%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : ITP001^5 : TPTP v9.2.1. Bugfixed v7.5.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n021.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 08:24:20 AM UTC 2026 % Result : Theorem 0.37s 0.60s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ITP001^5 : TPTP v9.2.1. Bugfixed v7.5.0. % 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 : n021.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 03:34:19 EDT 2026 % 0.17/0.34 % CPUTime : % 0.31/0.50 %----Proving TH0 % 0.37/0.60 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.37/0.60 % SZS status Theorem % 0.37/0.60 % SZS output start Proof % 0.37/0.60 ( % 0.37/0.60 (declare-sort $$unsorted 0) % 0.37/0.60 (declare-sort tptp.tp__i 0) % 0.37/0.60 (declare-sort tptp.del 0) % 0.37/0.60 (declare-const tptp.ind tptp.del) % 0.37/0.60 (declare-const tptp.surj__i (-> $$unsorted tptp.tp__i)) % 0.37/0.60 (declare-const tptp.inj__i (-> tptp.tp__i $$unsorted)) % 0.37/0.60 (declare-const tptp.c_2Ebool_2Eliteral__case (-> tptp.del tptp.del $$unsorted)) % 0.37/0.60 (declare-const tptp.ty_2Ebool_2Eitself (-> tptp.del tptp.del)) % 0.37/0.60 (declare-const tptp.c_2Ebool_2E_5C_2F $$unsorted) % 0.37/0.60 (declare-const tptp.c_2Ebool_2ETYPE__DEFINITION (-> tptp.del tptp.del $$unsorted)) % 0.37/0.60 (declare-const tptp.c_2Ebool_2Eitself__case (-> tptp.del tptp.del $$unsorted)) % 0.37/0.60 (declare-const tptp.c_2Emin_2E_40 (-> tptp.del $$unsorted)) % 0.37/0.60 (declare-const tptp.c_2Emin_2E_3D (-> tptp.del $$unsorted)) % 0.37/0.60 (declare-const tptp.c_2Ebool_2EARB (-> tptp.del $$unsorted)) % 0.37/0.60 (declare-const tptp.c_2Ebool_2E_3F (-> tptp.del $$unsorted)) % 0.37/0.60 (declare-const tptp.lam (-> tptp.del (-> $$unsorted $$unsorted) $$unsorted)) % 0.37/0.60 (declare-const tptp.ap (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.60 (declare-const tptp.c_2Emin_2E_3D_3D_3E $$unsorted) % 0.37/0.60 (declare-const tptp.c_2Ebool_2E_7E $$unsorted) % 0.37/0.60 (declare-const tptp.mem (-> $$unsorted tptp.del Bool)) % 0.37/0.60 (declare-const tptp.c_2Ebool_2Ethe__value (-> tptp.del $$unsorted)) % 0.37/0.60 (declare-const tptp.bool tptp.del) % 0.37/0.60 (declare-const tptp.p (-> $$unsorted Bool)) % 0.37/0.60 (declare-const tptp.c_2Ebool_2ELET (-> tptp.del tptp.del $$unsorted)) % 0.37/0.60 (declare-const tptp.c_2Ebool_2E_3F_21 (-> tptp.del $$unsorted)) % 0.37/0.60 (declare-const tptp.c_2Ebool_2ERES__EXISTS (-> tptp.del $$unsorted)) % 0.37/0.60 (declare-const tptp.c_2Ebool_2E_21 (-> tptp.del $$unsorted)) % 0.37/0.60 (declare-const tptp.c_2Ebool_2EBOUNDED $$unsorted) % 0.37/0.60 (declare-const tptp.c_2Ebool_2ECOND (-> tptp.del $$unsorted)) % 0.37/0.60 (declare-const tptp.c_2Ebool_2E_2F_5C $$unsorted) % 0.37/0.60 (declare-const tptp.c_2Ebool_2EIN (-> tptp.del $$unsorted)) % 0.37/0.60 (declare-const tptp.c_2Ebool_2EONE__ONE (-> tptp.del tptp.del $$unsorted)) % 0.37/0.60 (declare-const tptp.c_2Ebool_2EONTO (-> tptp.del tptp.del $$unsorted)) % 0.37/0.60 (declare-const tptp.c_2Ebool_2EF $$unsorted) % 0.37/0.60 (declare-const tptp.c_2Ebool_2ERES__SELECT (-> tptp.del $$unsorted)) % 0.37/0.60 (declare-const tptp.c_2Ebool_2ERES__ABSTRACT (-> tptp.del tptp.del $$unsorted)) % 0.37/0.60 (declare-const tptp.inj__o (-> Bool $$unsorted)) % 0.37/0.60 (declare-const tptp.c_2Ebool_2ET $$unsorted) % 0.37/0.60 (declare-const tptp.c_2Ebool_2ERES__EXISTS__UNIQUE (-> tptp.del $$unsorted)) % 0.37/0.60 (declare-const tptp.c_2Ebool_2EDATATYPE (-> tptp.del $$unsorted)) % 0.37/0.60 (declare-const tptp.arr (-> tptp.del tptp.del tptp.del)) % 0.37/0.60 (declare-const tptp.c_2Ebool_2ERES__FORALL (-> tptp.del $$unsorted)) % 0.37/0.60 (define @t1 () (@var "X" Bool)) % 0.37/0.60 (define @t2 () (_ tptp.inj__o @t1)) % 0.37/0.60 (define @t3 () (@list @t1)) % 0.37/0.60 (define @t4 () (@var "X" $$unsorted)) % 0.37/0.60 (define @t5 () (_ tptp.mem @t4)) % 0.37/0.60 (define @t6 () (@list @t4)) % 0.37/0.60 (define @t7 () (@var "B" tptp.del)) % 0.37/0.60 (define @t8 () (@var "F" $$unsorted)) % 0.37/0.60 (define @t9 () (_ (_ tptp.ap @t8) @t4)) % 0.37/0.60 (define @t10 () (@var "A" tptp.del)) % 0.37/0.60 (define @t11 () (_ @t5 @t10)) % 0.37/0.60 (define @t12 () (_ tptp.arr @t10)) % 0.37/0.60 (define @t13 () (_ @t12 @t7)) % 0.37/0.60 (define @t14 () (_ (_ tptp.mem @t8) @t13)) % 0.37/0.60 (define @t15 () (@list @t10 @t7 @t8)) % 0.37/0.60 (define @t16 () (@var "F" (-> $$unsorted $$unsorted))) % 0.37/0.60 (define @t17 () (_ (_ tptp.lam @t10) @t16)) % 0.37/0.60 (define @t18 () (_ @t16 @t4)) % 0.37/0.60 (define @t19 () (@var "G" $$unsorted)) % 0.37/0.60 (define @t20 () (@var "A_27a" tptp.del)) % 0.37/0.60 (define @t21 () (_ tptp.arr @t20)) % 0.37/0.60 (define @t22 () (_ @t21 tptp.bool)) % 0.37/0.60 (define @t23 () (_ tptp.c_2Emin_2E_3D @t20)) % 0.37/0.60 (define @t24 () (@list @t20)) % 0.37/0.60 (define @t25 () (@var "Y" $$unsorted)) % 0.37/0.60 (define @t26 () (_ tptp.arr tptp.bool)) % 0.37/0.60 (define @t27 () (_ @t26 tptp.bool)) % 0.37/0.60 (define @t28 () (_ @t26 @t27)) % 0.37/0.60 (define @t29 () (@var "R" $$unsorted)) % 0.37/0.60 (define @t30 () (_ tptp.p @t29)) % 0.37/0.60 (define @t31 () (@var "Q" $$unsorted)) % 0.37/0.60 (define @t32 () (_ tptp.p @t31)) % 0.37/0.60 (define @t33 () (_ tptp.ap tptp.c_2Emin_2E_3D_3D_3E)) % 0.37/0.60 (define @t34 () (_ (_ tptp.mem @t29) tptp.bool)) % 0.37/0.60 (define @t35 () (@list @t29)) % 0.37/0.60 (define @t36 () (_ tptp.mem @t31)) % 0.37/0.60 (define @t37 () (_ @t36 tptp.bool)) % 0.37/0.60 (define @t38 () (@list @t31)) % 0.37/0.60 (define @t39 () (_ tptp.arr @t22)) % 0.37/0.60 (define @t40 () (_ @t39 @t20)) % 0.37/0.60 (define @t41 () (_ tptp.c_2Emin_2E_40 @t20)) % 0.37/0.60 (define @t42 () (_ @t39 tptp.bool)) % 0.37/0.60 (define @t43 () (_ tptp.c_2Ebool_2E_21 @t20)) % 0.37/0.60 (define @t44 () (_ tptp.p (_ (_ tptp.ap @t31) @t4))) % 0.37/0.60 (define @t45 () (_ @t36 (_ @t12 tptp.bool))) % 0.37/0.60 (define @t46 () (@list @t10 @t31)) % 0.37/0.60 (define @t47 () (_ tptp.ap tptp.c_2Ebool_2E_2F_5C)) % 0.37/0.60 (define @t48 () (_ tptp.c_2Ebool_2E_3F @t20)) % 0.37/0.60 (define @t49 () (_ tptp.c_2Ebool_2E_3F_21 @t20)) % 0.37/0.60 (define @t50 () (_ tptp.c_2Ebool_2ECOND @t20)) % 0.37/0.60 (define @t51 () (_ tptp.c_2Ebool_2EDATATYPE @t20)) % 0.37/0.60 (define @t52 () (_ tptp.c_2Ebool_2EIN @t20)) % 0.37/0.60 (define @t53 () (@var "A_27b" tptp.del)) % 0.37/0.60 (define @t54 () (_ @t21 @t53)) % 0.37/0.60 (define @t55 () (_ tptp.arr @t54)) % 0.37/0.60 (define @t56 () (_ @t55 @t54)) % 0.37/0.60 (define @t57 () (_ (_ tptp.c_2Ebool_2ELET @t20) @t53)) % 0.37/0.60 (define @t58 () (@list @t20 @t53)) % 0.37/0.60 (define @t59 () (_ @t55 tptp.bool)) % 0.37/0.60 (define @t60 () (_ (_ tptp.c_2Ebool_2EONE__ONE @t20) @t53)) % 0.37/0.60 (define @t61 () (_ (_ tptp.c_2Ebool_2EONTO @t20) @t53)) % 0.37/0.60 (define @t62 () (_ @t39 @t42)) % 0.37/0.60 (define @t63 () (_ tptp.c_2Ebool_2ERES__EXISTS @t20)) % 0.37/0.60 (define @t64 () (_ tptp.c_2Ebool_2ERES__EXISTS__UNIQUE @t20)) % 0.37/0.60 (define @t65 () (_ tptp.c_2Ebool_2ERES__FORALL @t20)) % 0.37/0.60 (define @t66 () (_ tptp.c_2Ebool_2ERES__SELECT @t20)) % 0.37/0.60 (define @t67 () (_ tptp.arr @t53)) % 0.37/0.60 (define @t68 () (_ @t67 @t20)) % 0.37/0.60 (define @t69 () (_ (_ tptp.c_2Ebool_2ETYPE__DEFINITION @t20) @t53)) % 0.37/0.60 (define @t70 () (_ tptp.ty_2Ebool_2Eitself @t20)) % 0.37/0.60 (define @t71 () (_ (_ tptp.c_2Ebool_2Eliteral__case @t20) @t53)) % 0.37/0.60 (define @t72 () (@var "V1x" $$unsorted)) % 0.37/0.60 (define @t73 () (@list @t72)) % 0.37/0.60 (define @t74 () (_ tptp.lam tptp.bool)) % 0.37/0.60 (define @t75 () (@var "V0x" $$unsorted)) % 0.37/0.60 (define @t76 () (@list @t75)) % 0.37/0.60 (define @t77 () (_ tptp.lam @t20)) % 0.37/0.60 (define @t78 () (@var "V0P" $$unsorted)) % 0.37/0.60 (define @t79 () (@list @t78)) % 0.37/0.60 (define @t80 () (_ tptp.lam @t22)) % 0.37/0.60 (define @t81 () (_ tptp.ap @t41)) % 0.37/0.60 (define @t82 () (_ tptp.ap @t78)) % 0.37/0.60 (define @t83 () (_ @t82 (_ @t81 @t78))) % 0.37/0.60 (define @t84 () (@var "V2t" $$unsorted)) % 0.37/0.60 (define @t85 () (@var "V1t2" $$unsorted)) % 0.37/0.60 (define @t86 () (_ (_ tptp.ap (_ @t33 @t85)) @t84)) % 0.37/0.60 (define @t87 () (@var "V0t1" $$unsorted)) % 0.37/0.60 (define @t88 () (_ tptp.ap (_ @t33 @t87))) % 0.37/0.60 (define @t89 () (@list @t84)) % 0.37/0.60 (define @t90 () (_ tptp.ap (_ tptp.c_2Ebool_2E_21 tptp.bool))) % 0.37/0.60 (define @t91 () (@list @t85)) % 0.37/0.60 (define @t92 () (@list @t87)) % 0.37/0.60 (define @t93 () (@var "V0t" $$unsorted)) % 0.37/0.60 (define @t94 () (_ tptp.p @t93)) % 0.37/0.60 (define @t95 () (_ tptp.mem @t93)) % 0.37/0.60 (define @t96 () (_ @t95 tptp.bool)) % 0.37/0.60 (define @t97 () (@list @t93)) % 0.37/0.60 (define @t98 () (@var "V2y" $$unsorted)) % 0.37/0.60 (define @t99 () (_ tptp.ap @t23)) % 0.37/0.60 (define @t100 () (_ @t82 @t72)) % 0.37/0.60 (define @t101 () (_ tptp.ap @t43)) % 0.37/0.60 (define @t102 () (_ tptp.ap @t48)) % 0.37/0.60 (define @t103 () (@var "V0f" $$unsorted)) % 0.37/0.60 (define @t104 () (_ tptp.ap @t103)) % 0.37/0.60 (define @t105 () (@list @t103)) % 0.37/0.60 (define @t106 () (_ tptp.lam @t54)) % 0.37/0.60 (define @t107 () (_ @t106 (lambda @t105 (_ @t77 (lambda @t73 (_ @t104 @t72)))))) % 0.37/0.60 (define @t108 () (@var "V2t2" $$unsorted)) % 0.37/0.60 (define @t109 () (@var "V3x" $$unsorted)) % 0.37/0.60 (define @t110 () (_ tptp.ap (_ @t99 @t109))) % 0.37/0.60 (define @t111 () (_ tptp.ap (_ tptp.c_2Emin_2E_3D tptp.bool))) % 0.37/0.60 (define @t112 () (_ tptp.ap (_ @t111 @t93))) % 0.37/0.60 (define @t113 () (@var "V1t1" $$unsorted)) % 0.37/0.60 (define @t114 () (@list @t109)) % 0.37/0.60 (define @t115 () (@var "V2x2" $$unsorted)) % 0.37/0.60 (define @t116 () (@var "V1x1" $$unsorted)) % 0.37/0.60 (define @t117 () (_ tptp.ap (_ tptp.c_2Emin_2E_3D @t53))) % 0.37/0.60 (define @t118 () (@var "V2x" $$unsorted)) % 0.37/0.60 (define @t119 () (@var "V1y" $$unsorted)) % 0.37/0.60 (define @t120 () (@list @t118)) % 0.37/0.60 (define @t121 () (_ tptp.lam @t53)) % 0.37/0.60 (define @t122 () (_ tptp.ap (_ tptp.c_2Ebool_2E_21 @t53))) % 0.37/0.60 (define @t123 () (@var "V5x_27" $$unsorted)) % 0.37/0.60 (define @t124 () (@var "V1rep" $$unsorted)) % 0.37/0.60 (define @t125 () (_ tptp.ap @t124)) % 0.37/0.60 (define @t126 () (@var "V4x" $$unsorted)) % 0.37/0.60 (define @t127 () (@var "V3x_27_27" $$unsorted)) % 0.37/0.60 (define @t128 () (@var "V2x_27" $$unsorted)) % 0.37/0.60 (define @t129 () (@var "X" tptp.tp__i)) % 0.37/0.60 (define @t130 () (_ tptp.inj__i @t129)) % 0.37/0.60 (define @t131 () (@list @t129)) % 0.37/0.60 (define @t132 () (@var "V1f" $$unsorted)) % 0.37/0.60 (define @t133 () (@var "V1m" $$unsorted)) % 0.37/0.60 (define @t134 () (_ tptp.ap @t133)) % 0.37/0.60 (define @t135 () (_ @t134 @t118)) % 0.37/0.60 (define @t136 () (@var "V0p" $$unsorted)) % 0.37/0.60 (define @t137 () (_ (_ tptp.ap (_ (_ tptp.ap @t52) @t118)) @t136)) % 0.37/0.60 (define @t138 () (@list @t133)) % 0.37/0.60 (define @t139 () (@list @t136)) % 0.37/0.60 (define @t140 () (_ @t77 (lambda @t120 (_ (_ tptp.ap (_ @t47 @t137)) @t135)))) % 0.37/0.60 (define @t141 () (@var "V4y" $$unsorted)) % 0.37/0.60 (define @t142 () (_ tptp.ap (_ (_ tptp.ap @t65) @t136))) % 0.37/0.60 (define @t143 () (not true)) % 0.37/0.60 (assume @p1 (forall @t3 (= (_ tptp.p @t2) @t1))) % 0.37/0.60 (assume @p2 (forall @t3 (_ (_ tptp.mem @t2) tptp.bool))) % 0.37/0.60 (assume @p3 (forall @t6 (=> (_ @t5 tptp.bool) (= @t4 (_ tptp.inj__o (_ tptp.p @t4)))))) % 0.37/0.60 (assume @p4 (forall @t15 (=> @t14 (forall @t6 (=> @t11 (_ (_ tptp.mem @t9) @t7)))))) % 0.37/0.60 (assume @p5 (forall (@list @t10 @t7 @t16) (=> (forall @t6 (=> @t11 (_ (_ tptp.mem @t18) @t7))) (_ (_ tptp.mem @t17) @t13)))) % 0.37/0.60 (assume @p6 (forall @t15 (=> @t14 (forall (@list @t19) (=> (_ (_ tptp.mem @t19) @t13) (=> (forall @t6 (=> @t11 (= @t9 (_ (_ tptp.ap @t19) @t4)))) (= @t8 @t19))))))) % 0.37/0.60 (assume @p7 (forall (@list @t10 @t16 @t4) (=> @t11 (= (_ (_ tptp.ap @t17) @t4) @t18)))) % 0.37/0.60 (assume @p8 (forall @t24 (_ (_ tptp.mem @t23) (_ @t21 @t22)))) % 0.37/0.60 (assume @p9 (forall (@list @t10 @t4) (=> @t11 (forall (@list @t25) (=> (_ (_ tptp.mem @t25) @t10) (= (_ tptp.p (_ (_ tptp.ap (_ (_ tptp.ap (_ tptp.c_2Emin_2E_3D @t10)) @t4)) @t25)) (= @t4 @t25))))))) % 0.37/0.60 (assume @p10 (_ (_ tptp.mem tptp.c_2Emin_2E_3D_3D_3E) @t28)) % 0.37/0.60 (assume @p11 (forall @t38 (=> @t37 (forall @t35 (=> @t34 (= (_ tptp.p (_ (_ tptp.ap (_ @t33 @t31)) @t29)) (=> @t32 @t30))))))) % 0.37/0.60 (assume @p12 (forall @t24 (_ (_ tptp.mem @t41) @t40))) % 0.37/0.60 (assume @p13 (forall @t24 (_ (_ tptp.mem @t43) @t42))) % 0.37/0.60 (assume @p14 (forall @t46 (=> @t45 (= (_ tptp.p (_ (_ tptp.ap (_ tptp.c_2Ebool_2E_21 @t10)) @t31)) (forall @t6 (=> @t11 @t44)))))) % 0.37/0.60 (assume @p15 (_ (_ tptp.mem tptp.c_2Ebool_2E_2F_5C) @t28)) % 0.37/0.60 (assume @p16 (forall @t38 (=> @t37 (forall @t35 (=> @t34 (= (_ tptp.p (_ (_ tptp.ap (_ @t47 @t31)) @t29)) (and @t32 @t30))))))) % 0.37/0.60 (assume @p17 (forall @t24 (_ (_ tptp.mem @t48) @t42))) % 0.37/0.60 (assume @p18 (forall @t46 (=> @t45 (= (_ tptp.p (_ (_ tptp.ap (_ tptp.c_2Ebool_2E_3F @t10)) @t31)) (exists @t6 (and @t11 @t44)))))) % 0.37/0.60 (assume @p19 (forall @t24 (_ (_ tptp.mem @t49) @t42))) % 0.37/0.60 (assume @p20 (forall @t24 (_ (_ tptp.mem (_ tptp.c_2Ebool_2EARB @t20)) @t20))) % 0.37/0.60 (assume @p21 (_ (_ tptp.mem tptp.c_2Ebool_2EBOUNDED) @t27)) % 0.37/0.60 (assume @p22 (forall @t24 (_ (_ tptp.mem @t50) (_ @t26 (_ @t21 (_ @t21 @t20)))))) % 0.37/0.60 (assume @p23 (forall @t24 (_ (_ tptp.mem @t51) @t22))) % 0.37/0.60 (assume @p24 (_ (_ tptp.mem tptp.c_2Ebool_2EF) tptp.bool)) % 0.37/0.60 (assume @p25 (not (_ tptp.p tptp.c_2Ebool_2EF))) % 0.37/0.60 (assume @p26 (forall @t24 (_ (_ tptp.mem @t52) (_ @t21 @t42)))) % 0.37/0.60 (assume @p27 (forall @t58 (_ (_ tptp.mem @t57) @t56))) % 0.37/0.60 (assume @p28 (forall @t58 (_ (_ tptp.mem @t60) @t59))) % 0.37/0.60 (assume @p29 (forall @t58 (_ (_ tptp.mem @t61) @t59))) % 0.37/0.60 (assume @p30 (forall @t58 (_ (_ tptp.mem (_ (_ tptp.c_2Ebool_2ERES__ABSTRACT @t20) @t53)) (_ @t39 @t56)))) % 0.37/0.60 (assume @p31 (forall @t24 (_ (_ tptp.mem @t63) @t62))) % 0.37/0.60 (assume @p32 (forall @t24 (_ (_ tptp.mem @t64) @t62))) % 0.37/0.60 (assume @p33 (forall @t24 (_ (_ tptp.mem @t65) @t62))) % 0.37/0.60 (assume @p34 (forall @t24 (_ (_ tptp.mem @t66) (_ @t39 @t40)))) % 0.37/0.60 (assume @p35 (_ (_ tptp.mem tptp.c_2Ebool_2ET) tptp.bool)) % 0.37/0.60 (assume @p36 (_ tptp.p tptp.c_2Ebool_2ET)) % 0.37/0.60 (assume @p37 (forall @t58 (_ (_ tptp.mem @t69) (_ @t39 (_ (_ tptp.arr @t68) tptp.bool))))) % 0.37/0.60 (assume @p38 (_ (_ tptp.mem tptp.c_2Ebool_2E_5C_2F) @t28)) % 0.37/0.60 (assume @p39 (forall @t38 (=> @t37 (forall @t35 (=> @t34 (= (_ tptp.p (_ (_ tptp.ap (_ (_ tptp.ap tptp.c_2Ebool_2E_5C_2F) @t31)) @t29)) (or @t32 @t30))))))) % 0.37/0.60 (assume @p40 (forall @t58 (_ (_ tptp.mem (_ (_ tptp.c_2Ebool_2Eitself__case @t20) @t53)) (_ (_ tptp.arr @t70) (_ @t67 @t53))))) % 0.37/0.60 (assume @p41 (forall @t58 (_ (_ tptp.mem @t71) @t56))) % 0.37/0.60 (assume @p42 (forall @t24 (_ (_ tptp.mem (_ tptp.c_2Ebool_2Ethe__value @t20)) @t70))) % 0.37/0.60 (assume @p43 (_ (_ tptp.mem tptp.c_2Ebool_2E_7E) @t27)) % 0.37/0.60 (assume @p44 (forall @t38 (=> @t37 (= (_ tptp.p (_ (_ tptp.ap tptp.c_2Ebool_2E_7E) @t31)) (not @t32))))) % 0.37/0.60 (assume @p45 (= true (= (_ @t74 (lambda @t76 @t75)) (_ @t74 (lambda @t73 @t72))))) % 0.37/0.60 (assume @p46 (forall @t24 (= @t43 (_ @t80 (lambda @t79 (_ (_ tptp.ap (_ (_ tptp.ap (_ tptp.c_2Emin_2E_3D @t22)) @t78)) (_ @t77 (lambda @t73 tptp.c_2Ebool_2ET)))))))) % 0.37/0.60 (assume @p47 (forall @t24 (= @t48 (_ @t80 (lambda @t79 @t83))))) % 0.37/0.60 (assume @p48 (= tptp.c_2Ebool_2E_2F_5C (_ @t74 (lambda @t92 (_ @t74 (lambda @t91 (_ @t90 (_ @t74 (lambda @t89 (_ (_ tptp.ap (_ @t33 (_ @t88 @t86))) @t84)))))))))) % 0.37/0.60 (assume @p49 (= tptp.c_2Ebool_2E_5C_2F (_ @t74 (lambda @t92 (_ @t74 (lambda @t91 (_ @t90 (_ @t74 (lambda @t89 (_ (_ tptp.ap (_ @t33 (_ @t88 @t84))) (_ (_ tptp.ap (_ @t33 @t86)) @t84))))))))))) % 0.37/0.60 (assume @p50 (= false (forall @t97 (=> @t96 @t94)))) % 0.37/0.60 (assume @p51 (= tptp.c_2Ebool_2E_7E (_ @t74 (lambda @t97 (_ (_ tptp.ap (_ @t33 @t93)) tptp.c_2Ebool_2EF))))) % 0.37/0.60 (assume @p52 (forall @t24 (= @t49 (_ @t80 (lambda @t79 (_ (_ tptp.ap (_ @t47 (_ @t102 @t78))) (_ @t101 (_ @t77 (lambda @t73 (_ @t101 (_ @t77 (lambda (@list @t98) (_ (_ tptp.ap (_ @t33 (_ (_ tptp.ap (_ @t47 @t100)) (_ @t82 @t98)))) (_ (_ tptp.ap (_ @t99 @t72)) @t98)))))))))))))) % 0.37/0.60 (assume @p53 (forall @t58 (= @t57 @t107))) % 0.37/0.60 (assume @p54 (forall @t24 (= @t50 (_ @t74 (lambda @t97 (_ @t77 (lambda (@list @t113) (_ @t77 (lambda (@list @t108) (_ @t81 (_ @t77 (lambda @t114 (_ (_ tptp.ap (_ @t47 (_ (_ tptp.ap (_ @t33 (_ @t112 tptp.c_2Ebool_2ET))) (_ @t110 @t113)))) (_ (_ tptp.ap (_ @t33 (_ @t112 tptp.c_2Ebool_2EF))) (_ @t110 @t108))))))))))))))) % 0.37/0.60 (assume @p55 (forall @t58 (= @t60 (_ @t106 (lambda @t105 (_ @t101 (_ @t77 (lambda (@list @t116) (_ @t101 (_ @t77 (lambda (@list @t115) (_ (_ tptp.ap (_ @t33 (_ (_ tptp.ap (_ @t117 (_ @t104 @t116))) (_ @t104 @t115)))) (_ (_ tptp.ap (_ @t99 @t116)) @t115))))))))))))) % 0.37/0.60 (assume @p56 (forall @t58 (= @t61 (_ @t106 (lambda @t105 (_ @t122 (_ @t121 (lambda (@list @t119) (_ @t102 (_ @t77 (lambda @t120 (_ (_ tptp.ap (_ @t117 @t119)) (_ @t104 @t118))))))))))))) % 0.37/0.60 (assume @p57 (forall @t58 (= @t69 (_ @t80 (lambda @t79 (_ (_ tptp.lam @t68) (lambda (@list @t124) (_ (_ tptp.ap (_ @t47 (_ @t122 (_ @t121 (lambda (@list @t128) (_ @t122 (_ @t121 (lambda (@list @t127) (_ (_ tptp.ap (_ @t33 (_ (_ tptp.ap (_ @t99 (_ @t125 @t128))) (_ @t125 @t127)))) (_ (_ tptp.ap (_ @t117 @t128)) @t127)))))))))) (_ @t101 (_ @t77 (lambda (@list @t126) (_ (_ tptp.ap (_ @t111 (_ @t82 @t126))) (_ (_ tptp.ap (_ tptp.c_2Ebool_2E_3F @t53)) (_ @t121 (lambda (@list @t123) (_ (_ tptp.ap (_ @t99 @t126)) (_ @t125 @t123))))))))))))))))) % 0.37/0.60 (assume @p58 (forall @t97 (=> @t96 (or (= @t94 true) (= @t94 false))))) % 0.37/0.60 (assume @p59 (forall (@list @t20 @t53 @t93) (=> (_ @t95 @t54) (= (_ @t77 (lambda @t73 (_ (_ tptp.ap @t93) @t72))) @t93)))) % 0.37/0.60 (assume @p60 (forall (@list @t20 @t78) (=> (_ (_ tptp.mem @t78) @t22) (forall @t73 (=> (_ (_ tptp.mem @t72) @t20) (=> (_ tptp.p @t100) (_ tptp.p @t83))))))) % 0.37/0.60 (assume @p61 (forall @t131 (= (_ tptp.surj__i @t130) @t129))) % 0.37/0.60 (assume @p62 (forall @t131 (_ (_ tptp.mem @t130) tptp.ind))) % 0.37/0.60 (assume @p63 (forall @t6 (=> (_ @t5 tptp.ind) (= @t4 (_ tptp.inj__i (_ tptp.surj__i @t4)))))) % 0.37/0.60 (assume @p64 (exists @t105 (and (_ (_ tptp.mem @t103) (_ (_ tptp.arr tptp.ind) tptp.ind)) (_ tptp.p (_ (_ tptp.ap (_ (_ tptp.c_2Ebool_2EONE__ONE tptp.ind) tptp.ind)) @t103)) (not (_ tptp.p (_ (_ tptp.ap (_ (_ tptp.c_2Ebool_2EONTO tptp.ind) tptp.ind)) @t103)))))) % 0.37/0.60 (assume @p65 (forall @t58 (= @t71 @t107))) % 0.37/0.60 (assume @p66 (forall @t24 (= @t52 (_ @t77 (lambda @t76 (_ @t80 (lambda (@list @t132) (_ (_ tptp.ap @t132) @t75)))))))) % 0.37/0.60 (assume @p67 (forall @t24 (= @t65 (_ @t80 (lambda @t139 (_ @t80 (lambda @t138 (_ @t101 (_ @t77 (lambda @t120 (_ (_ tptp.ap (_ @t33 @t137)) @t135))))))))))) % 0.37/0.60 (assume @p68 (forall @t24 (= @t63 (_ @t80 (lambda @t139 (_ @t80 (lambda @t138 (_ @t102 @t140)))))))) % 0.37/0.60 (assume @p69 (forall @t24 (= @t64 (_ @t80 (lambda @t139 (_ @t80 (lambda @t138 (_ (_ tptp.ap (_ @t47 (_ (_ tptp.ap (_ (_ tptp.ap @t63) @t136)) (_ @t77 (lambda @t120 @t135))))) (_ @t142 (_ @t77 (lambda @t114 (_ @t142 (_ @t77 (lambda (@list @t141) (_ (_ tptp.ap (_ @t33 (_ (_ tptp.ap (_ @t47 (_ @t134 @t109))) (_ @t134 @t141)))) (_ @t110 @t141)))))))))))))))) % 0.37/0.60 (assume @p70 (forall @t24 (= @t66 (_ @t80 (lambda @t139 (_ @t80 (lambda @t138 (_ @t81 @t140)))))))) % 0.37/0.60 (assume @p71 (= tptp.c_2Ebool_2EBOUNDED (_ @t74 (lambda (@list (@var "V0v" $$unsorted)) tptp.c_2Ebool_2ET)))) % 0.37/0.60 (assume @p72 (forall @t24 (= @t51 (_ @t77 (lambda @t76 tptp.c_2Ebool_2ET))))) % 0.37/0.60 (assume @p73 @t143) % 0.37/0.60 (assume @p74 true) % 0.37/0.60 (step @p75 :rule evaluate :args (@t143)) % 0.37/0.60 (step @p76 false :rule eq_resolve :premises (@p73 @p75)) % 0.37/0.60 ) % 0.37/0.60 % SZS output end Proof % 0.37/0.60 % cvc5 exiting %------------------------------------------------------------------------------