptp.nil @t12)) % 0.44/0.69 (step @p212 :rule cong :premises (@p211) :args (@t67)) % 0.44/0.69 (step @p213 :rule nary_cong :premises (@p212 @p210) :args (@t68)) % 0.44/0.69 (step @p214 :rule cong :premises (@p210) :args (@t69)) % 0.44/0.69 (step @p215 :rule nary_cong :premises (@p214 @p211) :args (@t70)) % 0.44/0.69 (step @p216 :rule refl :args (@t74)) % 0.44/0.69 (step @p217 :rule nary_cong :premises (@p216 @p197 @p162 @p107 @p215 @p213) :args (@t75)) % 0.44/0.69 (step @p218 :rule refl :args (@t13)) % 0.44/0.69 (step @p219 :rule cong :premises (@p218 @p217) :args (@t76)) % 0.44/0.69 (step @p220 :rule cong :premises (@p219) :args (@t77)) % 0.44/0.69 (step @p221 :rule trans :premises (@p220 @p209)) % 0.44/0.69 (step @p222 :rule refl :args (@t15)) % 0.44/0.69 (step @p223 :rule cong :premises (@p222 @p221) :args (@t78)) % 0.44/0.69 (step @p224 :rule cong :premises (@p223) :args (@t79)) % 0.44/0.69 (step @p225 :rule trans :premises (@p224 @p174)) % 0.44/0.69 (step @p226 :rule refl :args (@t21)) % 0.44/0.69 (step @p227 :rule cong :premises (@p226 @p225) :args (@t80)) % 0.44/0.69 (step @p228 :rule cong :premises (@p227) :args (@t81)) % 0.44/0.69 (step @p229 :rule trans :premises (@p228 @p137)) % 0.44/0.69 (step @p230 :rule refl :args (@t17)) % 0.44/0.69 (step @p231 :rule cong :premises (@p230 @p229) :args (@t82)) % 0.44/0.69 (step @p232 :rule cong :premises (@p231) :args (@t83)) % 0.44/0.69 (step @p233 :rule trans :premises (@p232 @p128)) % 0.44/0.69 (step @p234 :rule cong :premises (@p233) :args (@t84)) % 0.44/0.69 (step @p235 :rule eq_resolve :premises (@p96 @p234)) % 0.44/0.69 (step @p236 :rule refl :args (@t162)) % 0.44/0.69 (step @p237 :rule bool-double-not-elim :args (@t147)) % 0.44/0.69 (step @p238 :rule nary_cong :premises (@p237 @p236) :args ((or (not @t163) @t162))) % 0.44/0.69 (step @p239 :rule refl :args (@t149)) % 0.44/0.69 (step @p240 :rule eq-symm :args (@t150 tptp.nil)) % 0.44/0.69 (step @p241 :rule cong :premises (@p240) :args (@t165)) % 0.44/0.69 (step @p242 :rule nary_cong :premises (@p241 @p239) :args (@t166)) % 0.44/0.69 (step @p243 :rule refl :args (@t153)) % 0.44/0.69 (step @p244 :rule nary_cong :premises (@p243 @p240) :args (@t167)) % 0.44/0.69 (step @p245 :rule refl :args (@t156)) % 0.44/0.69 (step @p246 :rule refl :args (@t157)) % 0.44/0.69 (step @p247 :rule refl :args (@t158)) % 0.44/0.69 (step @p248 :rule refl :args (@t160)) % 0.44/0.69 (step @p249 :rule nary_cong :premises (@p248 @p247 @p246 @p245 @p244 @p242) :args (@t168)) % 0.44/0.69 (step @p250 :rule cong :premises (@p249) :args (@t169)) % 0.44/0.69 (step @p251 :rule refl :args (@t163)) % 0.44/0.69 (step @p252 :rule cong :premises (@p251 @p250) :args ((=> @t163 @t169))) % 0.44/0.69 (assume-push @p337 @t163) % 0.44/0.69 (step @p254 :rule skolemize :premises (@p235)) % 0.44/0.69 (step-pop @p338 :rule scope :premises (@p254)) % 0.44/0.69 (step @p255 :rule process_scope :premises (@p338) :args (@t169)) % 0.44/0.69 (step @p257 :rule eq_resolve :premises (@p255 @p252)) % 0.44/0.69 (step @p258 :rule implies_elim :premises (@p257)) % 0.44/0.69 (step @p259 :rule eq_resolve :premises (@p258 @p238)) % 0.44/0.69 (step @p260 :rule chain_m_resolution :premises (@p259 @p235) :args (@t162 @t170 (@list @t147))) % 0.44/0.69 (step @p261 :rule bool-double-not-elim :args (@t155)) % 0.44/0.69 (step @p262 :rule refl :args (@t161)) % 0.44/0.69 (step @p263 :rule nary_cong :premises (@p262 @p261) :args ((or @t161 (not @t156)))) % 0.44/0.69 (step @p264 :rule cnf_or_neg :args (@t161 3)) % 0.44/0.69 (step @p265 :rule eq_resolve :premises (@p264 @p263)) % 0.44/0.69 (step @p266 :rule reordering :premises (@p265) :args ((or @t155 @t161))) % 0.44/0.69 (step @p267 :rule chain_m_resolution :premises (@p266 @p260) :args (@t155 @t170 @t171)) % 0.44/0.69 (step @p268 :rule true_intro :premises (@p267)) % 0.44/0.69 (step @p269 :rule refl :args (tptp.nil)) % 0.44/0.69 (step @p270 :rule aci_norm :args ((= @t177 @t175))) % 0.44/0.69 (step @p271 :rule cong :premises (@p270) :args (@t179)) % 0.44/0.69 (step @p272 :rule quant-merge-prenex :args ((= (forall @t9 @t181) @t179))) % 0.44/0.69 (step @p273 :rule alpha_equiv :args (@t182 (@list @t172) @t103)) % 0.44/0.69 (step @p274 :rule nary_cong :premises (@p116 @p273) :args (@t183)) % 0.44/0.69 (step @p275 :rule quant-miniscope-or :args ((= @t181 @t183))) % 0.44/0.69 (step @p276 :rule trans :premises (@p275 @p274)) % 0.44/0.69 (step @p277 :rule symm :premises (@p276)) % 0.44/0.69 (step @p278 :rule cong :premises (@p277) :args ((forall @t9 (or @t94 @t184)))) % 0.44/0.69 (step @p279 :rule trans :premises (@p278 @p272)) % 0.44/0.69 (step @p280 :rule trans :premises (@p279 @p271)) % 0.44/0.69 (step @p281 :rule bool-impl-elim :args (@t17 @t184)) % 0.44/0.69 (step @p282 :rule cong :premises (@p281) :args ((forall @t9 (=> @t17 @t184)))) % 0.44/0.69 (step @p283 :rule trans :premises (@p282 @p280)) % 0.44/0.69 (step @p284 :rule bool-impl-elim :args (@t21 @t5)) % 0.44/0.69 (step @p285 :rule cong :premises (@p284) :args (@t37)) % 0.44/0.69 (step @p286 :rule cong :premises (@p230 @p285) :args (@t38)) % 0.44/0.69 (step @p287 :rule cong :premises (@p286) :args (@t39)) % 0.44/0.69 (step @p288 :rule trans :premises (@p287 @p283)) % 0.44/0.69 (step @p289 :rule eq_resolve :premises (@p15 @p288)) % 0.44/0.69 (step @p290 :rule cong :premises (@p247 @p241) :args (@t185)) % 0.44/0.69 (step @p291 :rule refl :args (@t186)) % 0.44/0.69 (step @p292 :rule nary_cong :premises (@p248 @p291 @p290) :args (@t187)) % 0.44/0.69 (step @p293 :rule refl :args (@t188)) % 0.44/0.69 (step @p294 :rule cong :premises (@p293 @p292) :args ((=> @t188 @t187))) % 0.44/0.69 (assume-push @p339 @t188) % 0.44/0.69 (step @p296 :rule instantiate :premises (@p289) :args ((@list @t150 tptp.nil))) % 0.44/0.69 (step-pop @p340 :rule scope :premises (@p296)) % 0.44/0.69 (step @p297 :rule process_scope :premises (@p340) :args (@t187)) % 0.44/0.69 (step @p299 :rule eq_resolve :premises (@p297 @p294)) % 0.44/0.69 (step @p300 :rule implies_elim :premises (@p299)) % 0.44/0.69 (step @p301 :rule chain_m_resolution :premises (@p300 @p289) :args (@t190 (@list false) (@list @t188))) % 0.44/0.69 (step @p302 :rule bool-double-not-elim :args (@t159)) % 0.44/0.69 (step @p303 :rule nary_cong :premises (@p262 @p302) :args ((or @t161 (not @t160)))) % 0.44/0.69 (step @p304 :rule cnf_or_neg :args (@t161 0)) % 0.44/0.69 (step @p305 :rule eq_resolve :premises (@p304 @p303)) % 0.44/0.69 (step @p306 :rule reordering :premises (@p305) :args ((or @t159 @t161))) % 0.44/0.69 (step @p307 :rule chain_m_resolution :premises (@p306 @p260) :args (@t159 @t170 @t171)) % 0.44/0.69 (step @p308 :rule cnf_or_pos :args (@t190)) % 0.44/0.69 (step @p309 :rule reordering :premises (@p308) :args ((or @t186 @t160 @t189 (not @t190)))) % 0.44/0.69 (step @p310 :rule chain_m_resolution :premises (@p309 @p17 @p307 @p301) :args (@t189 (@list false false false) (@list @t41 @t159 @t190))) % 0.44/0.69 (step @p311 :rule cnf_or_neg :args (@t161 1)) % 0.44/0.69 (step @p312 :rule chain_m_resolution :premises (@p311 @p260) :args ((not @t158) @t170 @t171)) % 0.44/0.69 (step @p313 :rule bool-double-not-elim :args (@t151)) % 0.44/0.69 (step @p314 :rule refl :args (@t191)) % 0.44/0.69 (step @p315 :rule nary_cong :premises (@p314 @p247 @p313) :args ((or @t191 @t158 (not @t152)))) % 0.44/0.69 (step @p316 :rule cnf_equiv_pos2 :args (@t189)) % 0.44/0.69 (step @p317 :rule eq_resolve :premises (@p316 @p315)) % 0.44/0.69 (step @p318 :rule reordering :premises (@p317) :args ((or @t158 @t151 @t191))) % 0.44/0.69 (step @p319 :rule chain_m_resolution :premises (@p318 @p312 @p310) :args (@t151 @t192 (@list @t158 @t189))) % 0.44/0.69 (step @p320 :rule cnf_or_neg :args (@t161 4)) % 0.44/0.69 (step @p321 :rule chain_m_resolution :premises (@p320 @p260) :args ((not @t154) @t170 @t171)) % 0.44/0.69 (step @p322 :rule refl :args (@t152)) % 0.44/0.69 (step @p323 :rule bool-double-not-elim :args (@t149)) % 0.44/0.69 (step @p324 :rule refl :args (@t154)) % 0.44/0.69 (step @p325 :rule nary_cong :premises (@p324 @p323 @p322) :args ((or @t154 (not @t153) @t152))) % 0.44/0.69 (step @p326 :rule cnf_and_neg :args (@t154)) % 0.44/0.69 (step @p327 :rule eq_resolve :premises (@p326 @p325)) % 0.44/0.69 (step @p328 :rule reordering :premises (@p327) :args ((or @t149 @t154 @t152))) % 0.44/0.69 (step @p329 :rule chain_m_resolution :premises (@p328 @p321 @p319) :args (@t149 @t192 (@list @t154 @t151))) % 0.44/0.69 (step @p330 :rule symm :premises (@p319)) % 0.44/0.69 (step @p331 :rule trans :premises (@p330 @p329)) % 0.44/0.69 (step @p332 :rule cong :premises (@p331 @p269) :args (@t158)) % 0.44/0.69 (step @p333 :rule false_intro :premises (@p312)) % 0.44/0.69 (step @p334 :rule symm :premises (@p333)) % 0.44/0.69 (step @p335 :rule trans :premises (@p334 @p332 @p268)) % 0.44/0.69 (step @p336 false :rule eq_resolve :premises (@p335 @p98)) % 0.44/0.69 ) % 0.44/0.69 % SZS output end Proof % 0.44/0.69 % cvc5 exiting %------------------------------------------------------------------------------