%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : RNG055+2 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n014.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 08:45:31 AM UTC 2026 % Result : Theorem 0.72s 1.02s % Output : Proof 0.72s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : RNG055+2 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n014.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 14:04:28 EDT 2026 % 0.16/0.34 % CPUTime : % 0.30/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.72/1.02 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.72/1.02 % SZS status Theorem % 0.72/1.02 % SZS output start Proof % 0.72/1.02 ( % 0.72/1.02 (declare-sort $$unsorted 0) % 0.72/1.02 (declare-const tptp.xN $$unsorted) % 0.72/1.02 (declare-const tptp.xS $$unsorted) % 0.72/1.02 (declare-const tptp.aDimensionOf0 (-> $$unsorted $$unsorted)) % 0.72/1.02 (declare-const tptp.sdtlseqdt0 (-> $$unsorted $$unsorted Bool)) % 0.72/1.02 (declare-const tptp.smndt0 (-> $$unsorted $$unsorted)) % 0.72/1.02 (declare-const tptp.sz00 $$unsorted) % 0.72/1.02 (declare-const tptp.aNaturalNumber0 (-> $$unsorted Bool)) % 0.72/1.02 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.72/1.02 (declare-const tptp.xp $$unsorted) % 0.72/1.02 (declare-const tptp.sdtlbdtrb0 (-> $$unsorted $$unsorted $$unsorted)) % 0.72/1.02 (declare-const tptp.xG $$unsorted) % 0.72/1.02 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.72/1.02 (declare-const tptp.xF $$unsorted) % 0.72/1.02 (declare-const tptp.sz0z00 $$unsorted) % 0.72/1.02 (declare-const tptp.xC $$unsorted) % 0.72/1.02 (declare-const tptp.xR $$unsorted) % 0.72/1.02 (declare-const tptp.aScalar0 (-> $$unsorted Bool)) % 0.72/1.02 (declare-const tptp.sdtasasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.72/1.02 (declare-const tptp.xs $$unsorted) % 0.72/1.02 (declare-const tptp.szszuzczcdt0 (-> $$unsorted $$unsorted)) % 0.72/1.02 (declare-const tptp.xq $$unsorted) % 0.72/1.02 (declare-const tptp.xP $$unsorted) % 0.72/1.02 (declare-const tptp.aVector0 (-> $$unsorted Bool)) % 0.72/1.02 (declare-const tptp.xA $$unsorted) % 0.72/1.02 (declare-const tptp.xB $$unsorted) % 0.72/1.02 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 0.72/1.02 (declare-const tptp.sziznziztdt0 (-> $$unsorted $$unsorted)) % 0.72/1.02 (declare-const tptp.xt $$unsorted) % 0.72/1.02 (declare-const tptp.xD $$unsorted) % 0.72/1.02 (declare-const tptp.xE $$unsorted) % 0.72/1.02 (declare-const tptp.xH $$unsorted) % 0.72/1.02 (define @t1 () (@var "W0" $$unsorted)) % 0.72/1.02 (define @t2 () (tptp.aNaturalNumber0 @t1)) % 0.72/1.02 (define @t3 () (@list @t1)) % 0.72/1.02 (define @t4 () (tptp.szszuzczcdt0 @t1)) % 0.72/1.02 (define @t5 () (@var "W1" $$unsorted)) % 0.72/1.02 (define @t6 () (tptp.szszuzczcdt0 @t5)) % 0.72/1.02 (define @t7 () (tptp.aNaturalNumber0 @t5)) % 0.72/1.02 (define @t8 () (@list @t5)) % 0.72/1.02 (define @t9 () (= @t1 @t5)) % 0.72/1.02 (define @t10 () (and @t2 @t7)) % 0.72/1.02 (define @t11 () (@list @t1 @t5)) % 0.72/1.02 (define @t12 () (tptp.aScalar0 @t1)) % 0.72/1.02 (define @t13 () (tptp.sdtpldt0 @t1 @t5)) % 0.72/1.02 (define @t14 () (tptp.aScalar0 @t5)) % 0.72/1.02 (define @t15 () (and @t12 @t14)) % 0.72/1.02 (define @t16 () (tptp.sdtasdt0 @t1 @t5)) % 0.72/1.02 (define @t17 () (tptp.aScalar0 @t16)) % 0.72/1.02 (define @t18 () (forall @t11 (=> @t15 @t17))) % 0.72/1.02 (define @t19 () (tptp.smndt0 @t1)) % 0.72/1.02 (define @t20 () (tptp.smndt0 tptp.sz0z00)) % 0.72/1.02 (define @t21 () (tptp.smndt0 @t19)) % 0.72/1.02 (define @t22 () (tptp.sdtpldt0 @t19 @t1)) % 0.72/1.02 (define @t23 () (tptp.sdtpldt0 @t1 @t19)) % 0.72/1.02 (define @t24 () (tptp.sdtasdt0 tptp.sz0z00 @t1)) % 0.72/1.02 (define @t25 () (tptp.sdtasdt0 @t1 tptp.sz0z00)) % 0.72/1.02 (define @t26 () (tptp.sdtpldt0 tptp.sz0z00 @t1)) % 0.72/1.02 (define @t27 () (tptp.sdtpldt0 @t1 tptp.sz0z00)) % 0.72/1.02 (define @t28 () (and (= @t27 @t1) (= @t26 @t1) (= @t25 tptp.sz0z00) (= @t24 tptp.sz0z00) (= @t23 tptp.sz0z00) (= @t22 tptp.sz0z00) (= @t21 @t1) (= @t20 tptp.sz0z00))) % 0.72/1.02 (define @t29 () (=> @t12 @t28)) % 0.72/1.02 (define @t30 () (forall @t3 @t29)) % 0.72/1.02 (define @t31 () (@var "W2" $$unsorted)) % 0.72/1.02 (define @t32 () (tptp.sdtasdt0 @t5 @t31)) % 0.72/1.02 (define @t33 () (tptp.sdtpldt0 @t5 @t31)) % 0.72/1.02 (define @t34 () (and (= (tptp.sdtpldt0 @t13 @t31) (tptp.sdtpldt0 @t1 @t33)) (= @t13 (tptp.sdtpldt0 @t5 @t1)) (= (tptp.sdtasdt0 @t16 @t31) (tptp.sdtasdt0 @t1 @t32)) (= @t16 (tptp.sdtasdt0 @t5 @t1)))) % 0.72/1.02 (define @t35 () (tptp.aScalar0 @t31)) % 0.72/1.02 (define @t36 () (and @t12 @t14 @t35)) % 0.72/1.02 (define @t37 () (@list @t1 @t5 @t31)) % 0.72/1.02 (define @t38 () (forall @t37 (=> @t36 @t34))) % 0.72/1.02 (define @t39 () (tptp.sdtasdt0 @t1 @t31)) % 0.72/1.02 (define @t40 () (@var "W3" $$unsorted)) % 0.72/1.02 (define @t41 () (tptp.sdtasdt0 @t5 @t40)) % 0.72/1.02 (define @t42 () (and @t12 @t14 @t35 (tptp.aScalar0 @t40))) % 0.72/1.02 (define @t43 () (@list @t1 @t5 @t31 @t40)) % 0.72/1.02 (define @t44 () (tptp.smndt0 @t16)) % 0.72/1.02 (define @t45 () (tptp.smndt0 @t5)) % 0.72/1.02 (define @t46 () (tptp.sdtlseqdt0 @t1 @t5)) % 0.72/1.02 (define @t47 () (tptp.sdtlseqdt0 @t5 @t1)) % 0.72/1.02 (define @t48 () (tptp.sdtlseqdt0 @t31 @t40)) % 0.72/1.02 (define @t49 () (tptp.sdtlseqdt0 tptp.sz0z00 @t5)) % 0.72/1.02 (define @t50 () (tptp.sdtlseqdt0 tptp.sz0z00 @t1)) % 0.72/1.02 (define @t51 () (tptp.sdtasdt0 @t1 @t1)) % 0.72/1.02 (define @t52 () (tptp.aVector0 @t1)) % 0.72/1.02 (define @t53 () (tptp.aDimensionOf0 @t1)) % 0.72/1.02 (define @t54 () (tptp.aDimensionOf0 @t5)) % 0.72/1.02 (define @t55 () (tptp.aVector0 @t5)) % 0.72/1.02 (define @t56 () (tptp.sziznziztdt0 @t1)) % 0.72/1.02 (define @t57 () (tptp.sziznziztdt0 @t5)) % 0.72/1.02 (define @t58 () (= @t54 tptp.sz00)) % 0.72/1.02 (define @t59 () (= @t53 @t54)) % 0.72/1.02 (define @t60 () (and @t59 (not @t58))) % 0.72/1.02 (define @t61 () (and @t52 @t55)) % 0.72/1.02 (define @t62 () (tptp.sdtasasdt0 @t1 @t5)) % 0.72/1.02 (define @t63 () (tptp.sdtasasdt0 @t1 @t1)) % 0.72/1.02 (define @t64 () (tptp.aDimensionOf0 tptp.xs)) % 0.72/1.02 (define @t65 () (tptp.aDimensionOf0 tptp.xt)) % 0.72/1.02 (define @t66 () (tptp.aScalar0 tptp.xA)) % 0.72/1.02 (define @t67 () (tptp.aScalar0 tptp.xB)) % 0.72/1.02 (define @t68 () (tptp.aScalar0 tptp.xE)) % 0.72/1.02 (define @t69 () (tptp.sdtasdt0 tptp.xA tptp.xB)) % 0.72/1.02 (define @t70 () (= tptp.xH @t69)) % 0.72/1.02 (define @t71 () (tptp.aScalar0 tptp.xH)) % 0.72/1.02 (define @t72 () (tptp.sdtasdt0 tptp.xE tptp.xH)) % 0.72/1.02 (define @t73 () (= tptp.xP @t72)) % 0.72/1.02 (define @t74 () (tptp.aScalar0 tptp.xP)) % 0.72/1.02 (define @t75 () (tptp.sdtasdt0 tptp.xE tptp.xE)) % 0.72/1.02 (define @t76 () (tptp.sdtasdt0 tptp.xH tptp.xH)) % 0.72/1.02 (define @t77 () (tptp.sdtasdt0 @t76 @t75)) % 0.72/1.02 (define @t78 () (tptp.sdtasdt0 tptp.xP tptp.xP)) % 0.72/1.02 (define @t79 () (= @t78 @t77)) % 0.72/1.02 (define @t80 () (= tptp.sz0z00 @t20)) % 0.72/1.02 (define @t81 () (and (= @t1 @t27) (= @t1 @t26) (= tptp.sz0z00 @t25) (= tptp.sz0z00 @t24) (= tptp.sz0z00 @t23) (= tptp.sz0z00 @t22) (= @t1 @t21) @t80)) % 0.72/1.02 (define @t82 () (tptp.smndt0 tptp.xH)) % 0.72/1.02 (define @t83 () (tptp.smndt0 @t82)) % 0.72/1.02 (define @t84 () (= tptp.xH @t83)) % 0.72/1.02 (define @t85 () (and (= tptp.xH (tptp.sdtpldt0 tptp.xH tptp.sz0z00)) (= tptp.xH (tptp.sdtpldt0 tptp.sz0z00 tptp.xH)) (= tptp.sz0z00 (tptp.sdtasdt0 tptp.xH tptp.sz0z00)) (= tptp.sz0z00 (tptp.sdtasdt0 tptp.sz0z00 tptp.xH)) (= tptp.sz0z00 (tptp.sdtpldt0 tptp.xH @t82)) (= tptp.sz0z00 (tptp.sdtpldt0 @t82 tptp.xH)) @t84 @t80)) % 0.72/1.02 (define @t86 () (not @t71)) % 0.72/1.02 (define @t87 () (or @t86 @t85)) % 0.72/1.02 (define @t88 () (@list false false)) % 0.72/1.02 (define @t89 () (@list false)) % 0.72/1.02 (define @t90 () (not @t35)) % 0.72/1.02 (define @t91 () (not @t14)) % 0.72/1.02 (define @t92 () (not @t12)) % 0.72/1.02 (define @t93 () (or @t92 @t91 @t90 @t34)) % 0.72/1.02 (define @t94 () (or @t92 @t91 @t90)) % 0.72/1.02 (define @t95 () (tptp.sdtasdt0 tptp.xB tptp.xA)) % 0.72/1.02 (define @t96 () (= @t69 @t95)) % 0.72/1.02 (define @t97 () (tptp.sdtpldt0 tptp.xA tptp.xB)) % 0.72/1.02 (define @t98 () (and (= (tptp.sdtpldt0 @t97 tptp.xH) (tptp.sdtpldt0 tptp.xA (tptp.sdtpldt0 tptp.xB tptp.xH))) (= @t97 (tptp.sdtpldt0 tptp.xB tptp.xA)) (= (tptp.sdtasdt0 @t69 tptp.xH) (tptp.sdtasdt0 tptp.xA (tptp.sdtasdt0 tptp.xB tptp.xH))) @t96)) % 0.72/1.02 (define @t99 () (not @t67)) % 0.72/1.02 (define @t100 () (not @t66)) % 0.72/1.02 (define @t101 () (or @t100 @t99 @t86 @t98)) % 0.72/1.02 (define @t102 () (@list false false false false)) % 0.72/1.02 (define @t103 () (tptp.sdtasdt0 tptp.xH tptp.xE)) % 0.72/1.02 (define @t104 () (= @t72 @t103)) % 0.72/1.02 (define @t105 () (tptp.sdtpldt0 tptp.xH tptp.xE)) % 0.72/1.02 (define @t106 () (tptp.sdtpldt0 tptp.xE tptp.xH)) % 0.72/1.02 (define @t107 () (= @t106 @t105)) % 0.72/1.02 (define @t108 () (and (= (tptp.sdtpldt0 @t106 tptp.xP) (tptp.sdtpldt0 tptp.xE (tptp.sdtpldt0 tptp.xH tptp.xP))) @t107 (= (tptp.sdtasdt0 @t72 tptp.xP) (tptp.sdtasdt0 tptp.xE (tptp.sdtasdt0 tptp.xH tptp.xP))) @t104)) % 0.72/1.02 (define @t109 () (not @t74)) % 0.72/1.02 (define @t110 () (not @t68)) % 0.72/1.02 (define @t111 () (or @t110 @t86 @t109 @t108)) % 0.72/1.02 (define @t112 () (tptp.sdtasdt0 tptp.xE tptp.xP)) % 0.72/1.02 (define @t113 () (tptp.sdtasdt0 tptp.xP tptp.xE)) % 0.72/1.02 (define @t114 () (= @t113 @t112)) % 0.72/1.02 (define @t115 () (tptp.sdtpldt0 tptp.xE tptp.xP)) % 0.72/1.02 (define @t116 () (tptp.sdtpldt0 tptp.xP tptp.xE)) % 0.72/1.02 (define @t117 () (and (= (tptp.sdtpldt0 @t116 tptp.xH) (tptp.sdtpldt0 tptp.xP @t106)) (= @t116 @t115) (= (tptp.sdtasdt0 @t113 tptp.xH) (tptp.sdtasdt0 tptp.xP @t72)) @t114)) % 0.72/1.02 (define @t118 () (or @t109 @t110 @t86 @t117)) % 0.72/1.02 (define @t119 () (tptp.sdtasdt0 tptp.xH @t75)) % 0.72/1.02 (define @t120 () (= @t77 (tptp.sdtasdt0 tptp.xH @t119))) % 0.72/1.02 (define @t121 () (tptp.sdtpldt0 tptp.xH tptp.xH)) % 0.72/1.02 (define @t122 () (= (tptp.sdtpldt0 @t121 @t75) (tptp.sdtpldt0 tptp.xH (tptp.sdtpldt0 tptp.xH @t75)))) % 0.72/1.02 (define @t123 () (and @t122 @t120)) % 0.72/1.02 (define @t124 () (and @t122 (= @t121 @t121) @t120 (= @t76 @t76))) % 0.72/1.02 (define @t125 () (tptp.aScalar0 @t75)) % 0.72/1.02 (define @t126 () (not @t125)) % 0.72/1.02 (define @t127 () (or @t86 @t86 @t126 @t124)) % 0.72/1.02 (define @t128 () (forall @t37 @t93)) % 0.72/1.02 (define @t129 () (or @t86 @t86 @t126 @t123)) % 0.72/1.02 (define @t130 () (@list @t128)) % 0.72/1.02 (define @t131 () (or @t110 @t110 @t125)) % 0.72/1.02 (define @t132 () (@list false false false)) % 0.72/1.02 (define @t133 () (tptp.sdtasdt0 tptp.xH @t112)) % 0.72/1.02 (define @t134 () (= (tptp.sdtasdt0 @t103 tptp.xP) @t133)) % 0.72/1.02 (define @t135 () (= (tptp.sdtpldt0 @t105 tptp.xP) (tptp.sdtpldt0 tptp.xH @t115))) % 0.72/1.02 (define @t136 () (= @t103 @t72)) % 0.72/1.02 (define @t137 () (= @t105 @t106)) % 0.72/1.02 (define @t138 () (and @t135 @t137 @t134 @t136)) % 0.72/1.02 (define @t139 () (or @t86 @t110 @t109 @t138)) % 0.72/1.02 (define @t140 () (and @t135 @t107 @t134 @t104)) % 0.72/1.02 (define @t141 () (or @t86 @t110 @t109 @t140)) % 0.72/1.02 (define @t142 () (tptp.sdtasdt0 @t103 tptp.xE)) % 0.72/1.02 (define @t143 () (= (tptp.sdtpldt0 @t105 tptp.xE) (tptp.sdtpldt0 tptp.xH (tptp.sdtpldt0 tptp.xE tptp.xE)))) % 0.72/1.02 (define @t144 () (and @t143 @t137 (= @t142 @t119) @t136)) % 0.72/1.02 (define @t145 () (or @t86 @t110 @t110 @t144)) % 0.72/1.02 (define @t146 () (= @t119 @t142)) % 0.72/1.02 (define @t147 () (and @t143 @t107 @t146 @t104)) % 0.72/1.02 (define @t148 () (or @t86 @t110 @t110 @t147)) % 0.72/1.02 (define @t149 () (and @t70 @t73 @t84 @t96 @t120 @t104 @t114 @t134 @t146)) % 0.72/1.02 (assume @p1 (forall @t3 (=> @t2 true))) % 0.72/1.02 (assume @p2 (tptp.aNaturalNumber0 tptp.sz00)) % 0.72/1.02 (assume @p3 (forall @t3 (=> @t2 (and (tptp.aNaturalNumber0 @t4) (not (= @t4 tptp.sz00)))))) % 0.72/1.02 (assume @p4 (forall @t3 (=> (and @t2 (not (= @t1 tptp.sz00))) (exists @t8 (and @t7 (= @t1 @t6)))))) % 0.72/1.02 (assume @p5 (forall @t11 (=> @t10 (=> (= @t4 @t6) @t9)))) % 0.72/1.02 (assume @p6 (forall @t11 (=> @t10 (=> (tptp.iLess0 @t1 @t5) true)))) % 0.72/1.02 (assume @p7 (forall @t3 (=> @t2 (tptp.iLess0 @t1 @t4)))) % 0.72/1.02 (assume @p8 (forall @t3 (=> @t12 true))) % 0.72/1.02 (assume @p9 (tptp.aScalar0 tptp.sz0z00)) % 0.72/1.02 (assume @p10 (forall @t11 (=> @t15 (tptp.aScalar0 @t13)))) % 0.72/1.02 (assume @p11 @t18) % 0.72/1.02 (assume @p12 (forall @t3 (=> @t12 (tptp.aScalar0 @t19)))) % 0.72/1.02 (assume @p13 @t30) % 0.72/1.02 (assume @p14 @t38) % 0.72/1.02 (assume @p15 (forall @t37 (=> @t36 (and (= (tptp.sdtasdt0 @t1 @t33) (tptp.sdtpldt0 @t16 @t39)) (= (tptp.sdtasdt0 @t13 @t31) (tptp.sdtpldt0 @t39 @t32)))))) % 0.72/1.02 (assume @p16 (forall @t43 (=> @t42 (= (tptp.sdtasdt0 @t13 (tptp.sdtpldt0 @t31 @t40)) (tptp.sdtpldt0 (tptp.sdtpldt0 @t39 (tptp.sdtasdt0 @t1 @t40)) (tptp.sdtpldt0 @t32 @t41)))))) % 0.72/1.02 (assume @p17 (forall @t11 (=> @t15 (and (= (tptp.sdtasdt0 @t1 @t45) @t44) (= (tptp.sdtasdt0 @t19 @t5) @t44))))) % 0.72/1.02 (assume @p18 (forall @t11 (=> @t15 (= (tptp.sdtasdt0 @t19 @t45) @t16)))) % 0.72/1.02 (assume @p19 (forall @t11 (=> @t15 (=> @t46 true)))) % 0.72/1.02 (assume @p20 (forall @t3 (=> @t12 (tptp.sdtlseqdt0 @t1 @t1)))) % 0.72/1.02 (assume @p21 (forall @t11 (=> @t15 (=> (and @t46 @t47) @t9)))) % 0.72/1.02 (assume @p22 (forall @t37 (=> @t36 (=> (and @t46 (tptp.sdtlseqdt0 @t5 @t31)) (tptp.sdtlseqdt0 @t1 @t31))))) % 0.72/1.02 (assume @p23 (forall @t43 (=> @t42 (=> (and @t46 @t48) (tptp.sdtlseqdt0 (tptp.sdtpldt0 @t1 @t31) (tptp.sdtpldt0 @t5 @t40)))))) % 0.72/1.02 (assume @p24 (forall @t43 (=> @t42 (=> (and @t46 (tptp.sdtlseqdt0 tptp.sz0z00 @t31) @t48) (tptp.sdtlseqdt0 @t39 @t41))))) % 0.72/1.02 (assume @p25 (forall @t11 (=> @t15 (or @t46 @t47)))) % 0.72/1.02 (assume @p26 (forall @t11 (=> @t15 (=> (and @t50 @t49) (and (tptp.sdtlseqdt0 tptp.sz0z00 @t13) (tptp.sdtlseqdt0 tptp.sz0z00 @t16)))))) % 0.72/1.02 (assume @p27 (forall @t3 (=> @t12 (tptp.sdtlseqdt0 tptp.sz0z00 @t51)))) % 0.72/1.02 (assume @p28 (forall @t11 (=> @t15 (=> (and @t50 @t49 (= @t51 (tptp.sdtasdt0 @t5 @t5))) @t9)))) % 0.72/1.02 (assume @p29 (forall @t3 (=> @t52 true))) % 0.72/1.02 (assume @p30 (forall @t3 (=> @t52 (tptp.aNaturalNumber0 @t53)))) % 0.72/1.02 (assume @p31 (forall @t11 (=> (and @t52 @t7) (tptp.aScalar0 (tptp.sdtlbdtrb0 @t1 @t5))))) % 0.72/1.02 (assume @p32 (forall @t3 (=> @t52 (=> (not (= @t53 tptp.sz00)) (forall @t8 (= (= @t5 @t56) (and @t55 (= (tptp.szszuzczcdt0 @t54) @t53) (forall (@list @t31) (=> (tptp.aNaturalNumber0 @t31) (= (tptp.sdtlbdtrb0 @t5 @t31) (tptp.sdtlbdtrb0 @t1 @t31))))))))))) % 0.72/1.02 (assume @p33 (forall @t11 (=> @t61 (=> @t60 (= (tptp.aDimensionOf0 @t56) (tptp.aDimensionOf0 @t57)))))) % 0.72/1.02 (assume @p34 (forall @t11 (=> @t61 (=> @t59 (tptp.aScalar0 @t62))))) % 0.72/1.02 (assume @p35 (forall @t11 (=> @t61 (=> (and @t59 @t58) (= @t62 tptp.sz0z00))))) % 0.72/1.02 (assume @p36 (forall @t11 (=> @t61 (=> @t60 (= @t62 (tptp.sdtpldt0 (tptp.sdtasasdt0 @t56 @t57) (tptp.sdtasdt0 (tptp.sdtlbdtrb0 @t1 @t53) (tptp.sdtlbdtrb0 @t5 @t54)))))))) % 0.72/1.02 (assume @p37 (forall @t3 (=> @t52 (tptp.sdtlseqdt0 tptp.sz0z00 @t63)))) % 0.72/1.02 (assume @p38 (and (tptp.aVector0 tptp.xs) (tptp.aVector0 tptp.xt))) % 0.72/1.02 (assume @p39 (forall @t11 (=> @t61 (=> @t59 (=> (tptp.iLess0 @t53 @t64) (tptp.sdtlseqdt0 (tptp.sdtasdt0 @t62 @t62) (tptp.sdtasdt0 @t63 (tptp.sdtasasdt0 @t5 @t5)))))))) % 0.72/1.02 (assume @p40 (= @t64 @t65)) % 0.72/1.02 (assume @p41 (not (= @t64 tptp.sz00))) % 0.72/1.02 (assume @p42 (and (tptp.aVector0 tptp.xp) (= (tptp.szszuzczcdt0 (tptp.aDimensionOf0 tptp.xp)) @t64) (forall @t3 (=> @t2 (= (tptp.sdtlbdtrb0 tptp.xp @t1) (tptp.sdtlbdtrb0 tptp.xs @t1)))) (= tptp.xp (tptp.sziznziztdt0 tptp.xs)))) % 0.72/1.02 (assume @p43 (and (tptp.aVector0 tptp.xq) (= (tptp.szszuzczcdt0 (tptp.aDimensionOf0 tptp.xq)) @t65) (forall @t3 (=> @t2 (= (tptp.sdtlbdtrb0 tptp.xq @t1) (tptp.sdtlbdtrb0 tptp.xt @t1)))) (= tptp.xq (tptp.sziznziztdt0 tptp.xt)))) % 0.72/1.02 (assume @p44 (and @t66 (= tptp.xA (tptp.sdtlbdtrb0 tptp.xs @t64)))) % 0.72/1.02 (assume @p45 (and @t67 (= tptp.xB (tptp.sdtlbdtrb0 tptp.xt @t65)))) % 0.72/1.02 (assume @p46 (and (tptp.aScalar0 tptp.xC) (= tptp.xC (tptp.sdtasasdt0 tptp.xp tptp.xp)))) % 0.72/1.02 (assume @p47 (and (tptp.aScalar0 tptp.xD) (= tptp.xD (tptp.sdtasasdt0 tptp.xq tptp.xq)))) % 0.72/1.02 (assume @p48 (and @t68 (= tptp.xE (tptp.sdtasasdt0 tptp.xp tptp.xq)))) % 0.72/1.02 (assume @p49 (and (tptp.aScalar0 tptp.xF) (= tptp.xF (tptp.sdtasdt0 tptp.xA tptp.xA)))) % 0.72/1.02 (assume @p50 (and (tptp.aScalar0 tptp.xG) (= tptp.xG (tptp.sdtasdt0 tptp.xB tptp.xB)))) % 0.72/1.02 (assume @p51 (and @t71 @t70)) % 0.72/1.02 (assume @p52 (and (tptp.aScalar0 tptp.xR) (= tptp.xR (tptp.sdtasdt0 tptp.xC tptp.xG)))) % 0.72/1.02 (assume @p53 (and @t74 @t73)) % 0.72/1.02 (assume @p54 (and (tptp.aScalar0 tptp.xS) (= tptp.xS (tptp.sdtasdt0 tptp.xF tptp.xD)))) % 0.72/1.02 (assume @p55 (and (tptp.aScalar0 tptp.xN) (= tptp.xN (tptp.sdtasdt0 tptp.xR tptp.xS)))) % 0.72/1.02 (assume @p56 (tptp.sdtlseqdt0 @t75 (tptp.sdtasdt0 tptp.xC tptp.xD))) % 0.72/1.02 (assume @p57 (not @t79)) % 0.72/1.02 (assume @p58 true) % 0.72/1.02 (step @p59 :rule and_elim :premises (@p51) :args (1)) % 0.72/1.02 (step @p60 :rule and_elim :premises (@p53) :args (1)) % 0.72/1.02 (step @p61 :rule bool-impl-elim :args (@t12 @t81)) % 0.72/1.02 (step @p62 :rule cong :premises (@p61) :args ((forall @t3 (=> @t12 @t81)))) % 0.72/1.02 (step @p63 :rule eq-symm :args (@t20 tptp.sz0z00)) % 0.72/1.02 (step @p64 :rule eq-symm :args (@t21 @t1)) % 0.72/1.02 (step @p65 :rule eq-symm :args (@t22 tptp.sz0z00)) % 0.72/1.02 (step @p66 :rule eq-symm :args (@t23 tptp.sz0z00)) % 0.72/1.02 (step @p67 :rule eq-symm :args (@t24 tptp.sz0z00)) % 0.72/1.02 (step @p68 :rule eq-symm :args (@t25 tptp.sz0z00)) % 0.72/1.02 (step @p69 :rule eq-symm :args (@t26 @t1)) % 0.72/1.02 (step @p70 :rule eq-symm :args (@t27 @t1)) % 0.72/1.02 (step @p71 :rule nary_cong :premises (@p70 @p69 @p68 @p67 @p66 @p65 @p64 @p63) :args (@t28)) % 0.72/1.02 (step @p72 :rule refl :args (@t12)) % 0.72/1.02 (step @p73 :rule cong :premises (@p72 @p71) :args (@t29)) % 0.72/1.02 (step @p74 :rule cong :premises (@p73) :args (@t30)) % 0.72/1.02 (step @p75 :rule trans :premises (@p74 @p62)) % 0.72/1.02 (step @p76 :rule eq_resolve :premises (@p13 @p75)) % 0.72/1.02 (step @p77 :rule instantiate :premises (@p76) :args ((@list tptp.xH))) % 0.72/1.02 (step @p78 :rule and_elim :premises (@p51) :args (0)) % 0.72/1.02 (step @p79 :rule cnf_or_pos :args (@t87)) % 0.72/1.02 (step @p80 :rule reordering :premises (@p79) :args ((or @t86 @t85 (not @t87)))) % 0.72/1.02 (step @p81 :rule chain_m_resolution :premises (@p80 @p78 @p77) :args (@t85 @t88 (@list @t71 @t87))) % 0.72/1.02 (step @p82 :rule cnf_and_pos :args (@t85 6)) % 0.72/1.02 (step @p83 :rule reordering :premises (@p82) :args ((or @t84 (not @t85)))) % 0.72/1.02 (step @p84 :rule chain_m_resolution :premises (@p83 @p81) :args (@t84 @t89 (@list @t85))) % 0.72/1.02 (step @p85 :rule aci_norm :args ((= (or @t94 @t34) @t93))) % 0.72/1.02 (step @p86 :rule refl :args (@t34)) % 0.72/1.02 (step @p87 :rule aci_norm :args ((= (or @t92 (or @t91 @t90)) @t94))) % 0.72/1.02 (step @p88 :rule bool-and-de-morgan :args (@t14 @t35 true)) % 0.72/1.02 (step @p89 :rule refl :args (@t92)) % 0.72/1.02 (step @p90 :rule nary_cong :premises (@p89 @p88) :args ((or @t92 (not (and @t14 @t35))))) % 0.72/1.02 (step @p91 :rule bool-and-de-morgan :args (@t12 @t14 (and @t35))) % 0.72/1.02 (step @p92 :rule trans :premises (@p91 @p90)) % 0.72/1.02 (step @p93 :rule trans :premises (@p92 @p87)) % 0.72/1.02 (step @p94 :rule nary_cong :premises (@p93 @p86) :args ((or (not @t36) @t34))) % 0.72/1.02 (step @p95 :rule trans :premises (@p94 @p85)) % 0.72/1.02 (step @p96 :rule bool-impl-elim :args (@t36 @t34)) % 0.72/1.02 (step @p97 :rule trans :premises (@p96 @p95)) % 0.72/1.02 (step @p98 :rule cong :premises (@p97) :args (@t38)) % 0.72/1.02 (step @p99 :rule eq_resolve :premises (@p14 @p98)) % 0.72/1.02 (step @p100 :rule instantiate :premises (@p99) :args ((@list tptp.xA tptp.xB tptp.xH))) % 0.72/1.02 (step @p101 :rule and_elim :premises (@p45) :args (0)) % 0.72/1.02 (step @p102 :rule and_elim :premises (@p44) :args (0)) % 0.72/1.02 (step @p103 :rule cnf_or_pos :args (@t101)) % 0.72/1.02 (step @p104 :rule reordering :premises (@p103) :args ((or @t100 @t99 @t86 @t98 (not @t101)))) % 0.72/1.02 (step @p105 :rule chain_m_resolution :premises (@p104 @p102 @p101 @p78 @p100) :args (@t98 @t102 (@list @t66 @t67 @t71 @t101))) % 0.72/1.02 (step @p106 :rule cnf_and_pos :args (@t98 3)) % 0.72/1.02 (step @p107 :rule reordering :premises (@p106) :args ((or @t96 (not @t98)))) % 0.72/1.02 (step @p108 :rule chain_m_resolution :premises (@p107 @p105) :args (@t96 @t89 (@list @t98))) % 0.72/1.02 (step @p109 :rule instantiate :premises (@p99) :args ((@list tptp.xE tptp.xH tptp.xP))) % 0.72/1.02 (step @p110 :rule and_elim :premises (@p53) :args (0)) % 0.72/1.02 (step @p111 :rule and_elim :premises (@p48) :args (0)) % 0.72/1.02 (step @p112 :rule cnf_or_pos :args (@t111)) % 0.72/1.02 (step @p113 :rule reordering :premises (@p112) :args ((or @t110 @t86 @t109 @t108 (not @t111)))) % 0.72/1.02 (step @p114 :rule chain_m_resolution :premises (@p113 @p111 @p78 @p110 @p109) :args (@t108 @t102 (@list @t68 @t71 @t74 @t111))) % 0.72/1.02 (step @p115 :rule cnf_and_pos :args (@t108 3)) % 0.72/1.02 (step @p116 :rule reordering :premises (@p115) :args ((or @t104 (not @t108)))) % 0.72/1.02 (step @p117 :rule chain_m_resolution :premises (@p116 @p114) :args (@t104 @t89 (@list @t108))) % 0.72/1.02 (step @p118 :rule instantiate :premises (@p99) :args ((@list tptp.xP tptp.xE tptp.xH))) % 0.72/1.02 (step @p119 :rule cnf_or_pos :args (@t118)) % 0.72/1.02 (step @p120 :rule reordering :premises (@p119) :args ((or @t110 @t86 @t109 @t117 (not @t118)))) % 0.72/1.02 (step @p121 :rule chain_m_resolution :premises (@p120 @p111 @p78 @p110 @p118) :args (@t117 @t102 (@list @t68 @t71 @t74 @t118))) % 0.72/1.02 (step @p122 :rule cnf_and_pos :args (@t117 3)) % 0.72/1.02 (step @p123 :rule reordering :premises (@p122) :args ((or @t114 (not @t117)))) % 0.72/1.02 (step @p124 :rule chain_m_resolution :premises (@p123 @p121) :args (@t114 @t89 (@list @t117))) % 0.72/1.02 (step @p125 :rule aci_norm :args ((= (and @t122 true @t120 true) @t123))) % 0.72/1.02 (step @p126 :rule eq-refl :args (@t76)) % 0.72/1.02 (step @p127 :rule refl :args (@t120)) % 0.72/1.02 (step @p128 :rule eq-refl :args (@t121)) % 0.72/1.02 (step @p129 :rule refl :args (@t122)) % 0.72/1.02 (step @p130 :rule nary_cong :premises (@p129 @p128 @p127 @p126) :args (@t124)) % 0.72/1.02 (step @p131 :rule trans :premises (@p130 @p125)) % 0.72/1.02 (step @p132 :rule refl :args (@t126)) % 0.72/1.02 (step @p133 :rule refl :args (@t86)) % 0.72/1.02 (step @p134 :rule nary_cong :premises (@p133 @p133 @p132 @p131) :args (@t127)) % 0.72/1.02 (step @p135 :rule refl :args (@t128)) % 0.72/1.02 (step @p136 :rule cong :premises (@p135 @p134) :args ((=> @t128 @t127))) % 0.72/1.02 (assume-push @p250 @t128) % 0.72/1.02 (step @p138 :rule instantiate :premises (@p99) :args ((@list tptp.xH tptp.xH @t75))) % 0.72/1.02 (step-pop @p251 :rule scope :premises (@p138)) % 0.72/1.02 (step @p139 :rule process_scope :premises (@p251) :args (@t127)) % 0.72/1.02 (step @p141 :rule eq_resolve :premises (@p139 @p136)) % 0.72/1.02 (step @p142 :rule implies_elim :premises (@p141)) % 0.72/1.02 (step @p143 :rule chain_m_resolution :premises (@p142 @p99) :args (@t129 @t89 @t130)) % 0.72/1.02 (step @p144 :rule aci_norm :args ((= (or (or @t92 @t91) @t17) (or @t92 @t91 @t17)))) % 0.72/1.02 (step @p145 :rule refl :args (@t17)) % 0.72/1.02 (step @p146 :rule bool-and-de-morgan :args (@t12 @t14 true)) % 0.72/1.02 (step @p147 :rule nary_cong :premises (@p146 @p145) :args ((or (not @t15) @t17))) % 0.72/1.02 (step @p148 :rule trans :premises (@p147 @p144)) % 0.72/1.02 (step @p149 :rule bool-impl-elim :args (@t15 @t17)) % 0.72/1.02 (step @p150 :rule trans :premises (@p149 @p148)) % 0.72/1.02 (step @p151 :rule cong :premises (@p150) :args (@t18)) % 0.72/1.02 (step @p152 :rule eq_resolve :premises (@p11 @p151)) % 0.72/1.02 (step @p153 :rule instantiate :premises (@p152) :args ((@list tptp.xE tptp.xE))) % 0.72/1.02 (step @p154 :rule cnf_or_pos :args (@t131)) % 0.72/1.02 (step @p155 :rule factoring :premises (@p154)) % 0.72/1.02 (step @p156 :rule reordering :premises (@p155) :args ((or @t110 @t125 (not @t131)))) % 0.72/1.02 (step @p157 :rule chain_m_resolution :premises (@p156 @p111 @p153) :args (@t125 @t88 (@list @t68 @t131))) % 0.72/1.02 (step @p158 :rule cnf_or_pos :args (@t129)) % 0.72/1.02 (step @p159 :rule factoring :premises (@p158)) % 0.72/1.02 (step @p160 :rule reordering :premises (@p159) :args ((or @t86 @t126 @t123 (not @t129)))) % 0.72/1.02 (step @p161 :rule chain_m_resolution :premises (@p160 @p78 @p157 @p143) :args (@t123 @t132 (@list @t71 @t125 @t129))) % 0.72/1.02 (step @p162 :rule cnf_and_pos :args (@t123 1)) % 0.72/1.02 (step @p163 :rule reordering :premises (@p162) :args ((or @t120 (not @t123)))) % 0.72/1.02 (step @p164 :rule chain_m_resolution :premises (@p163 @p161) :args (@t120 @t89 (@list @t123))) % 0.72/1.02 (step @p165 :rule eq-symm :args (@t103 @t72)) % 0.72/1.02 (step @p166 :rule refl :args (@t134)) % 0.72/1.02 (step @p167 :rule eq-symm :args (@t105 @t106)) % 0.72/1.02 (step @p168 :rule refl :args (@t135)) % 0.72/1.02 (step @p169 :rule nary_cong :premises (@p168 @p167 @p166 @p165) :args (@t138)) % 0.72/1.02 (step @p170 :rule refl :args (@t109)) % 0.72/1.02 (step @p171 :rule refl :args (@t110)) % 0.72/1.02 (step @p172 :rule nary_cong :premises (@p133 @p171 @p170 @p169) :args (@t139)) % 0.72/1.02 (step @p173 :rule cong :premises (@p135 @p172) :args ((=> @t128 @t139))) % 0.72/1.02 (assume-push @p252 @t128) % 0.72/1.02 (step @p175 :rule instantiate :premises (@p99) :args ((@list tptp.xH tptp.xE tptp.xP))) % 0.72/1.02 (step-pop @p253 :rule scope :premises (@p175)) % 0.72/1.02 (step @p176 :rule process_scope :premises (@p253) :args (@t139)) % 0.72/1.02 (step @p178 :rule eq_resolve :premises (@p176 @p173)) % 0.72/1.02 (step @p179 :rule implies_elim :premises (@p178)) % 0.72/1.02 (step @p180 :rule chain_m_resolution :premises (@p179 @p99) :args (@t141 @t89 @t130)) % 0.72/1.02 (step @p181 :rule cnf_or_pos :args (@t141)) % 0.72/1.02 (step @p182 :rule reordering :premises (@p181) :args ((or @t110 @t86 @t109 @t140 (not @t141)))) % 0.72/1.02 (step @p183 :rule chain_m_resolution :premises (@p182 @p111 @p78 @p110 @p180) :args (@t140 @t102 (@list @t68 @t71 @t74 @t141))) % 0.72/1.02 (step @p184 :rule cnf_and_pos :args (@t140 2)) % 0.72/1.02 (step @p185 :rule reordering :premises (@p184) :args ((or @t134 (not @t140)))) % 0.72/1.02 (step @p186 :rule chain_m_resolution :premises (@p185 @p183) :args (@t134 @t89 (@list @t140))) % 0.72/1.02 (step @p187 :rule eq-symm :args (@t142 @t119)) % 0.72/1.02 (step @p188 :rule refl :args (@t143)) % 0.72/1.02 (step @p189 :rule nary_cong :premises (@p188 @p167 @p187 @p165) :args (@t144)) % 0.72/1.02 (step @p190 :rule nary_cong :premises (@p133 @p171 @p171 @p189) :args (@t145)) % 0.72/1.02 (step @p191 :rule cong :premises (@p135 @p190) :args ((=> @t128 @t145))) % 0.72/1.02 (assume-push @p254 @t128) % 0.72/1.02 (step @p193 :rule instantiate :premises (@p99) :args ((@list tptp.xH tptp.xE tptp.xE))) % 0.72/1.02 (step-pop @p255 :rule scope :premises (@p193)) % 0.72/1.02 (step @p194 :rule process_scope :premises (@p255) :args (@t145)) % 0.72/1.02 (step @p196 :rule eq_resolve :premises (@p194 @p191)) % 0.72/1.02 (step @p197 :rule implies_elim :premises (@p196)) % 0.72/1.02 (step @p198 :rule chain_m_resolution :premises (@p197 @p99) :args (@t148 @t89 @t130)) % 0.72/1.02 (step @p199 :rule cnf_or_pos :args (@t148)) % 0.72/1.02 (step @p200 :rule factoring :premises (@p199)) % 0.72/1.02 (step @p201 :rule reordering :premises (@p200) :args ((or @t110 @t86 @t147 (not @t148)))) % 0.72/1.02 (step @p202 :rule chain_m_resolution :premises (@p201 @p111 @p78 @p198) :args (@t147 @t132 (@list @t68 @t71 @t148))) % 0.72/1.02 (step @p203 :rule cnf_and_pos :args (@t147 2)) % 0.72/1.02 (step @p204 :rule reordering :premises (@p203) :args ((or @t146 (not @t147)))) % 0.72/1.02 (step @p205 :rule chain_m_resolution :premises (@p204 @p202) :args (@t146 @t89 (@list @t147))) % 0.72/1.02 (assume-push @p256 @t70) % 0.72/1.02 (assume-push @p257 @t73) % 0.72/1.02 (assume-push @p258 @t84) % 0.72/1.02 (assume-push @p259 @t96) % 0.72/1.02 (assume-push @p260 @t120) % 0.72/1.02 (assume-push @p261 @t104) % 0.72/1.02 (assume-push @p262 @t114) % 0.72/1.02 (assume-push @p263 @t134) % 0.72/1.02 (assume-push @p264 @t146) % 0.72/1.02 (step @p215 :rule symm :premises (@p164)) % 0.72/1.02 (step @p216 :rule refl :args (@t119)) % 0.72/1.02 (step @p217 :rule symm :premises (@p84)) % 0.72/1.02 (step @p218 :rule cong :premises (@p217 @p216) :args ((tptp.sdtasdt0 @t83 @t119))) % 0.72/1.02 (step @p219 :rule symm :premises (@p59)) % 0.72/1.02 (step @p220 :rule symm :premises (@p108)) % 0.72/1.02 (step @p221 :rule trans :premises (@p220 @p219)) % 0.72/1.02 (step @p222 :rule trans :premises (@p221 @p84)) % 0.72/1.02 (step @p223 :rule cong :premises (@p222 @p216) :args ((tptp.sdtasdt0 @t95 @t119))) % 0.72/1.02 (step @p224 :rule symm :premises (@p205)) % 0.72/1.02 (step @p225 :rule refl :args (tptp.xE)) % 0.72/1.02 (step @p226 :rule trans :premises (@p60 @p117)) % 0.72/1.02 (step @p227 :rule cong :premises (@p226 @p225) :args (@t113)) % 0.72/1.02 (step @p228 :rule symm :premises (@p124)) % 0.72/1.02 (step @p229 :rule trans :premises (@p228 @p227 @p224)) % 0.72/1.02 (step @p230 :rule symm :premises (@p221)) % 0.72/1.02 (step @p231 :rule cong :premises (@p230 @p229) :args (@t133)) % 0.72/1.02 (step @p232 :rule refl :args (tptp.xP)) % 0.72/1.02 (step @p233 :rule cong :premises (@p226 @p232) :args (@t78)) % 0.72/1.02 (step @p234 :rule trans :premises (@p233 @p186 @p231 @p223 @p218 @p215)) % 0.72/1.02 (step-pop @p265 :rule scope :premises (@p234)) % 0.72/1.02 (step-pop @p266 :rule scope :premises (@p265)) % 0.72/1.02 (step-pop @p267 :rule scope :premises (@p266)) % 0.72/1.02 (step-pop @p268 :rule scope :premises (@p267)) % 0.72/1.02 (step-pop @p269 :rule scope :premises (@p268)) % 0.72/1.02 (step-pop @p270 :rule scope :premises (@p269)) % 0.72/1.02 (step-pop @p271 :rule scope :premises (@p270)) % 0.72/1.02 (step-pop @p272 :rule scope :premises (@p271)) % 0.72/1.02 (step-pop @p273 :rule scope :premises (@p272)) % 0.72/1.02 (step @p235 :rule process_scope :premises (@p273) :args (@t79)) % 0.72/1.02 (step @p245 :rule implies_elim :premises (@p235)) % 0.72/1.02 (step @p246 :rule cnf_and_neg :args (@t149)) % 0.72/1.02 (step @p247 :rule resolution :premises (@p246 @p245) :args (true @t149)) % 0.72/1.02 (step @p248 :rule reordering :premises (@p247) :args ((or @t79 (not @t70) (not @t73) (not @t84) (not @t96) (not @t120) (not @t104) (not @t114) (not @t134) (not @t146)))) % 0.72/1.02 (step @p249 false :rule chain_m_resolution :premises (@p248 @p205 @p186 @p164 @p124 @p117 @p108 @p84 @p57 @p60 @p59) :args (false (@list false false false false false false false true false false) (@list @t146 @t134 @t120 @t114 @t104 @t96 @t84 @t79 @t73 @t70))) % 0.72/1.02 ) % 0.72/1.02 % SZS output end Proof % 0.72/1.02 % cvc5 exiting %------------------------------------------------------------------------------