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cvc5---1.3.4.THM-Prf.s

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%------------------------------------------------------------------------------
% File     : cvc5---1.3.4
% Problem  : SWC385+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 08:59:07 AM UTC 2026

% Result   : Theorem 0.39s 0.68s
% Output   : Proof 0.39s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SWC385+1 : TPTP v9.2.1. Released v2.4.0.
% 0.12/0.14  % Command  : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.35  % Computer : n001.cluster.edu
% 0.18/0.35  % Model    : x86_64 x86_64
% 0.18/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35  % Memory   : 8042.1875MB
% 0.18/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.18/0.36  % CPULimit : 300
% 0.18/0.36  % WCLimit  : 300
% 0.18/0.36  % DateTime : Tue Jun  2 19:46:05 EDT 2026
% 0.18/0.36  % CPUTime  : 
% 0.29/0.53  %----Proving TF0_NAR, FOF, or CNF
% 0.39/0.68  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15...
% 0.39/0.68  % SZS status Theorem
% 0.39/0.68  % SZS output start Proof
% 0.39/0.68  (
% 0.39/0.68  (declare-sort $$unsorted 0)
% 0.39/0.68  (declare-const tptp.tl (-> $$unsorted $$unsorted))
% 0.39/0.68  (declare-const tptp.hd (-> $$unsorted $$unsorted))
% 0.39/0.68  (declare-const tptp.duplicatefreeP (-> $$unsorted Bool))
% 0.39/0.68  (declare-const tptp.strictorderedP (-> $$unsorted Bool))
% 0.39/0.68  (declare-const tptp.geq (-> $$unsorted $$unsorted Bool))
% 0.39/0.68  (declare-const tptp.strictorderP (-> $$unsorted Bool))
% 0.39/0.68  (declare-const tptp.equalelemsP (-> $$unsorted Bool))
% 0.39/0.68  (declare-const tptp.totalorderP (-> $$unsorted Bool))
% 0.39/0.68  (declare-const tptp.neq (-> $$unsorted $$unsorted Bool))
% 0.39/0.68  (declare-const tptp.totalorderedP (-> $$unsorted Bool))
% 0.39/0.68  (declare-const tptp.singletonP (-> $$unsorted Bool))
% 0.39/0.68  (declare-const tptp.cons (-> $$unsorted $$unsorted $$unsorted))
% 0.39/0.68  (declare-const tptp.app (-> $$unsorted $$unsorted $$unsorted))
% 0.39/0.68  (declare-const tptp.nil $$unsorted)
% 0.39/0.68  (declare-const tptp.memberP (-> $$unsorted $$unsorted Bool))
% 0.39/0.68  (declare-const tptp.lt (-> $$unsorted $$unsorted Bool))
% 0.39/0.68  (declare-const tptp.frontsegP (-> $$unsorted $$unsorted Bool))
% 0.39/0.68  (declare-const tptp.rearsegP (-> $$unsorted $$unsorted Bool))
% 0.39/0.68  (declare-const tptp.gt (-> $$unsorted $$unsorted Bool))
% 0.39/0.68  (declare-const tptp.ssList (-> $$unsorted Bool))
% 0.39/0.68  (declare-const tptp.segmentP (-> $$unsorted $$unsorted Bool))
% 0.39/0.68  (declare-const tptp.cyclefreeP (-> $$unsorted Bool))
% 0.39/0.68  (declare-const tptp.ssItem (-> $$unsorted Bool))
% 0.39/0.68  (declare-const tptp.leq (-> $$unsorted $$unsorted Bool))
% 0.39/0.68  (define @t1 () (@var "V" $$unsorted))
% 0.39/0.68  (define @t2 () (@var "U" $$unsorted))
% 0.39/0.68  (define @t3 () (= @t2 @t1))
% 0.39/0.68  (define @t4 () (not @t3))
% 0.39/0.68  (define @t5 () (= (tptp.neq @t2 @t1) @t4))
% 0.39/0.68  (define @t6 () (tptp.ssItem @t1))
% 0.39/0.68  (define @t7 () (@list @t1))
% 0.39/0.68  (define @t8 () (tptp.ssItem @t2))
% 0.39/0.68  (define @t9 () (@list @t2))
% 0.39/0.68  (define @t10 () (@var "X" $$unsorted))
% 0.39/0.68  (define @t11 () (tptp.cons @t1 @t10))
% 0.39/0.68  (define @t12 () (@var "W" $$unsorted))
% 0.39/0.68  (define @t13 () (tptp.ssList @t10))
% 0.39/0.68  (define @t14 () (@list @t10))
% 0.39/0.68  (define @t15 () (tptp.ssList @t12))
% 0.39/0.68  (define @t16 () (@list @t12))
% 0.39/0.68  (define @t17 () (tptp.ssList @t2))
% 0.39/0.68  (define @t18 () (tptp.cons @t1 tptp.nil))
% 0.39/0.68  (define @t19 () (tptp.singletonP @t2))
% 0.39/0.68  (define @t20 () (tptp.app @t1 @t12))
% 0.39/0.68  (define @t21 () (tptp.frontsegP @t2 @t1))
% 0.39/0.68  (define @t22 () (tptp.ssList @t1))
% 0.39/0.68  (define @t23 () (tptp.app @t12 @t1))
% 0.39/0.68  (define @t24 () (tptp.rearsegP @t2 @t1))
% 0.39/0.68  (define @t25 () (tptp.segmentP @t2 @t1))
% 0.39/0.68  (define @t26 () (tptp.leq @t12 @t1))
% 0.39/0.68  (define @t27 () (tptp.leq @t1 @t12))
% 0.39/0.68  (define @t28 () (@var "Z" $$unsorted))
% 0.39/0.68  (define @t29 () (@var "Y" $$unsorted))
% 0.39/0.68  (define @t30 () (= (tptp.app (tptp.app @t10 (tptp.cons @t1 @t29)) (tptp.cons @t12 @t28)) @t2))
% 0.39/0.68  (define @t31 () (tptp.ssList @t28))
% 0.39/0.68  (define @t32 () (@list @t28))
% 0.39/0.68  (define @t33 () (tptp.ssList @t29))
% 0.39/0.68  (define @t34 () (@list @t29))
% 0.39/0.68  (define @t35 () (tptp.ssItem @t12))
% 0.39/0.68  (define @t36 () (tptp.lt @t1 @t12))
% 0.39/0.68  (define @t37 () (= @t1 @t12))
% 0.39/0.68  (define @t38 () (tptp.cons @t1 @t2))
% 0.39/0.68  (define @t39 () (= @t1 @t2))
% 0.39/0.68  (define @t40 () (tptp.cons @t12 @t1))
% 0.39/0.68  (define @t41 () (= tptp.nil @t2))
% 0.39/0.68  (define @t42 () (tptp.hd @t2))
% 0.39/0.68  (define @t43 () (not @t41))
% 0.39/0.68  (define @t44 () (tptp.tl @t2))
% 0.39/0.68  (define @t45 () (tptp.app @t2 @t1))
% 0.39/0.68  (define @t46 () (tptp.app @t1 @t2))
% 0.39/0.68  (define @t47 () (tptp.leq @t1 @t2))
% 0.39/0.68  (define @t48 () (tptp.leq @t2 @t1))
% 0.39/0.68  (define @t49 () (tptp.geq @t2 @t1))
% 0.39/0.68  (define @t50 () (tptp.lt @t1 @t2))
% 0.39/0.68  (define @t51 () (tptp.lt @t2 @t1))
% 0.39/0.68  (define @t52 () (tptp.lt @t2 @t12))
% 0.39/0.68  (define @t53 () (tptp.gt @t2 @t1))
% 0.39/0.68  (define @t54 () (tptp.memberP @t12 @t2))
% 0.39/0.68  (define @t55 () (tptp.app @t12 @t2))
% 0.39/0.68  (define @t56 () (tptp.segmentP @t1 @t12))
% 0.39/0.68  (define @t57 () (tptp.segmentP @t1 @t2))
% 0.39/0.68  (define @t58 () (tptp.cons @t2 tptp.nil))
% 0.39/0.68  (define @t59 () (tptp.hd @t1))
% 0.39/0.68  (define @t60 () (= tptp.nil @t1))
% 0.39/0.68  (define @t61 () (not @t60))
% 0.39/0.68  (define @t62 () (tptp.cons @t2 @t1))
% 0.39/0.68  (define @t63 () (= @t12 @t2))
% 0.39/0.68  (define @t64 () (and @t19 @t57))
% 0.39/0.68  (define @t65 () (not (tptp.singletonP @t12)))
% 0.39/0.68  (define @t66 () (and @t65 (tptp.neq @t10 tptp.nil)))
% 0.39/0.68  (define @t67 () (not (tptp.segmentP @t10 @t12)))
% 0.39/0.68  (define @t68 () (tptp.neq @t1 tptp.nil))
% 0.39/0.68  (define @t69 () (not @t68))
% 0.39/0.68  (define @t70 () (not (= @t2 @t12)))
% 0.39/0.68  (define @t71 () (not (= @t1 @t10)))
% 0.39/0.68  (define @t72 () (or @t71 @t70 @t69 @t67 @t66 @t64))
% 0.39/0.68  (define @t73 () (forall @t14 (=> @t13 @t72)))
% 0.39/0.68  (define @t74 () (=> @t15 @t73))
% 0.39/0.68  (define @t75 () (forall @t16 @t74))
% 0.39/0.68  (define @t76 () (=> @t22 @t75))
% 0.39/0.68  (define @t77 () (forall @t7 @t76))
% 0.39/0.68  (define @t78 () (=> @t17 @t77))
% 0.39/0.68  (define @t79 () (forall @t9 @t78))
% 0.39/0.68  (define @t80 () (not @t79))
% 0.39/0.68  (define @t81 () (@var "BOUND_VARIABLE_10956" $$unsorted))
% 0.39/0.68  (define @t82 () (tptp.neq @t81 tptp.nil))
% 0.39/0.68  (define @t83 () (not @t19))
% 0.39/0.68  (define @t84 () (and @t83 @t82))
% 0.39/0.68  (define @t85 () (tptp.segmentP @t81 @t2))
% 0.39/0.68  (define @t86 () (not @t85))
% 0.39/0.68  (define @t87 () (and @t19 @t85))
% 0.39/0.68  (define @t88 () (not @t82))
% 0.39/0.68  (define @t89 () (not (tptp.ssList @t81)))
% 0.39/0.68  (define @t90 () (not @t17))
% 0.39/0.68  (define @t91 () (or @t90 @t89 @t88 @t87 @t86 @t84))
% 0.39/0.68  (define @t92 () (or @t89 @t88 @t87 @t86 @t84))
% 0.39/0.68  (define @t93 () (or @t90 @t92))
% 0.39/0.68  (define @t94 () (@list @t2 @t81))
% 0.39/0.68  (define @t95 () (forall @t94 @t93))
% 0.39/0.68  (define @t96 () (@list @t81))
% 0.39/0.68  (define @t97 () (forall @t96 @t93))
% 0.39/0.68  (define @t98 () (forall @t96 @t92))
% 0.39/0.68  (define @t99 () (or @t90 @t98))
% 0.39/0.68  (define @t100 () (and @t83 @t68))
% 0.39/0.68  (define @t101 () (not @t57))
% 0.39/0.68  (define @t102 () (not @t22))
% 0.39/0.68  (define @t103 () (or @t102 @t69 @t64 @t101 @t100))
% 0.39/0.68  (define @t104 () (or @t90 (forall @t7 @t103)))
% 0.39/0.68  (define @t105 () (or @t90 @t103))
% 0.39/0.68  (define @t106 () (or @t102 @t69 @t64 @t90 @t101 @t100))
% 0.39/0.68  (define @t107 () (or @t69 @t64 @t102 @t90 @t101 @t100))
% 0.39/0.68  (define @t108 () (or @t90 @t101 @t100))
% 0.39/0.68  (define @t109 () (not (= @t2 @t2)))
% 0.39/0.68  (define @t110 () (or @t90 @t109 @t101 @t100))
% 0.39/0.68  (define @t111 () (and @t65 @t68))
% 0.39/0.68  (define @t112 () (not @t56))
% 0.39/0.68  (define @t113 () (not @t15))
% 0.39/0.68  (define @t114 () (or @t70 @t113 @t70 @t112 @t111))
% 0.39/0.68  (define @t115 () (or @t113 @t70 @t112 @t111))
% 0.39/0.68  (define @t116 () (forall @t16 @t115))
% 0.39/0.68  (define @t117 () (or @t69 @t64 @t102 @t116))
% 0.39/0.68  (define @t118 () (or @t69 @t64 @t102 @t115))
% 0.39/0.68  (define @t119 () (or @t113 @t70 @t69 @t64 @t102 @t112 @t111))
% 0.39/0.68  (define @t120 () (or @t70 @t69 @t64 @t102 @t112 @t111))
% 0.39/0.68  (define @t121 () (or @t102 @t112 @t111))
% 0.39/0.68  (define @t122 () (not (= @t1 @t1)))
% 0.39/0.68  (define @t123 () (or @t102 @t122 @t112 @t111))
% 0.39/0.68  (define @t124 () (not @t13))
% 0.39/0.68  (define @t125 () (or @t71 @t124 @t71 @t67 @t66))
% 0.39/0.68  (define @t126 () (or @t124 @t71 @t67 @t66))
% 0.39/0.68  (define @t127 () (forall @t14 @t126))
% 0.39/0.68  (define @t128 () (or @t70 @t69 @t64 @t127))
% 0.39/0.68  (define @t129 () (or @t70 @t69 @t64 @t126))
% 0.39/0.68  (define @t130 () (or @t124 @t71 @t70 @t69 @t67 @t66 @t64))
% 0.39/0.68  (define @t131 () (forall @t94 @t91))
% 0.39/0.68  (define @t132 () (@quantifiers_skolemize @t131 1))
% 0.39/0.68  (define @t133 () (tptp.neq @t132 tptp.nil))
% 0.39/0.68  (define @t134 () (@quantifiers_skolemize @t131 0))
% 0.39/0.68  (define @t135 () (tptp.singletonP @t134))
% 0.39/0.68  (define @t136 () (not @t135))
% 0.39/0.68  (define @t137 () (and @t136 @t133))
% 0.39/0.68  (define @t138 () (tptp.segmentP @t132 @t134))
% 0.39/0.68  (define @t139 () (not @t138))
% 0.39/0.68  (define @t140 () (and @t135 @t138))
% 0.39/0.68  (define @t141 () (not @t133))
% 0.39/0.68  (define @t142 () (or (not (tptp.ssList @t134)) (not (tptp.ssList @t132)) @t141 @t140 @t139 @t137))
% 0.39/0.68  (define @t143 () (@list true))
% 0.39/0.68  (define @t144 () (@list @t142))
% 0.39/0.68  (assume @p1 (forall @t9 (=> @t8 (forall @t7 (=> @t6 @t5)))))
% 0.39/0.68  (assume @p2 (exists @t9 (and @t8 (exists @t7 (and @t6 @t4)))))
% 0.39/0.68  (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)))))))))))
% 0.39/0.68  (assume @p4 (forall @t9 (=> @t17 (= @t19 (exists @t7 (and @t6 (= @t18 @t2)))))))
% 0.39/0.68  (assume @p5 (forall @t9 (=> @t17 (forall @t7 (=> @t22 (= @t21 (exists @t16 (and @t15 (= @t20 @t2)))))))))
% 0.39/0.68  (assume @p6 (forall @t9 (=> @t17 (forall @t7 (=> @t22 (= @t24 (exists @t16 (and @t15 (= @t23 @t2)))))))))
% 0.39/0.68  (assume @p7 (forall @t9 (=> @t17 (forall @t7 (=> @t22 (= @t25 (exists @t16 (and @t15 (exists @t14 (and @t13 (= (tptp.app @t23 @t10) @t2)))))))))))
% 0.39/0.68  (assume @p8 (forall @t9 (=> @t17 (= (tptp.cyclefreeP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t35 (forall @t14 (=> @t13 (forall @t34 (=> @t33 (forall @t32 (=> @t31 (=> @t30 (not (and @t27 @t26)))))))))))))))))
% 0.39/0.68  (assume @p9 (forall @t9 (=> @t17 (= (tptp.totalorderP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t35 (forall @t14 (=> @t13 (forall @t34 (=> @t33 (forall @t32 (=> @t31 (=> @t30 (or @t27 @t26))))))))))))))))
% 0.39/0.68  (assume @p10 (forall @t9 (=> @t17 (= (tptp.strictorderP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t35 (forall @t14 (=> @t13 (forall @t34 (=> @t33 (forall @t32 (=> @t31 (=> @t30 (or @t36 (tptp.lt @t12 @t1)))))))))))))))))
% 0.39/0.68  (assume @p11 (forall @t9 (=> @t17 (= (tptp.totalorderedP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t35 (forall @t14 (=> @t13 (forall @t34 (=> @t33 (forall @t32 (=> @t31 (=> @t30 @t27)))))))))))))))
% 0.39/0.68  (assume @p12 (forall @t9 (=> @t17 (= (tptp.strictorderedP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t35 (forall @t14 (=> @t13 (forall @t34 (=> @t33 (forall @t32 (=> @t31 (=> @t30 @t36)))))))))))))))
% 0.39/0.68  (assume @p13 (forall @t9 (=> @t17 (= (tptp.duplicatefreeP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t35 (forall @t14 (=> @t13 (forall @t34 (=> @t33 (forall @t32 (=> @t31 (=> @t30 (not @t37))))))))))))))))
% 0.39/0.68  (assume @p14 (forall @t9 (=> @t17 (= (tptp.equalelemsP @t2) (forall @t7 (=> @t6 (forall @t16 (=> @t35 (forall @t14 (=> @t13 (forall @t34 (=> @t33 (=> (= (tptp.app @t10 (tptp.cons @t1 (tptp.cons @t12 @t29))) @t2) @t37)))))))))))))
% 0.39/0.68  (assume @p15 (forall @t9 (=> @t17 (forall @t7 (=> @t22 @t5)))))
% 0.39/0.68  (assume @p16 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (tptp.ssList @t38))))))
% 0.39/0.68  (assume @p17 (tptp.ssList tptp.nil))
% 0.39/0.68  (assume @p18 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= @t38 @t2)))))))
% 0.39/0.68  (assume @p19 (forall @t9 (=> @t17 (forall @t7 (=> @t22 (forall @t16 (=> @t35 (forall @t14 (=> (tptp.ssItem @t10) (=> (= (tptp.cons @t12 @t2) (tptp.cons @t10 @t1)) (and (= @t12 @t10) @t39)))))))))))
% 0.39/0.68  (assume @p20 (forall @t9 (=> @t17 (or @t41 (exists @t7 (and @t22 (exists @t16 (and @t35 (= @t40 @t2)))))))))
% 0.39/0.68  (assume @p21 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (not (= tptp.nil @t38)))))))
% 0.39/0.68  (assume @p22 (forall @t9 (=> @t17 (=> @t43 (tptp.ssItem @t42)))))
% 0.39/0.68  (assume @p23 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.hd @t38) @t1))))))
% 0.39/0.68  (assume @p24 (forall @t9 (=> @t17 (=> @t43 (tptp.ssList @t44)))))
% 0.39/0.68  (assume @p25 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= (tptp.tl @t38) @t2))))))
% 0.39/0.68  (assume @p26 (forall @t9 (=> @t17 (forall @t7 (=> @t22 (tptp.ssList @t45))))))
% 0.39/0.68  (assume @p27 (forall @t9 (=> @t17 (forall @t7 (=> @t22 (forall @t16 (=> @t35 (= (tptp.cons @t12 @t46) (tptp.app @t40 @t2)))))))))
% 0.39/0.68  (assume @p28 (forall @t9 (=> @t17 (= (tptp.app tptp.nil @t2) @t2))))
% 0.39/0.68  (assume @p29 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> (and @t48 @t47) @t3))))))
% 0.39/0.68  (assume @p30 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t35 (=> (and @t48 @t27) (tptp.leq @t2 @t12)))))))))
% 0.39/0.68  (assume @p31 (forall @t9 (=> @t8 (tptp.leq @t2 @t2))))
% 0.39/0.68  (assume @p32 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t49 @t47))))))
% 0.39/0.68  (assume @p33 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t51 (not @t50)))))))
% 0.39/0.68  (assume @p34 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t35 (=> (and @t51 @t36) @t52))))))))
% 0.39/0.68  (assume @p35 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t53 @t50))))))
% 0.39/0.68  (assume @p36 (forall @t9 (=> @t8 (forall @t7 (=> @t22 (forall @t16 (=> @t15 (= (tptp.memberP @t20 @t2) (or (tptp.memberP @t1 @t2) @t54)))))))))
% 0.39/0.68  (assume @p37 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t15 (= (tptp.memberP (tptp.cons @t1 @t12) @t2) (or @t3 @t54)))))))))
% 0.39/0.68  (assume @p38 (forall @t9 (=> @t8 (not (tptp.memberP tptp.nil @t2)))))
% 0.39/0.68  (assume @p39 (not (tptp.singletonP tptp.nil)))
% 0.39/0.68  (assume @p40 (forall @t9 (=> @t17 (forall @t7 (=> @t22 (forall @t16 (=> @t15 (=> (and @t21 (tptp.frontsegP @t1 @t12)) (tptp.frontsegP @t2 @t12)))))))))
% 0.39/0.68  (assume @p41 (forall @t9 (=> @t17 (forall @t7 (=> @t22 (=> (and @t21 (tptp.frontsegP @t1 @t2)) @t3))))))
% 0.39/0.68  (assume @p42 (forall @t9 (=> @t17 (tptp.frontsegP @t2 @t2))))
% 0.39/0.68  (assume @p43 (forall @t9 (=> @t17 (forall @t7 (=> @t22 (forall @t16 (=> @t15 (=> @t21 (tptp.frontsegP (tptp.app @t2 @t12) @t1)))))))))
% 0.39/0.68  (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))))))))))))
% 0.39/0.68  (assume @p45 (forall @t9 (=> @t17 (tptp.frontsegP @t2 tptp.nil))))
% 0.39/0.68  (assume @p46 (forall @t9 (=> @t17 (= (tptp.frontsegP tptp.nil @t2) @t41))))
% 0.39/0.68  (assume @p47 (forall @t9 (=> @t17 (forall @t7 (=> @t22 (forall @t16 (=> @t15 (=> (and @t24 (tptp.rearsegP @t1 @t12)) (tptp.rearsegP @t2 @t12)))))))))
% 0.39/0.68  (assume @p48 (forall @t9 (=> @t17 (forall @t7 (=> @t22 (=> (and @t24 (tptp.rearsegP @t1 @t2)) @t3))))))
% 0.39/0.68  (assume @p49 (forall @t9 (=> @t17 (tptp.rearsegP @t2 @t2))))
% 0.39/0.68  (assume @p50 (forall @t9 (=> @t17 (forall @t7 (=> @t22 (forall @t16 (=> @t15 (=> @t24 (tptp.rearsegP @t55 @t1)))))))))
% 0.39/0.68  (assume @p51 (forall @t9 (=> @t17 (tptp.rearsegP @t2 tptp.nil))))
% 0.39/0.68  (assume @p52 (forall @t9 (=> @t17 (= (tptp.rearsegP tptp.nil @t2) @t41))))
% 0.39/0.68  (assume @p53 (forall @t9 (=> @t17 (forall @t7 (=> @t22 (forall @t16 (=> @t15 (=> (and @t25 @t56) (tptp.segmentP @t2 @t12)))))))))
% 0.39/0.68  (assume @p54 (forall @t9 (=> @t17 (forall @t7 (=> @t22 (=> (and @t25 @t57) @t3))))))
% 0.39/0.68  (assume @p55 (forall @t9 (=> @t17 (tptp.segmentP @t2 @t2))))
% 0.39/0.68  (assume @p56 (forall @t9 (=> @t17 (forall @t7 (=> @t22 (forall @t16 (=> @t15 (forall @t14 (=> @t13 (=> @t25 (tptp.segmentP (tptp.app @t55 @t10) @t1)))))))))))
% 0.39/0.68  (assume @p57 (forall @t9 (=> @t17 (tptp.segmentP @t2 tptp.nil))))
% 0.39/0.68  (assume @p58 (forall @t9 (=> @t17 (= (tptp.segmentP tptp.nil @t2) @t41))))
% 0.39/0.68  (assume @p59 (forall @t9 (=> @t8 (tptp.cyclefreeP @t58))))
% 0.39/0.68  (assume @p60 (tptp.cyclefreeP tptp.nil))
% 0.39/0.68  (assume @p61 (forall @t9 (=> @t8 (tptp.totalorderP @t58))))
% 0.39/0.68  (assume @p62 (tptp.totalorderP tptp.nil))
% 0.39/0.68  (assume @p63 (forall @t9 (=> @t8 (tptp.strictorderP @t58))))
% 0.39/0.68  (assume @p64 (tptp.strictorderP tptp.nil))
% 0.39/0.68  (assume @p65 (forall @t9 (=> @t8 (tptp.totalorderedP @t58))))
% 0.39/0.68  (assume @p66 (tptp.totalorderedP tptp.nil))
% 0.39/0.68  (assume @p67 (forall @t9 (=> @t8 (forall @t7 (=> @t22 (= (tptp.totalorderedP @t62) (or @t60 (and @t61 (tptp.totalorderedP @t1) (tptp.leq @t2 @t59)))))))))
% 0.39/0.68  (assume @p68 (forall @t9 (=> @t8 (tptp.strictorderedP @t58))))
% 0.39/0.68  (assume @p69 (tptp.strictorderedP tptp.nil))
% 0.39/0.68  (assume @p70 (forall @t9 (=> @t8 (forall @t7 (=> @t22 (= (tptp.strictorderedP @t62) (or @t60 (and @t61 (tptp.strictorderedP @t1) (tptp.lt @t2 @t59)))))))))
% 0.39/0.68  (assume @p71 (forall @t9 (=> @t8 (tptp.duplicatefreeP @t58))))
% 0.39/0.68  (assume @p72 (tptp.duplicatefreeP tptp.nil))
% 0.39/0.68  (assume @p73 (forall @t9 (=> @t8 (tptp.equalelemsP @t58))))
% 0.39/0.68  (assume @p74 (tptp.equalelemsP tptp.nil))
% 0.39/0.68  (assume @p75 (forall @t9 (=> @t17 (=> @t43 (exists @t7 (and @t6 (= @t42 @t1)))))))
% 0.39/0.68  (assume @p76 (forall @t9 (=> @t17 (=> @t43 (exists @t7 (and @t22 (= @t44 @t1)))))))
% 0.39/0.68  (assume @p77 (forall @t9 (=> @t17 (forall @t7 (=> @t22 (=> (and @t61 @t43 (= @t59 @t42) (= (tptp.tl @t1) @t44)) @t39))))))
% 0.39/0.68  (assume @p78 (forall @t9 (=> @t17 (=> @t43 (= (tptp.cons @t42 @t44) @t2)))))
% 0.39/0.68  (assume @p79 (forall @t9 (=> @t17 (forall @t7 (=> @t22 (forall @t16 (=> @t15 (=> (= @t23 @t45) @t63))))))))
% 0.39/0.68  (assume @p80 (forall @t9 (=> @t17 (forall @t7 (=> @t22 (forall @t16 (=> @t15 (=> (= @t20 @t46) @t63))))))))
% 0.39/0.68  (assume @p81 (forall @t9 (=> @t17 (forall @t7 (=> @t6 (= @t38 (tptp.app @t18 @t2)))))))
% 0.39/0.68  (assume @p82 (forall @t9 (=> @t17 (forall @t7 (=> @t22 (forall @t16 (=> @t15 (= (tptp.app @t45 @t12) (tptp.app @t2 @t20)))))))))
% 0.39/0.68  (assume @p83 (forall @t9 (=> @t17 (forall @t7 (=> @t22 (= (= tptp.nil @t45) (and @t60 @t41)))))))
% 0.39/0.68  (assume @p84 (forall @t9 (=> @t17 (= (tptp.app @t2 tptp.nil) @t2))))
% 0.39/0.68  (assume @p85 (forall @t9 (=> @t17 (forall @t7 (=> @t22 (=> @t43 (= (tptp.hd @t45) @t42)))))))
% 0.39/0.68  (assume @p86 (forall @t9 (=> @t17 (forall @t7 (=> @t22 (=> @t43 (= (tptp.tl @t45) (tptp.app @t44 @t1))))))))
% 0.39/0.68  (assume @p87 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> (and @t49 (tptp.geq @t1 @t2)) @t3))))))
% 0.39/0.68  (assume @p88 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t35 (=> (and @t49 (tptp.geq @t1 @t12)) (tptp.geq @t2 @t12)))))))))
% 0.39/0.68  (assume @p89 (forall @t9 (=> @t8 (tptp.geq @t2 @t2))))
% 0.39/0.68  (assume @p90 (forall @t9 (=> @t8 (not (tptp.lt @t2 @t2)))))
% 0.39/0.68  (assume @p91 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t35 (=> (and @t48 @t36) @t52))))))))
% 0.39/0.68  (assume @p92 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t48 (or @t3 @t51)))))))
% 0.39/0.68  (assume @p93 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (= @t51 (and @t4 @t48)))))))
% 0.39/0.68  (assume @p94 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (=> @t53 (not (tptp.gt @t1 @t2))))))))
% 0.39/0.68  (assume @p95 (forall @t9 (=> @t8 (forall @t7 (=> @t6 (forall @t16 (=> @t35 (=> (and @t53 (tptp.gt @t1 @t12)) (tptp.gt @t2 @t12)))))))))
% 0.39/0.68  (assume @p96 @t80)
% 0.39/0.68  (assume @p97 true)
% 0.39/0.68  (step @p98 :rule aci_norm :args ((= @t93 @t91)))
% 0.39/0.68  (step @p99 :rule cong :premises (@p98) :args (@t95))
% 0.39/0.68  (step @p100 :rule quant-merge-prenex :args ((= (forall @t9 @t97) @t95)))
% 0.39/0.68  (step @p101 :rule alpha_equiv :args (@t98 (@list @t81) (@list @t1)))
% 0.39/0.68  (step @p102 :rule refl :args (@t90))
% 0.39/0.68  (step @p103 :rule nary_cong :premises (@p102 @p101) :args (@t99))
% 0.39/0.68  (step @p104 :rule quant-miniscope-or :args ((= @t97 @t99)))
% 0.39/0.68  (step @p105 :rule trans :premises (@p104 @p103))
% 0.39/0.68  (step @p106 :rule symm :premises (@p105))
% 0.39/0.68  (step @p107 :rule cong :premises (@p106) :args ((forall @t9 @t104)))
% 0.39/0.68  (step @p108 :rule trans :premises (@p107 @p100))
% 0.39/0.68  (step @p109 :rule trans :premises (@p108 @p99))
% 0.39/0.68  (step @p110 :rule aci_norm :args ((= (or @t90 @t104) @t104)))
% 0.39/0.68  (step @p111 :rule bool-impl-elim :args (@t17 @t104))
% 0.39/0.68  (step @p112 :rule trans :premises (@p111 @p110))
% 0.39/0.68  (step @p113 :rule cong :premises (@p112) :args ((forall @t9 (=> @t17 @t104))))
% 0.39/0.68  (step @p114 :rule trans :premises (@p113 @p109))
% 0.39/0.68  (step @p115 :rule quant-miniscope-or :args ((= (forall @t7 @t105) @t104)))
% 0.39/0.68  (step @p116 :rule aci_norm :args ((= @t106 @t105)))
% 0.39/0.68  (step @p117 :rule cong :premises (@p116) :args ((forall @t7 @t106)))
% 0.39/0.68  (step @p118 :rule trans :premises (@p117 @p115))
% 0.39/0.68  (step @p119 :rule aci_norm :args ((= (or @t102 @t107) @t106)))
% 0.39/0.68  (step @p120 :rule bool-impl-elim :args (@t22 @t107))
% 0.39/0.68  (step @p121 :rule trans :premises (@p120 @p119))
% 0.39/0.68  (step @p122 :rule cong :premises (@p121) :args ((forall @t7 (=> @t22 @t107))))
% 0.39/0.68  (step @p123 :rule trans :premises (@p122 @p118))
% 0.39/0.68  (step @p124 :rule aci_norm :args ((= (or @t69 @t64 @t102 @t108) @t107)))
% 0.39/0.68  (step @p125 :rule aci_norm :args ((= (or @t90 false @t101 @t100) @t108)))
% 0.39/0.68  (step @p126 :rule refl :args (@t100))
% 0.39/0.68  (step @p127 :rule refl :args (@t101))
% 0.39/0.68  (step @p128 :rule evaluate :args ((not true)))
% 0.39/0.68  (step @p129 :rule eq-refl :args (@t2))
% 0.39/0.68  (step @p130 :rule cong :premises (@p129) :args (@t109))
% 0.39/0.68  (step @p131 :rule trans :premises (@p130 @p128))
% 0.39/0.68  (step @p132 :rule refl :args (@t90))
% 0.39/0.68  (step @p133 :rule nary_cong :premises (@p132 @p131 @p127 @p126) :args (@t110))
% 0.39/0.68  (step @p134 :rule trans :premises (@p133 @p125))
% 0.39/0.68  (step @p135 :rule quant-var-elim-eq :args ((= (forall @t16 (or (not @t63) @t113 @t70 @t112 @t111)) @t110)))
% 0.39/0.68  (step @p136 :rule refl :args (@t111))
% 0.39/0.68  (step @p137 :rule refl :args (@t112))
% 0.39/0.68  (step @p138 :rule refl :args (@t70))
% 0.39/0.68  (step @p139 :rule refl :args (@t113))
% 0.39/0.68  (step @p140 :rule eq-symm :args (@t2 @t12))
% 0.39/0.68  (step @p141 :rule cong :premises (@p140) :args (@t70))
% 0.39/0.68  (step @p142 :rule nary_cong :premises (@p141 @p139 @p138 @p137 @p136) :args (@t114))
% 0.39/0.68  (step @p143 :rule aci_norm :args ((= @t115 @t114)))
% 0.39/0.68  (step @p144 :rule trans :premises (@p143 @p142))
% 0.39/0.68  (step @p145 :rule cong :premises (@p144) :args (@t116))
% 0.39/0.68  (step @p146 :rule trans :premises (@p145 @p135))
% 0.39/0.68  (step @p147 :rule trans :premises (@p146 @p134))
% 0.39/0.68  (step @p148 :rule refl :args (@t102))
% 0.39/0.68  (step @p149 :rule refl :args (@t64))
% 0.39/0.68  (step @p150 :rule refl :args (@t69))
% 0.39/0.68  (step @p151 :rule nary_cong :premises (@p150 @p149 @p148 @p147) :args (@t117))
% 0.39/0.68  (step @p152 :rule trans :premises (@p151 @p124))
% 0.39/0.68  (step @p153 :rule quant-miniscope-or :args ((= (forall @t16 @t118) @t117)))
% 0.39/0.68  (step @p154 :rule aci_norm :args ((= @t119 @t118)))
% 0.39/0.68  (step @p155 :rule cong :premises (@p154) :args ((forall @t16 @t119)))
% 0.39/0.68  (step @p156 :rule trans :premises (@p155 @p153))
% 0.39/0.68  (step @p157 :rule trans :premises (@p156 @p152))
% 0.39/0.68  (step @p158 :rule aci_norm :args ((= (or @t113 @t120) @t119)))
% 0.39/0.68  (step @p159 :rule bool-impl-elim :args (@t15 @t120))
% 0.39/0.68  (step @p160 :rule trans :premises (@p159 @p158))
% 0.39/0.68  (step @p161 :rule cong :premises (@p160) :args ((forall @t16 (=> @t15 @t120))))
% 0.39/0.68  (step @p162 :rule trans :premises (@p161 @p157))
% 0.39/0.68  (step @p163 :rule aci_norm :args ((= (or @t70 @t69 @t64 @t121) @t120)))
% 0.39/0.68  (step @p164 :rule aci_norm :args ((= (or @t102 false @t112 @t111) @t121)))
% 0.39/0.68  (step @p165 :rule refl :args (@t111))
% 0.39/0.68  (step @p166 :rule refl :args (@t112))
% 0.39/0.68  (step @p167 :rule eq-refl :args (@t1))
% 0.39/0.68  (step @p168 :rule cong :premises (@p167) :args (@t122))
% 0.39/0.68  (step @p169 :rule trans :premises (@p168 @p128))
% 0.39/0.68  (step @p170 :rule nary_cong :premises (@p148 @p169 @p166 @p165) :args (@t123))
% 0.39/0.68  (step @p171 :rule trans :premises (@p170 @p164))
% 0.39/0.68  (step @p172 :rule quant-var-elim-eq :args ((= (forall @t14 (or (not (= @t10 @t1)) @t124 @t71 @t67 @t66)) @t123)))
% 0.39/0.68  (step @p173 :rule refl :args (@t66))
% 0.39/0.68  (step @p174 :rule refl :args (@t67))
% 0.39/0.68  (step @p175 :rule refl :args (@t71))
% 0.39/0.68  (step @p176 :rule refl :args (@t124))
% 0.39/0.68  (step @p177 :rule eq-symm :args (@t1 @t10))
% 0.39/0.68  (step @p178 :rule cong :premises (@p177) :args (@t71))
% 0.39/0.68  (step @p179 :rule nary_cong :premises (@p178 @p176 @p175 @p174 @p173) :args (@t125))
% 0.39/0.68  (step @p180 :rule aci_norm :args ((= @t126 @t125)))
% 0.39/0.68  (step @p181 :rule trans :premises (@p180 @p179))
% 0.39/0.68  (step @p182 :rule cong :premises (@p181) :args (@t127))
% 0.39/0.68  (step @p183 :rule trans :premises (@p182 @p172))
% 0.39/0.68  (step @p184 :rule trans :premises (@p183 @p171))
% 0.39/0.68  (step @p185 :rule refl :args (@t70))
% 0.39/0.68  (step @p186 :rule nary_cong :premises (@p185 @p150 @p149 @p184) :args (@t128))
% 0.39/0.68  (step @p187 :rule trans :premises (@p186 @p163))
% 0.39/0.68  (step @p188 :rule quant-miniscope-or :args ((= (forall @t14 @t129) @t128)))
% 0.39/0.68  (step @p189 :rule aci_norm :args ((= @t130 @t129)))
% 0.39/0.68  (step @p190 :rule cong :premises (@p189) :args ((forall @t14 @t130)))
% 0.39/0.68  (step @p191 :rule trans :premises (@p190 @p188))
% 0.39/0.68  (step @p192 :rule trans :premises (@p191 @p187))
% 0.39/0.68  (step @p193 :rule aci_norm :args ((= (or @t124 @t72) @t130)))
% 0.39/0.68  (step @p194 :rule bool-impl-elim :args (@t13 @t72))
% 0.39/0.68  (step @p195 :rule trans :premises (@p194 @p193))
% 0.39/0.68  (step @p196 :rule cong :premises (@p195) :args (@t73))
% 0.39/0.68  (step @p197 :rule trans :premises (@p196 @p192))
% 0.39/0.68  (step @p198 :rule refl :args (@t15))
% 0.39/0.68  (step @p199 :rule cong :premises (@p198 @p197) :args (@t74))
% 0.39/0.68  (step @p200 :rule cong :premises (@p199) :args (@t75))
% 0.39/0.68  (step @p201 :rule trans :premises (@p200 @p162))
% 0.39/0.68  (step @p202 :rule refl :args (@t22))
% 0.39/0.68  (step @p203 :rule cong :premises (@p202 @p201) :args (@t76))
% 0.39/0.68  (step @p204 :rule cong :premises (@p203) :args (@t77))
% 0.39/0.68  (step @p205 :rule trans :premises (@p204 @p123))
% 0.39/0.68  (step @p206 :rule refl :args (@t17))
% 0.39/0.68  (step @p207 :rule cong :premises (@p206 @p205) :args (@t78))
% 0.39/0.68  (step @p208 :rule cong :premises (@p207) :args (@t79))
% 0.39/0.68  (step @p209 :rule trans :premises (@p208 @p114))
% 0.39/0.68  (step @p210 :rule cong :premises (@p209) :args (@t80))
% 0.39/0.68  (step @p211 :rule eq_resolve :premises (@p96 @p210))
% 0.39/0.68  (step @p212 :rule skolemize :premises (@p211))
% 0.39/0.68  (step @p213 :rule cnf_or_neg :args (@t142 3))
% 0.39/0.68  (step @p214 :rule chain_m_resolution :premises (@p213 @p212) :args ((not @t140) @t143 @t144))
% 0.39/0.68  (step @p215 :rule bool-double-not-elim :args (@t138))
% 0.39/0.68  (step @p216 :rule refl :args (@t142))
% 0.39/0.68  (step @p217 :rule nary_cong :premises (@p216 @p215) :args ((or @t142 (not @t139))))
% 0.39/0.68  (step @p218 :rule cnf_or_neg :args (@t142 4))
% 0.39/0.68  (step @p219 :rule eq_resolve :premises (@p218 @p217))
% 0.39/0.68  (step @p220 :rule reordering :premises (@p219) :args ((or @t138 @t142)))
% 0.39/0.68  (step @p221 :rule chain_m_resolution :premises (@p220 @p212) :args (@t138 @t143 @t144))
% 0.39/0.68  (step @p222 :rule cnf_or_neg :args (@t142 5))
% 0.39/0.68  (step @p223 :rule chain_m_resolution :premises (@p222 @p212) :args ((not @t137) @t143 @t144))
% 0.39/0.68  (step @p224 :rule bool-double-not-elim :args (@t133))
% 0.39/0.68  (step @p225 :rule nary_cong :premises (@p216 @p224) :args ((or @t142 (not @t141))))
% 0.39/0.68  (step @p226 :rule cnf_or_neg :args (@t142 2))
% 0.39/0.68  (step @p227 :rule eq_resolve :premises (@p226 @p225))
% 0.39/0.68  (step @p228 :rule reordering :premises (@p227) :args ((or @t133 @t142)))
% 0.39/0.68  (step @p229 :rule chain_m_resolution :premises (@p228 @p212) :args (@t133 @t143 @t144))
% 0.39/0.68  (step @p230 :rule refl :args (@t141))
% 0.39/0.68  (step @p231 :rule bool-double-not-elim :args (@t135))
% 0.39/0.68  (step @p232 :rule refl :args (@t137))
% 0.39/0.68  (step @p233 :rule nary_cong :premises (@p232 @p231 @p230) :args ((or @t137 (not @t136) @t141)))
% 0.39/0.68  (step @p234 :rule cnf_and_neg :args (@t137))
% 0.39/0.68  (step @p235 :rule eq_resolve :premises (@p234 @p233))
% 0.39/0.68  (step @p236 :rule reordering :premises (@p235) :args ((or @t141 @t135 @t137)))
% 0.39/0.68  (step @p237 :rule chain_m_resolution :premises (@p236 @p229 @p223) :args (@t135 (@list false true) (@list @t133 @t137)))
% 0.39/0.68  (step @p238 :rule cnf_and_neg :args (@t140))
% 0.39/0.68  (step @p239 :rule reordering :premises (@p238) :args ((or @t140 @t139 @t136)))
% 0.39/0.68  (step @p240 false :rule chain_m_resolution :premises (@p239 @p237 @p221 @p214) :args (false (@list false false true) (@list @t135 @t138 @t140)))
% 0.39/0.68  )
% 0.39/0.68  % SZS output end Proof
% 0.39/0.68  % cvc5 exiting
%------------------------------------------------------------------------------