%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWC391+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 : n001.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 08:59:08 AM UTC 2026 % Result : Theorem 0.37s 0.65s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWC391+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 % 0.17/0.34 % Computer : n001.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 19:46:35 EDT 2026 % 0.17/0.35 % CPUTime : % 0.30/0.52 %----Proving TF0_NAR, FOF, or CNF % 0.37/0.65 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.37/0.65 % SZS status Theorem % 0.37/0.65 % SZS output start Proof % 0.37/0.65 ( % 0.37/0.65 (declare-sort $$unsorted 0) % 0.37/0.65 (declare-const tptp.tl (-> $$unsorted $$unsorted)) % 0.37/0.65 (declare-const tptp.hd (-> $$unsorted $$unsorted)) % 0.37/0.65 (declare-const tptp.duplicatefreeP (-> $$unsorted Bool)) % 0.37/0.65 (declare-const tptp.strictorderedP (-> $$unsorted Bool)) % 0.37/0.65 (declare-const tptp.geq (-> $$unsorted $$unsorted Bool)) % 0.37/0.65 (declare-const tptp.strictorderP (-> $$unsorted Bool)) % 0.37/0.65 (declare-const tptp.equalelemsP (-> $$unsorted Bool)) % 0.37/0.65 (declare-const tptp.totalorderP (-> $$unsorted Bool)) % 0.37/0.65 (declare-const tptp.neq (-> $$unsorted $$unsorted Bool)) % 0.37/0.65 (declare-const tptp.totalorderedP (-> $$unsorted Bool)) % 0.37/0.65 (declare-const tptp.singletonP (-> $$unsorted Bool)) % 0.37/0.65 (declare-const tptp.cons (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.65 (declare-const tptp.app (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.65 (declare-const tptp.nil $$unsorted) % 0.37/0.65 (declare-const tptp.memberP (-> $$unsorted $$unsorted Bool)) % 0.37/0.65 (declare-const tptp.lt (-> $$unsorted $$unsorted Bool)) % 0.37/0.65 (declare-const tptp.frontsegP (-> $$unsorted $$unsorted Bool)) % 0.37/0.65 (declare-const tptp.rearsegP (-> $$unsorted $$unsorted Bool)) % 0.37/0.65 (declare-const tptp.gt (-> $$unsorted $$unsorted Bool)) % 0.37/0.65 (declare-const tptp.ssList (-> $$unsorted Bool)) % 0.37/0.65 (declare-const tptp.segmentP (-> $$unsorted $$unsorted Bool)) % 0.37/0.65 (declare-const tptp.cyclefreeP (-> $$unsorted Bool)) % 0.37/0.65 (declare-const tptp.ssItem (-> $$unsorted Bool)) % 0.37/0.65 (declare-const tptp.leq (-> $$unsorted $$unsorted Bool)) % 0.37/0.65 (define @t1 () (@var "V" $$unsorted)) % 0.37/0.65 (define @t2 () (@var "U" $$unsorted)) % 0.37/0.65 (define @t3 () (= @t2 @t1)) % 0.37/0.65 (define @t4 () (not @t3)) % 0.37/0.65 (define @t5 () (= (tptp.neq @t2 @t1) @t4)) % 0.37/0.65 (define @t6 () (tptp.ssItem @t1)) % 0.37/0.65 (define @t7 () (@list @t1)) % 0.37/0.65 (define @t8 () (tptp.ssItem @t2)) % 0.37/0.65 (define @t9 () (@list @t2)) % 0.37/0.65 (define @t10 () (@var "X" $$unsorted)) % 0.37/0.65 (define @t11 () (tptp.cons @t1 @t10)) % 0.37/0.65 (define @t12 () (@var "W" $$unsorted)) % 0.37/0.65 (define @t13 () (tptp.ssList @t10)) % 0.37/0.65 (define @t14 () (@list @t10)) % 0.37/0.65 (define @t15 () (tptp.ssList @t12)) % 0.37/0.65 (define @t16 () (@list @t12)) % 0.37/0.65 (define @t17 () (tptp.ssList @t2)) % 0.37/0.65 (define @t18 () (tptp.cons @t1 tptp.nil)) % 0.37/0.65 (define @t19 () (tptp.app @t1 @t12)) % 0.37/0.65 (define @t20 () (tptp.frontsegP @t2 @t1)) % 0.37/0.65 (define @t21 () (tptp.ssList @t1)) % 0.37/0.65 (define @t22 () (tptp.app @t12 @t1)) % 0.37/0.65 (define @t23 () (tptp.rearsegP @t2 @t1)) % 0.37/0.65 (define @t24 () (tptp.segmentP @t2 @t1)) % 0.37/0.65 (define @t25 () (tptp.leq @t12 @t1)) % 0.37/0.65 (define @t26 () (tptp.leq @t1 @t12)) % 0.37/0.65 (define @t27 () (@var "Z" $$unsorted)) % 0.37/0.65 (define @t28 () (@var "Y" $$unsorted)) % 0.37/0.65 (define @t29 () (= (tptp.app (tptp.app @t10 (tptp.cons @t1 @t28)) (tptp.cons @t12 @t27)) @t2)) % 0.37/0.65 (define @t30 () (tptp.ssList @t27)) % 0.37/0.65 (define @t31 () (@list @t27)) % 0.37/0.65 (define @t32 () (tptp.ssList @t28)) % 0.37/0.65 (define @t33 () (@list @t28)) % 0.37/0.65 (define @t34 () (tptp.ssItem @t12)) % 0.37/0.65 (define @t35 () (tptp.lt @t1 @t12)) % 0.37/0.65 (define @t36 () (= @t1 @t12)) % 0.37/0.65 (define @t37 () (not @t36)) % 0.37/0.65 (define @t38 () (tptp.cons @t1 @t2)) % 0.37/0.65 (define @t39 () (= @t1 @t2)) % 0.37/0.65 (define @t40 () (= @t12 @t10)) % 0.37/0.65 (define @t41 () (tptp.cons @t12 @t1)) % 0.37/0.65 (define @t42 () (= tptp.nil @t2)) % 0.37/0.65 (define @t43 () (tptp.hd @t2)) % 0.37/0.65 (define @t44 () (not @t42)) % 0.37/0.65 (define @t45 () (tptp.tl @t2)) % 0.37/0.65 (define @t46 () (tptp.app @t2 @t1)) % 0.37/0.65 (define @t47 () (tptp.app @t1 @t2)) % 0.37/0.65 (define @t48 () (tptp.leq @t1 @t2)) % 0.37/0.65 (define @t49 () (tptp.leq @t2 @t1)) % 0.37/0.65 (define @t50 () (tptp.geq @t2 @t1)) % 0.37/0.65 (define @t51 () (tptp.lt @t1 @t2)) % 0.37/0.65 (define @t52 () (tptp.lt @t2 @t1)) % 0.37/0.65 (define @t53 () (tptp.lt @t2 @t12)) % 0.37/0.65 (define @t54 () (tptp.gt @t2 @t1)) % 0.37/0.65 (define @t55 () (tptp.memberP @t12 @t2)) % 0.37/0.65 (define @t56 () (tptp.app @t12 @t2)) % 0.37/0.65 (define @t57 () (tptp.cons @t2 tptp.nil)) % 0.37/0.65 (define @t58 () (tptp.hd @t1)) % 0.37/0.65 (define @t59 () (= tptp.nil @t1)) % 0.37/0.65 (define @t60 () (not @t59)) % 0.37/0.65 (define @t61 () (tptp.cons @t2 @t1)) % 0.37/0.65 (define @t62 () (= @t12 @t2)) % 0.37/0.65 (define @t63 () (tptp.memberP @t1 @t28)) % 0.37/0.65 (define @t64 () (not (tptp.memberP @t2 @t28))) % 0.37/0.65 (define @t65 () (or @t64 @t63)) % 0.37/0.65 (define @t66 () (tptp.ssItem @t28)) % 0.37/0.65 (define @t67 () (forall @t33 (=> @t66 @t65))) % 0.37/0.65 (define @t68 () (not (= @t10 @t12))) % 0.37/0.65 (define @t69 () (not (= @t2 @t12))) % 0.37/0.65 (define @t70 () (not (= @t1 @t10))) % 0.37/0.65 (define @t71 () (or @t70 @t69 @t68 @t67)) % 0.37/0.65 (define @t72 () (=> @t13 @t71)) % 0.37/0.65 (define @t73 () (forall @t14 @t72)) % 0.37/0.65 (define @t74 () (=> @t15 @t73)) % 0.37/0.65 (define @t75 () (forall @t16 @t74)) % 0.37/0.65 (define @t76 () (=> @t21 @t75)) % 0.37/0.65 (define @t77 () (forall @t7 @t76)) % 0.37/0.65 (define @t78 () (=> @t17 @t77)) % 0.37/0.65 (define @t79 () (forall @t9 @t78)) % 0.37/0.65 (define @t80 () (not @t79)) % 0.37/0.65 (define @t81 () (not @t17)) % 0.37/0.65 (define @t82 () (@var "BOUND_VARIABLE_10960" $$unsorted)) % 0.37/0.65 (define @t83 () (@list @t82)) % 0.37/0.65 (define @t84 () (not (tptp.ssItem @t82))) % 0.37/0.65 (define @t85 () (tptp.memberP @t2 @t82)) % 0.37/0.65 (define @t86 () (not @t85)) % 0.37/0.65 (define @t87 () (or @t81 @t84 @t86 @t85)) % 0.37/0.65 (define @t88 () (not (= @t2 @t2))) % 0.37/0.65 (define @t89 () (or @t81 @t88 @t84 @t86 @t85)) % 0.37/0.65 (define @t90 () (tptp.memberP @t1 @t82)) % 0.37/0.65 (define @t91 () (not @t21)) % 0.37/0.65 (define @t92 () (not @t39)) % 0.37/0.65 (define @t93 () (or @t4 @t91 @t4 @t84 @t86 @t90)) % 0.37/0.65 (define @t94 () (or @t91 @t4 @t84 @t86 @t90)) % 0.37/0.65 (define @t95 () (forall @t7 @t94)) % 0.37/0.65 (define @t96 () (forall @t83 @t95)) % 0.37/0.65 (define @t97 () (forall (@list @t82 @t1) @t94)) % 0.37/0.65 (define @t98 () (@list @t1 @t82)) % 0.37/0.65 (define @t99 () (or @t84 @t86 @t90)) % 0.37/0.65 (define @t100 () (or @t91 @t99 @t4)) % 0.37/0.65 (define @t101 () (forall @t98 @t100)) % 0.37/0.65 (define @t102 () (forall @t83 @t100)) % 0.37/0.65 (define @t103 () (forall @t83 @t99)) % 0.37/0.65 (define @t104 () (or @t91 @t103 @t4)) % 0.37/0.65 (define @t105 () (not @t66)) % 0.37/0.65 (define @t106 () (or @t105 @t64 @t63)) % 0.37/0.65 (define @t107 () (forall @t33 @t106)) % 0.37/0.65 (define @t108 () (or @t91 @t107 @t4)) % 0.37/0.65 (define @t109 () (forall @t7 @t108)) % 0.37/0.65 (define @t110 () (or @t81 @t109)) % 0.37/0.65 (define @t111 () (or @t81 @t108)) % 0.37/0.65 (define @t112 () (or @t91 @t107 @t81 @t4)) % 0.37/0.65 (define @t113 () (or @t107 @t91 @t81 @t4)) % 0.37/0.65 (define @t114 () (or @t81 @t4)) % 0.37/0.65 (define @t115 () (or @t81 @t88 @t92)) % 0.37/0.65 (define @t116 () (not @t15)) % 0.37/0.65 (define @t117 () (or @t69 @t116 @t69 @t37)) % 0.37/0.65 (define @t118 () (or @t116 @t69 @t37)) % 0.37/0.65 (define @t119 () (forall @t16 @t118)) % 0.37/0.65 (define @t120 () (or @t107 @t91 @t119)) % 0.37/0.65 (define @t121 () (or @t107 @t91 @t118)) % 0.37/0.65 (define @t122 () (or @t116 @t69 @t107 @t91 @t37)) % 0.37/0.65 (define @t123 () (or @t69 @t107 @t91 @t37)) % 0.37/0.65 (define @t124 () (or @t91 @t37)) % 0.37/0.65 (define @t125 () (not (= @t12 @t1))) % 0.37/0.65 (define @t126 () (not (= @t1 @t1))) % 0.37/0.65 (define @t127 () (or @t91 @t126 @t125)) % 0.37/0.65 (define @t128 () (not @t40)) % 0.37/0.65 (define @t129 () (not @t13)) % 0.37/0.65 (define @t130 () (or @t70 @t129 @t70 @t128)) % 0.37/0.65 (define @t131 () (or @t129 @t70 @t128)) % 0.37/0.65 (define @t132 () (forall @t14 @t131)) % 0.37/0.65 (define @t133 () (or @t69 @t107 @t132)) % 0.37/0.65 (define @t134 () (or @t69 @t107 @t131)) % 0.37/0.65 (define @t135 () (or @t129 @t70 @t69 @t128 @t107)) % 0.37/0.65 (define @t136 () (or @t70 @t69 @t128 @t107)) % 0.37/0.65 (assume @p1 (forall @t9 (=> @t8 (forall @t7 (=> @t6 @t5))))) % 0.37/0.65 (assume @p2 (exists @t9 (and @t8 (exists @t7 (and @t6 @t4))))) % 0.37/0.65 (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))))))))))) % 0.37/0.65 (assume @p4 (forall @t9 (=> @t17 (= (tptp.singletonP @t2) (exists @t7 (and @t6 (= @t18 @t2))))))) % 0.37/0.65 (assume @p5 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t20 (exists @t16 (and @t15 (= @t19 @t2))))))))) % 0.37/0.65 (assume @p6 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t23 (exists @t16 (and @t15 (= @t22 @t2))))))))) % 0.37/0.65 (assume @p7 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= @t24 (exists @t16 (and @t15 (exists @t14 (and @t13 (= (tptp.app @t22 @t10) @t2))))))))))) % 0.37/0.65 (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))))))))))))))))) % 0.37/0.65 (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)))))))))))))))) % 0.37/0.65 (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))))))))))))))))) % 0.37/0.65 (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))))))))))))))) % 0.37/0.65 (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))))))))))))))) % 0.37/0.65 (assume @p13 (forall @t9 (=> @t17 (= (tptp.duplicatefreeP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t34 (forall @t14 (=> @t13 (forall @t33 (=> @t32 (forall @t31 (=> @t30 (=> @t29 @t37))))))))))))))) % 0.37/0.65 (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))))))))))))) % 0.37/0.65 (assume @p15 (forall @t9 (=> @t17 (forall @t7 (=> @t21 @t5))))) % 0.37/0.65 (assume @p16 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (tptp.ssList @t38)))))) % 0.37/0.65 (assume @p17 (tptp.ssList tptp.nil)) % 0.37/0.65 (assume @p18 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= @t38 @t2))))))) % 0.37/0.65 (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 @t40 @t39))))))))))) % 0.37/0.65 (assume @p20 (forall @t9 (=> @t17 (or @t42 (exists @t7 (and @t21 (exists @t16 (and @t34 (= @t41 @t2))))))))) % 0.37/0.65 (assume @p21 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= tptp.nil @t38))))))) % 0.37/0.65 (assume @p22 (forall @t9 (=> @t17 (=> @t44 (tptp.ssItem @t43))))) % 0.37/0.65 (assume @p23 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.hd @t38) @t1)))))) % 0.37/0.65 (assume @p24 (forall @t9 (=> @t17 (=> @t44 (tptp.ssList @t45))))) % 0.37/0.65 (assume @p25 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.tl @t38) @t2)))))) % 0.37/0.65 (assume @p26 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (tptp.ssList @t46)))))) % 0.37/0.65 (assume @p27 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t34 (= (tptp.cons @t12 @t47) (tptp.app @t41 @t2))))))))) % 0.37/0.65 (assume @p28 (forall @t9 (=> @t17 (= (tptp.app tptp.nil @t2) @t2)))) % 0.37/0.65 (assume @p29 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> (and @t49 @t48) @t3)))))) % 0.37/0.65 (assume @p30 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t49 @t26) (tptp.leq @t2 @t12))))))))) % 0.37/0.65 (assume @p31 (forall @t9 (=> @t8 (tptp.leq @t2 @t2)))) % 0.37/0.65 (assume @p32 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t50 @t48)))))) % 0.37/0.65 (assume @p33 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t52 (not @t51))))))) % 0.37/0.65 (assume @p34 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t52 @t35) @t53)))))))) % 0.37/0.65 (assume @p35 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t54 @t51)))))) % 0.37/0.65 (assume @p36 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (= (tptp.memberP @t19 @t2) (or (tptp.memberP @t1 @t2) @t55))))))))) % 0.37/0.65 (assume @p37 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t15 (= (tptp.memberP (tptp.cons @t1 @t12) @t2) (or @t3 @t55))))))))) % 0.37/0.65 (assume @p38 (forall @t9 (=> @t8 (not (tptp.memberP tptp.nil @t2))))) % 0.37/0.65 (assume @p39 (not (tptp.singletonP tptp.nil))) % 0.37/0.65 (assume @p40 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t20 (tptp.frontsegP @t1 @t12)) (tptp.frontsegP @t2 @t12))))))))) % 0.37/0.65 (assume @p41 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t20 (tptp.frontsegP @t1 @t2)) @t3)))))) % 0.37/0.65 (assume @p42 (forall @t9 (=> @t17 (tptp.frontsegP @t2 @t2)))) % 0.37/0.65 (assume @p43 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> @t20 (tptp.frontsegP (tptp.app @t2 @t12) @t1))))))))) % 0.37/0.65 (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)))))))))))) % 0.37/0.65 (assume @p45 (forall @t9 (=> @t17 (tptp.frontsegP @t2 tptp.nil)))) % 0.37/0.65 (assume @p46 (forall @t9 (=> @t17 (= (tptp.frontsegP tptp.nil @t2) @t42)))) % 0.37/0.65 (assume @p47 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t23 (tptp.rearsegP @t1 @t12)) (tptp.rearsegP @t2 @t12))))))))) % 0.37/0.65 (assume @p48 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t23 (tptp.rearsegP @t1 @t2)) @t3)))))) % 0.37/0.65 (assume @p49 (forall @t9 (=> @t17 (tptp.rearsegP @t2 @t2)))) % 0.37/0.65 (assume @p50 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> @t23 (tptp.rearsegP @t56 @t1))))))))) % 0.37/0.65 (assume @p51 (forall @t9 (=> @t17 (tptp.rearsegP @t2 tptp.nil)))) % 0.37/0.65 (assume @p52 (forall @t9 (=> @t17 (= (tptp.rearsegP tptp.nil @t2) @t42)))) % 0.37/0.65 (assume @p53 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (and @t24 (tptp.segmentP @t1 @t12)) (tptp.segmentP @t2 @t12))))))))) % 0.37/0.65 (assume @p54 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t24 (tptp.segmentP @t1 @t2)) @t3)))))) % 0.37/0.65 (assume @p55 (forall @t9 (=> @t17 (tptp.segmentP @t2 @t2)))) % 0.37/0.65 (assume @p56 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (forall @t14 (=> @t13 (=> @t24 (tptp.segmentP (tptp.app @t56 @t10) @t1))))))))))) % 0.37/0.65 (assume @p57 (forall @t9 (=> @t17 (tptp.segmentP @t2 tptp.nil)))) % 0.37/0.65 (assume @p58 (forall @t9 (=> @t17 (= (tptp.segmentP tptp.nil @t2) @t42)))) % 0.37/0.65 (assume @p59 (forall @t9 (=> @t8 (tptp.cyclefreeP @t57)))) % 0.37/0.65 (assume @p60 (tptp.cyclefreeP tptp.nil)) % 0.37/0.65 (assume @p61 (forall @t9 (=> @t8 (tptp.totalorderP @t57)))) % 0.37/0.65 (assume @p62 (tptp.totalorderP tptp.nil)) % 0.37/0.65 (assume @p63 (forall @t9 (=> @t8 (tptp.strictorderP @t57)))) % 0.37/0.65 (assume @p64 (tptp.strictorderP tptp.nil)) % 0.37/0.65 (assume @p65 (forall @t9 (=> @t8 (tptp.totalorderedP @t57)))) % 0.37/0.65 (assume @p66 (tptp.totalorderedP tptp.nil)) % 0.37/0.65 (assume @p67 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (= (tptp.totalorderedP @t61) (or @t59 (and @t60 (tptp.totalorderedP @t1) (tptp.leq @t2 @t58))))))))) % 0.37/0.65 (assume @p68 (forall @t9 (=> @t8 (tptp.strictorderedP @t57)))) % 0.37/0.65 (assume @p69 (tptp.strictorderedP tptp.nil)) % 0.37/0.65 (assume @p70 (forall @t9 (=> @t8 (forall @t7 (=> @t21 (= (tptp.strictorderedP @t61) (or @t59 (and @t60 (tptp.strictorderedP @t1) (tptp.lt @t2 @t58))))))))) % 0.37/0.65 (assume @p71 (forall @t9 (=> @t8 (tptp.duplicatefreeP @t57)))) % 0.37/0.65 (assume @p72 (tptp.duplicatefreeP tptp.nil)) % 0.37/0.65 (assume @p73 (forall @t9 (=> @t8 (tptp.equalelemsP @t57)))) % 0.37/0.65 (assume @p74 (tptp.equalelemsP tptp.nil)) % 0.37/0.65 (assume @p75 (forall @t9 (=> @t17 (=> @t44 (exists @t7 (and @t6 (= @t43 @t1))))))) % 0.37/0.65 (assume @p76 (forall @t9 (=> @t17 (=> @t44 (exists @t7 (and @t21 (= @t45 @t1))))))) % 0.37/0.65 (assume @p77 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> (and @t60 @t44 (= @t58 @t43) (= (tptp.tl @t1) @t45)) @t39)))))) % 0.37/0.65 (assume @p78 (forall @t9 (=> @t17 (=> @t44 (= (tptp.cons @t43 @t45) @t2))))) % 0.37/0.65 (assume @p79 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (= @t22 @t46) @t62)))))))) % 0.37/0.65 (assume @p80 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (=> (= @t19 @t47) @t62)))))))) % 0.37/0.65 (assume @p81 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= @t38 (tptp.app @t18 @t2))))))) % 0.37/0.65 (assume @p82 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (forall @t16 (=> @t15 (= (tptp.app @t46 @t12) (tptp.app @t2 @t19))))))))) % 0.37/0.65 (assume @p83 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (= (= tptp.nil @t46) (and @t59 @t42))))))) % 0.37/0.65 (assume @p84 (forall @t9 (=> @t17 (= (tptp.app @t2 tptp.nil) @t2)))) % 0.37/0.65 (assume @p85 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> @t44 (= (tptp.hd @t46) @t43))))))) % 0.37/0.65 (assume @p86 (forall @t9 (=> @t17 (forall @t7 (=> @t21 (=> @t44 (= (tptp.tl @t46) (tptp.app @t45 @t1)))))))) % 0.37/0.65 (assume @p87 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> (and @t50 (tptp.geq @t1 @t2)) @t3)))))) % 0.37/0.65 (assume @p88 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t50 (tptp.geq @t1 @t12)) (tptp.geq @t2 @t12))))))))) % 0.37/0.65 (assume @p89 (forall @t9 (=> @t8 (tptp.geq @t2 @t2)))) % 0.37/0.65 (assume @p90 (forall @t9 (=> @t8 (not (tptp.lt @t2 @t2))))) % 0.37/0.65 (assume @p91 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t49 @t35) @t53)))))))) % 0.37/0.65 (assume @p92 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t49 (or @t3 @t52))))))) % 0.37/0.65 (assume @p93 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t52 (and @t4 @t49))))))) % 0.37/0.65 (assume @p94 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t54 (not (tptp.gt @t1 @t2)))))))) % 0.37/0.65 (assume @p95 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t34 (=> (and @t54 (tptp.gt @t1 @t12)) (tptp.gt @t2 @t12))))))))) % 0.37/0.65 (assume @p96 @t80) % 0.37/0.65 (assume @p97 true) % 0.37/0.65 (step @p98 :rule evaluate :args ((not true))) % 0.37/0.65 (step @p99 :rule quant-unused-vars :args ((= (forall @t9 true) true))) % 0.37/0.65 (step @p100 :rule bool-impl-true1 :args (@t17)) % 0.37/0.65 (step @p101 :rule absorb :args ((= (or @t81 true) true))) % 0.37/0.65 (step @p102 :rule quant-unused-vars :args ((= (forall @t83 true) true))) % 0.37/0.65 (step @p103 :rule bool-or-taut2 :args ((or @t81 @t84) @t85 false false)) % 0.37/0.65 (step @p104 :rule cong :premises (@p103) :args ((forall @t83 @t87))) % 0.37/0.65 (step @p105 :rule trans :premises (@p104 @p102)) % 0.37/0.65 (step @p106 :rule aci_norm :args ((= (or @t81 false @t84 @t86 @t85) @t87))) % 0.37/0.65 (step @p107 :rule refl :args (@t85)) % 0.37/0.65 (step @p108 :rule refl :args (@t86)) % 0.37/0.65 (step @p109 :rule refl :args (@t84)) % 0.37/0.65 (step @p110 :rule eq-refl :args (@t2)) % 0.37/0.65 (step @p111 :rule cong :premises (@p110) :args (@t88)) % 0.37/0.65 (step @p112 :rule trans :premises (@p111 @p98)) % 0.37/0.65 (step @p113 :rule refl :args (@t81)) % 0.37/0.65 (step @p114 :rule nary_cong :premises (@p113 @p112 @p109 @p108 @p107) :args (@t89)) % 0.37/0.65 (step @p115 :rule trans :premises (@p114 @p106)) % 0.37/0.65 (step @p116 :rule cong :premises (@p115) :args ((forall @t83 @t89))) % 0.37/0.65 (step @p117 :rule trans :premises (@p116 @p105)) % 0.37/0.65 (step @p118 :rule quant-var-elim-eq :args ((= (forall @t7 (or @t92 @t91 @t4 @t84 @t86 @t90)) @t89))) % 0.37/0.65 (step @p119 :rule refl :args (@t90)) % 0.37/0.65 (step @p120 :rule refl :args (@t86)) % 0.37/0.65 (step @p121 :rule refl :args (@t84)) % 0.37/0.65 (step @p122 :rule refl :args (@t4)) % 0.37/0.65 (step @p123 :rule refl :args (@t91)) % 0.37/0.65 (step @p124 :rule eq-symm :args (@t2 @t1)) % 0.37/0.65 (step @p125 :rule cong :premises (@p124) :args (@t4)) % 0.37/0.65 (step @p126 :rule nary_cong :premises (@p125 @p123 @p122 @p121 @p120 @p119) :args (@t93)) % 0.37/0.65 (step @p127 :rule aci_norm :args ((= @t94 @t93))) % 0.37/0.65 (step @p128 :rule trans :premises (@p127 @p126)) % 0.37/0.65 (step @p129 :rule cong :premises (@p128) :args (@t95)) % 0.37/0.65 (step @p130 :rule trans :premises (@p129 @p118)) % 0.37/0.65 (step @p131 :rule cong :premises (@p130) :args (@t96)) % 0.37/0.65 (step @p132 :rule quant-merge-prenex :args ((= @t96 @t97))) % 0.37/0.65 (step @p133 :rule symm :premises (@p132)) % 0.37/0.65 (step @p134 :rule quant_var_reordering :args ((= (forall @t98 @t94) @t97))) % 0.37/0.65 (step @p135 :rule trans :premises (@p134 @p133 @p131)) % 0.37/0.65 (step @p136 :rule trans :premises (@p135 @p117)) % 0.37/0.65 (step @p137 :rule aci_norm :args ((= @t100 @t94))) % 0.37/0.65 (step @p138 :rule cong :premises (@p137) :args (@t101)) % 0.37/0.65 (step @p139 :rule trans :premises (@p138 @p136)) % 0.37/0.65 (step @p140 :rule quant-merge-prenex :args ((= (forall @t7 @t102) @t101))) % 0.37/0.65 (step @p141 :rule alpha_equiv :args (@t103 (@list @t82) (@list @t28))) % 0.37/0.65 (step @p142 :rule nary_cong :premises (@p123 @p141 @p122) :args (@t104)) % 0.37/0.65 (step @p143 :rule quant-miniscope-or :args ((= @t102 @t104))) % 0.37/0.65 (step @p144 :rule trans :premises (@p143 @p142)) % 0.37/0.65 (step @p145 :rule symm 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0.37/0.65 (step @p160 :rule trans :premises (@p159 @p155)) % 0.37/0.65 (step @p161 :rule aci_norm :args ((= (or @t107 @t91 @t114) @t113))) % 0.37/0.65 (step @p162 :rule aci_norm :args ((= (or @t81 false @t4) @t114))) % 0.37/0.65 (step @p163 :rule eq-symm :args (@t1 @t2)) % 0.37/0.65 (step @p164 :rule cong :premises (@p163) :args (@t92)) % 0.37/0.65 (step @p165 :rule nary_cong :premises (@p113 @p112 @p164) :args (@t115)) % 0.37/0.65 (step @p166 :rule trans :premises (@p165 @p162)) % 0.37/0.65 (step @p167 :rule quant-var-elim-eq :args ((= (forall @t16 (or (not @t62) @t116 @t69 @t37)) @t115))) % 0.37/0.65 (step @p168 :rule refl :args (@t37)) % 0.37/0.65 (step @p169 :rule refl :args (@t69)) % 0.37/0.65 (step @p170 :rule refl :args (@t116)) % 0.37/0.65 (step @p171 :rule eq-symm :args (@t2 @t12)) % 0.37/0.65 (step @p172 :rule cong :premises (@p171) :args (@t69)) % 0.37/0.65 (step @p173 :rule nary_cong :premises (@p172 @p170 @p169 @p168) :args (@t117)) % 0.37/0.65 (step @p174 :rule aci_norm 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0.37/0.65 (step @p219 :rule cong :premises (@p218) :args ((forall @t14 @t135))) % 0.37/0.65 (step @p220 :rule trans :premises (@p219 @p217)) % 0.37/0.65 (step @p221 :rule trans :premises (@p220 @p216)) % 0.37/0.65 (step @p222 :rule aci_norm :args ((= (or @t129 @t136) @t135))) % 0.37/0.65 (step @p223 :rule bool-impl-elim :args (@t13 @t136)) % 0.37/0.65 (step @p224 :rule trans :premises (@p223 @p222)) % 0.37/0.65 (step @p225 :rule cong :premises (@p224) :args ((forall @t14 (=> @t13 @t136)))) % 0.37/0.65 (step @p226 :rule trans :premises (@p225 @p221)) % 0.37/0.65 (step @p227 :rule aci_norm :args ((= (or @t105 @t65) @t106))) % 0.37/0.65 (step @p228 :rule bool-impl-elim :args (@t66 @t65)) % 0.37/0.65 (step @p229 :rule trans :premises (@p228 @p227)) % 0.37/0.65 (step @p230 :rule cong :premises (@p229) :args (@t67)) % 0.37/0.65 (step @p231 :rule eq-symm :args (@t10 @t12)) % 0.37/0.65 (step @p232 :rule cong :premises (@p231) :args (@t68)) % 0.37/0.65 (step @p233 :rule refl :args (@t70)) % 0.37/0.65 (step @p234 :rule nary_cong :premises (@p233 @p214 @p232 @p230) :args (@t71)) % 0.37/0.65 (step @p235 :rule refl :args (@t13)) % 0.37/0.65 (step @p236 :rule cong :premises (@p235 @p234) :args (@t72)) % 0.37/0.65 (step @p237 :rule cong :premises (@p236) :args (@t73)) % 0.37/0.65 (step @p238 :rule trans :premises (@p237 @p226)) % 0.37/0.65 (step @p239 :rule refl :args (@t15)) % 0.37/0.65 (step @p240 :rule cong :premises (@p239 @p238) :args (@t74)) % 0.37/0.65 (step @p241 :rule cong :premises (@p240) :args (@t75)) % 0.37/0.65 (step @p242 :rule trans :premises (@p241 @p192)) % 0.37/0.65 (step @p243 :rule refl :args (@t21)) % 0.37/0.65 (step @p244 :rule cong :premises (@p243 @p242) :args (@t76)) % 0.37/0.65 (step @p245 :rule cong :premises (@p244) :args (@t77)) % 0.37/0.65 (step @p246 :rule trans :premises (@p245 @p160)) % 0.37/0.65 (step @p247 :rule refl :args (@t17)) % 0.37/0.65 (step @p248 :rule cong :premises (@p247 @p246) :args (@t78)) % 0.37/0.65 (step @p249 :rule trans :premises (@p248 @p100)) % 0.37/0.65 (step @p250 :rule cong :premises (@p249) :args (@t79)) % 0.37/0.65 (step @p251 :rule trans :premises (@p250 @p99)) % 0.37/0.65 (step @p252 :rule cong :premises (@p251) :args (@t80)) % 0.37/0.65 (step @p253 :rule trans :premises (@p252 @p98)) % 0.37/0.65 (step @p254 false :rule eq_resolve :premises (@p96 @p253)) % 0.37/0.65 ) % 0.37/0.65 % SZS output end Proof % 0.37/0.65 % cvc5 exiting %------------------------------------------------------------------------------