%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWW473+5 : TPTP v9.2.1. Released v5.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n029.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 09:05:04 AM UTC 2026 % Result : Theorem 0.39s 1.02s % Output : Proof 0.83s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWW473+5 : TPTP v9.2.1. Released v5.3.0. % 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 : n029.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 22:08:47 EDT 2026 % 0.16/0.35 % CPUTime : % 0.37/0.56 %----Proving TF0_NAR, FOF, or CNF % 0.39/1.02 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.39/1.02 % SZS status Theorem % 0.39/1.02 % SZS output start Proof % 0.39/1.02 ( % 0.39/1.02 (declare-sort $$unsorted 0) % 0.39/1.02 (declare-const tptp.order (-> $$unsorted Bool)) % 0.39/1.02 (declare-const tptp.finite_finite_1 (-> $$unsorted Bool)) % 0.39/1.02 (declare-const tptp.pn $$unsorted) % 0.39/1.02 (declare-const tptp.na $$unsorted) % 0.39/1.02 (declare-const tptp.pname $$unsorted) % 0.39/1.02 (declare-const tptp.u $$unsorted) % 0.39/1.02 (declare-const tptp.fun (-> $$unsorted $$unsorted $$unsorted)) % 0.39/1.02 (declare-const tptp.minus_minus (-> $$unsorted $$unsorted)) % 0.39/1.02 (declare-const tptp.mgt_call $$unsorted) % 0.39/1.02 (declare-const tptp.finite_finite (-> $$unsorted $$unsorted)) % 0.39/1.02 (declare-const tptp.p $$unsorted) % 0.39/1.02 (declare-const tptp.bool $$unsorted) % 0.39/1.02 (declare-const tptp.suc $$unsorted) % 0.39/1.02 (declare-const tptp.combi (-> $$unsorted $$unsorted)) % 0.39/1.02 (declare-const tptp.fequal (-> $$unsorted $$unsorted)) % 0.39/1.02 (declare-const tptp.combc (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.39/1.02 (declare-const tptp.combs (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.39/1.02 (declare-const tptp.finite_card (-> $$unsorted $$unsorted)) % 0.39/1.02 (declare-const tptp.ti (-> $$unsorted $$unsorted $$unsorted)) % 0.39/1.02 (declare-const tptp.g $$unsorted) % 0.39/1.02 (declare-const tptp.nat $$unsorted) % 0.39/1.02 (declare-const tptp.combb (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.39/1.02 (declare-const tptp.x_a $$unsorted) % 0.39/1.02 (declare-const tptp.ord_less_eq (-> $$unsorted $$unsorted)) % 0.39/1.02 (declare-const tptp.fNot $$unsorted) % 0.39/1.02 (declare-const tptp.preorder (-> $$unsorted Bool)) % 0.39/1.02 (declare-const tptp.collect (-> $$unsorted $$unsorted)) % 0.39/1.02 (declare-const tptp.image (-> $$unsorted $$unsorted $$unsorted)) % 0.39/1.02 (declare-const tptp.member (-> $$unsorted $$unsorted)) % 0.39/1.02 (declare-const tptp.insert (-> $$unsorted $$unsorted)) % 0.39/1.02 (declare-const tptp.fconj $$unsorted) % 0.39/1.02 (declare-const tptp.fdisj $$unsorted) % 0.39/1.02 (declare-const tptp.hBOOL (-> $$unsorted Bool)) % 0.39/1.02 (declare-const tptp.fimplies $$unsorted) % 0.39/1.02 (declare-const tptp.undefined (-> $$unsorted $$unsorted)) % 0.39/1.02 (declare-const tptp.hAPP (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.39/1.02 (define @t1 () (@var "X_a" $$unsorted)) % 0.39/1.02 (define @t2 () (@var "X_c" $$unsorted)) % 0.39/1.02 (define @t3 () (@var "X_b" $$unsorted)) % 0.39/1.02 (define @t4 () (tptp.combb @t3 @t2 @t1)) % 0.39/1.02 (define @t5 () (tptp.fun @t1 @t2)) % 0.39/1.02 (define @t6 () (tptp.fun @t1 @t3)) % 0.39/1.02 (define @t7 () (tptp.fun @t6 @t5)) % 0.39/1.02 (define @t8 () (tptp.fun @t3 @t2)) % 0.39/1.02 (define @t9 () (tptp.combc @t1 @t3 @t2)) % 0.39/1.02 (define @t10 () (tptp.fun @t3 @t5)) % 0.39/1.02 (define @t11 () (tptp.fun @t1 @t8)) % 0.39/1.02 (define @t12 () (@list @t1 @t3 @t2)) % 0.39/1.02 (define @t13 () (tptp.combi @t1)) % 0.39/1.02 (define @t14 () (@list @t1)) % 0.39/1.02 (define @t15 () (tptp.combs @t1 @t3 @t2)) % 0.39/1.02 (define @t16 () (tptp.finite_card @t2)) % 0.39/1.02 (define @t17 () (tptp.fun @t2 tptp.bool)) % 0.39/1.02 (define @t18 () (tptp.finite_finite @t3)) % 0.39/1.02 (define @t19 () (tptp.fun @t3 tptp.bool)) % 0.39/1.02 (define @t20 () (tptp.fun @t19 tptp.bool)) % 0.39/1.02 (define @t21 () (@list @t3)) % 0.39/1.02 (define @t22 () (tptp.minus_minus tptp.nat)) % 0.39/1.02 (define @t23 () (tptp.fun tptp.nat tptp.nat)) % 0.39/1.02 (define @t24 () (tptp.undefined @t1)) % 0.39/1.02 (define @t25 () (tptp.ord_less_eq @t1)) % 0.39/1.02 (define @t26 () (tptp.fun @t1 tptp.bool)) % 0.39/1.02 (define @t27 () (tptp.fun @t1 @t26)) % 0.39/1.02 (define @t28 () (tptp.preorder @t1)) % 0.39/1.02 (define @t29 () (tptp.collect @t3)) % 0.39/1.02 (define @t30 () (tptp.fun @t19 @t19)) % 0.39/1.02 (define @t31 () (tptp.image @t3 @t2)) % 0.39/1.02 (define @t32 () (tptp.fun @t19 @t17)) % 0.39/1.02 (define @t33 () (tptp.insert @t3)) % 0.39/1.02 (define @t34 () (tptp.fun tptp.bool tptp.bool)) % 0.39/1.02 (define @t35 () (tptp.fun tptp.bool @t34)) % 0.39/1.02 (define @t36 () (tptp.fequal @t1)) % 0.39/1.02 (define @t37 () (@var "B_2" $$unsorted)) % 0.39/1.02 (define @t38 () (@var "B_1_1" $$unsorted)) % 0.39/1.02 (define @t39 () (tptp.hAPP @t1 @t2 @t38 @t37)) % 0.39/1.02 (define @t40 () (@list @t1 @t2 @t38 @t37)) % 0.39/1.02 (define @t41 () (tptp.member @t3)) % 0.39/1.02 (define @t42 () (tptp.fun @t3 @t20)) % 0.39/1.02 (define @t43 () (tptp.fun tptp.x_a tptp.bool)) % 0.39/1.02 (define @t44 () (tptp.fun @t43 tptp.bool)) % 0.39/1.02 (define @t45 () (tptp.fun tptp.pname tptp.bool)) % 0.39/1.02 (define @t46 () (tptp.fun tptp.pname tptp.x_a)) % 0.39/1.02 (define @t47 () (@var "Ts" $$unsorted)) % 0.39/1.02 (define @t48 () (@var "G_1" $$unsorted)) % 0.39/1.02 (define @t49 () (tptp.ord_less_eq @t43)) % 0.39/1.02 (define @t50 () (@var "A_1" $$unsorted)) % 0.39/1.02 (define @t51 () (tptp.ord_less_eq @t19)) % 0.39/1.02 (define @t52 () (tptp.fun @t19 @t20)) % 0.39/1.02 (define @t53 () (tptp.hBOOL (tptp.hAPP @t19 tptp.bool @t18 @t50))) % 0.39/1.02 (define @t54 () (@list @t3 @t50)) % 0.39/1.02 (define @t55 () (@var "F_1" $$unsorted)) % 0.39/1.02 (define @t56 () (@var "H" $$unsorted)) % 0.39/1.02 (define @t57 () (tptp.finite_finite @t2)) % 0.39/1.02 (define @t58 () (@var "A_2" $$unsorted)) % 0.39/1.02 (define @t59 () (tptp.hAPP @t3 @t30 @t33 @t58)) % 0.39/1.02 (define @t60 () (tptp.hAPP @t19 @t19 @t59 @t50)) % 0.39/1.02 (define @t61 () (tptp.hBOOL (tptp.hAPP @t19 tptp.bool @t18 @t60))) % 0.39/1.02 (define @t62 () (@list @t3 @t58 @t50)) % 0.39/1.02 (define @t63 () (tptp.finite_card @t3)) % 0.39/1.02 (define @t64 () (tptp.hAPP @t19 tptp.nat @t63 @t50)) % 0.39/1.02 (define @t65 () (@var "F" $$unsorted)) % 0.39/1.02 (define @t66 () (tptp.hAPP @t8 @t32 @t31 @t65)) % 0.39/1.02 (define @t67 () (tptp.hAPP @t19 @t17 @t66 @t50)) % 0.39/1.02 (define @t68 () (tptp.ord_less_eq tptp.nat)) % 0.39/1.02 (define @t69 () (tptp.fun tptp.nat tptp.bool)) % 0.39/1.02 (define @t70 () (@list @t2 @t3 @t65 @t50)) % 0.39/1.02 (define @t71 () (@var "B" $$unsorted)) % 0.39/1.02 (define @t72 () (tptp.hAPP @t19 tptp.nat @t63 @t71)) % 0.39/1.02 (define @t73 () (tptp.hAPP tptp.nat @t69 @t68 @t64)) % 0.39/1.02 (define @t74 () (tptp.hAPP @t19 @t20 @t51 @t50)) % 0.39/1.02 (define @t75 () (tptp.hBOOL (tptp.hAPP @t19 tptp.bool @t74 @t71))) % 0.39/1.02 (define @t76 () (tptp.hBOOL (tptp.hAPP @t19 tptp.bool @t18 @t71))) % 0.39/1.02 (define @t77 () (@list @t3 @t50 @t71)) % 0.39/1.02 (define @t78 () (tptp.ti @t19 @t71)) % 0.39/1.02 (define @t79 () (tptp.ti @t19 @t50)) % 0.39/1.02 (define @t80 () (= @t79 @t78)) % 0.39/1.02 (define @t81 () (@var "X_2" $$unsorted)) % 0.39/1.02 (define @t82 () (tptp.hAPP @t3 @t30 @t33 @t81)) % 0.39/1.02 (define @t83 () (tptp.hAPP @t19 @t19 @t82 @t50)) % 0.39/1.02 (define @t84 () (tptp.hAPP @t19 tptp.nat @t63 @t83)) % 0.39/1.02 (define @t85 () (@list @t3 @t81 @t50)) % 0.39/1.02 (define @t86 () (tptp.hAPP @t3 @t20 @t41 @t81)) % 0.39/1.02 (define @t87 () (tptp.hBOOL (tptp.hAPP @t19 tptp.bool @t86 @t50))) % 0.39/1.02 (define @t88 () (not @t87)) % 0.39/1.02 (define @t89 () (=> @t88 (= @t84 (tptp.hAPP tptp.nat tptp.nat tptp.suc @t64)))) % 0.39/1.02 (define @t90 () (@var "Q_1" $$unsorted)) % 0.39/1.02 (define @t91 () (@var "Pa" $$unsorted)) % 0.39/1.02 (define @t92 () (tptp.combb tptp.bool @t34 @t3)) % 0.39/1.02 (define @t93 () (tptp.fun @t3 @t34)) % 0.39/1.02 (define @t94 () (tptp.fun @t19 @t93)) % 0.39/1.02 (define @t95 () (tptp.hAPP @t35 @t94 @t92 tptp.fconj)) % 0.39/1.02 (define @t96 () (tptp.combs @t3 tptp.bool tptp.bool)) % 0.39/1.02 (define @t97 () (tptp.hBOOL (tptp.hAPP @t19 tptp.bool @t18 (tptp.hAPP @t19 @t19 @t29 @t90)))) % 0.39/1.02 (define @t98 () (tptp.hAPP @t19 @t19 @t29 @t91)) % 0.39/1.02 (define @t99 () (tptp.hBOOL (tptp.hAPP @t19 tptp.bool @t18 @t98))) % 0.39/1.02 (define @t100 () (@var "N_1" $$unsorted)) % 0.39/1.02 (define @t101 () (@var "M_2" $$unsorted)) % 0.39/1.02 (define @t102 () (tptp.hAPP tptp.nat @t23 @t22 @t101)) % 0.39/1.02 (define @t103 () (tptp.hAPP tptp.nat tptp.nat @t102 @t100)) % 0.39/1.02 (define @t104 () (tptp.hAPP tptp.nat tptp.nat tptp.suc @t101)) % 0.39/1.02 (define @t105 () (tptp.hAPP tptp.nat @t23 @t22 @t104)) % 0.39/1.02 (define @t106 () (tptp.hAPP tptp.nat tptp.nat @t105 @t100)) % 0.39/1.02 (define @t107 () (tptp.hAPP tptp.nat @t69 @t68 @t100)) % 0.39/1.02 (define @t108 () (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool @t107 @t101))) % 0.39/1.02 (define @t109 () (@var "K" $$unsorted)) % 0.39/1.02 (define @t110 () (tptp.fun tptp.nat @t69)) % 0.39/1.02 (define @t111 () (tptp.hAPP @t110 @t110 (tptp.combc tptp.nat tptp.nat tptp.bool) @t68)) % 0.39/1.02 (define @t112 () (tptp.collect tptp.nat)) % 0.39/1.02 (define @t113 () (tptp.finite_finite tptp.nat)) % 0.39/1.02 (define @t114 () (@var "Na" $$unsorted)) % 0.39/1.02 (define @t115 () (tptp.hAPP tptp.nat tptp.nat tptp.suc @t114)) % 0.39/1.02 (define @t116 () (@var "Y" $$unsorted)) % 0.39/1.02 (define @t117 () (@var "X" $$unsorted)) % 0.39/1.02 (define @t118 () (@var "Nat" $$unsorted)) % 0.39/1.02 (define @t119 () (@var "Nat_1" $$unsorted)) % 0.39/1.02 (define @t120 () (tptp.hAPP tptp.nat tptp.nat tptp.suc @t100)) % 0.39/1.02 (define @t121 () (@list @t100)) % 0.39/1.02 (define @t122 () (= @t101 @t100)) % 0.39/1.02 (define @t123 () (tptp.hAPP tptp.nat @t69 @t68 @t101)) % 0.39/1.02 (define @t124 () (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool @t123 @t100))) % 0.39/1.02 (define @t125 () (@list @t101 @t100)) % 0.39/1.02 (define @t126 () (@var "K_1" $$unsorted)) % 0.39/1.02 (define @t127 () (@var "I_1" $$unsorted)) % 0.39/1.02 (define @t128 () (tptp.hAPP tptp.nat @t69 @t68 @t127)) % 0.39/1.02 (define @t129 () (@var "J" $$unsorted)) % 0.39/1.02 (define @t130 () (tptp.hAPP tptp.nat @t23 @t22 @t127)) % 0.39/1.02 (define @t131 () (tptp.hAPP @t35 @t94 @t92 tptp.fdisj)) % 0.39/1.02 (define @t132 () (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool @t123 @t120))) % 0.39/1.02 (define @t133 () (@var "M_3" $$unsorted)) % 0.39/1.02 (define @t134 () (tptp.hAPP tptp.nat @t69 @t68 @t114)) % 0.39/1.02 (define @t135 () (tptp.hAPP tptp.nat @t69 @t68 @t115)) % 0.39/1.02 (define @t136 () (tptp.hAPP tptp.nat @t69 @t68 @t133)) % 0.39/1.02 (define @t137 () (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool @t136 @t114))) % 0.39/1.02 (define @t138 () (@list @t133 @t114)) % 0.39/1.02 (define @t139 () (tptp.hAPP tptp.nat @t69 @t68 @t120)) % 0.39/1.02 (define @t140 () (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat @t23 @t22 @t114) @t109)) % 0.39/1.02 (define @t141 () (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat @t23 @t22 @t133) @t109)) % 0.39/1.02 (define @t142 () (tptp.hAPP tptp.nat @t69 @t68 @t109)) % 0.39/1.02 (define @t143 () (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool @t142 @t114))) % 0.39/1.02 (define @t144 () (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool @t142 @t133))) % 0.39/1.02 (define @t145 () (@list @t114 @t109 @t133)) % 0.39/1.02 (define @t146 () (tptp.hAPP tptp.nat @t23 @t22 @t100)) % 0.39/1.02 (define @t147 () (tptp.hAPP tptp.nat @t69 @t68 @t126)) % 0.39/1.02 (define @t148 () (@var "L" $$unsorted)) % 0.39/1.02 (define @t149 () (@list @t148 @t101 @t100)) % 0.39/1.02 (define @t150 () (tptp.hAPP tptp.nat @t23 @t22 @t148)) % 0.39/1.02 (define @t151 () (tptp.ord_less_eq @t17)) % 0.39/1.02 (define @t152 () (tptp.fun @t17 tptp.bool)) % 0.39/1.02 (define @t153 () (@var "C_2" $$unsorted)) % 0.39/1.02 (define @t154 () (tptp.fun @t2 @t3)) % 0.39/1.02 (define @t155 () (tptp.hAPP @t154 (tptp.fun @t17 @t19) (tptp.image @t2 @t3) @t65)) % 0.39/1.02 (define @t156 () (tptp.hAPP @t17 @t19 @t155 @t50)) % 0.39/1.02 (define @t157 () (tptp.hAPP @t19 @t20 @t51 @t71)) % 0.39/1.02 (define @t158 () (tptp.hBOOL (tptp.hAPP @t19 tptp.bool @t157 @t156))) % 0.39/1.02 (define @t159 () (@list @t2 @t3 @t65 @t50 @t71)) % 0.39/1.02 (define @t160 () (@var "N_3" $$unsorted)) % 0.39/1.02 (define @t161 () (tptp.ord_less_eq @t3)) % 0.39/1.02 (define @t162 () (@var "N_2" $$unsorted)) % 0.39/1.02 (define @t163 () (tptp.hAPP tptp.nat tptp.nat tptp.suc @t162)) % 0.39/1.02 (define @t164 () (@list @t162)) % 0.39/1.02 (define @t165 () (@var "X_1" $$unsorted)) % 0.39/1.02 (define @t166 () (tptp.hAPP @t3 @t2 @t65 @t165)) % 0.39/1.02 (define @t167 () (tptp.fun @t3 @t17)) % 0.39/1.02 (define @t168 () (tptp.hAPP @t42 @t30 (tptp.combc @t3 @t19 tptp.bool) @t41)) % 0.39/1.02 (define @t169 () (tptp.hAPP @t3 @t20 @t41 @t165)) % 0.39/1.02 (define @t170 () (tptp.hBOOL (tptp.hAPP @t19 tptp.bool @t169 @t50))) % 0.39/1.02 (define @t171 () (@list @t165)) % 0.39/1.02 (define @t172 () (@var "B_1" $$unsorted)) % 0.39/1.02 (define @t173 () (tptp.hBOOL (tptp.hAPP @t19 tptp.bool (tptp.hAPP @t3 @t20 @t41 @t172) @t156))) % 0.39/1.02 (define @t174 () (tptp.member @t2)) % 0.39/1.02 (define @t175 () (tptp.ti @t3 @t172)) % 0.39/1.02 (define @t176 () (tptp.hBOOL (tptp.hAPP @t19 tptp.bool @t157 @t50))) % 0.39/1.02 (define @t177 () (@var "C_1" $$unsorted)) % 0.39/1.02 (define @t178 () (tptp.hAPP @t3 @t20 @t41 @t177)) % 0.39/1.02 (define @t179 () (tptp.hAPP @t3 @t30 @t33 @t172)) % 0.39/1.02 (define @t180 () (tptp.hAPP @t19 @t19 @t179 @t71)) % 0.39/1.02 (define @t181 () (tptp.hAPP @t3 @t20 @t41 @t58)) % 0.39/1.02 (define @t182 () (tptp.hBOOL (tptp.hAPP @t19 tptp.bool @t181 @t180))) % 0.39/1.02 (define @t183 () (= (tptp.ti @t3 @t58) @t175)) % 0.39/1.02 (define @t184 () (tptp.hBOOL (tptp.hAPP @t19 tptp.bool @t181 @t71))) % 0.39/1.02 (define @t185 () (@list @t3 @t172 @t58 @t71)) % 0.39/1.02 (define @t186 () (tptp.hBOOL (tptp.hAPP @t19 tptp.bool @t181 @t50))) % 0.39/1.02 (define @t187 () (tptp.hBOOL (tptp.hAPP @t19 tptp.bool @t181 (tptp.hAPP @t19 @t19 @t179 @t50)))) % 0.39/1.02 (define @t188 () (@list @t3 @t58 @t172 @t50)) % 0.39/1.02 (define @t189 () (tptp.hAPP @t19 @t19 @t59 @t71)) % 0.39/1.02 (define @t190 () (@list @t3 @t58 @t71)) % 0.39/1.02 (define @t191 () (tptp.fun @t3 @t19)) % 0.39/1.02 (define @t192 () (tptp.hAPP @t191 @t191 (tptp.combc @t3 @t3 tptp.bool) (tptp.fequal @t3))) % 0.39/1.02 (define @t193 () (tptp.hAPP @t3 @t19 @t192 @t58)) % 0.39/1.02 (define @t194 () (@var "Y_2" $$unsorted)) % 0.39/1.02 (define @t195 () (tptp.hAPP @t3 @t30 @t33 @t194)) % 0.39/1.02 (define @t196 () (tptp.hAPP @t19 @t19 @t195 @t50)) % 0.39/1.02 (define @t197 () (tptp.hBOOL (tptp.hAPP @t3 tptp.bool @t50 @t81))) % 0.39/1.02 (define @t198 () (tptp.hAPP @t19 @t19 @t82 @t71)) % 0.39/1.02 (define @t199 () (tptp.hBOOL (tptp.hAPP @t19 tptp.bool @t86 @t71))) % 0.39/1.02 (define @t200 () (@list @t3 @t71 @t81 @t50)) % 0.39/1.02 (define @t201 () (@list @t3 @t81 @t50 @t71)) % 0.39/1.02 (define @t202 () (@var "C" $$unsorted)) % 0.39/1.02 (define @t203 () (@var "G" $$unsorted)) % 0.39/1.02 (define @t204 () (tptp.hAPP @t2 @t3 @t65 @t165)) % 0.39/1.02 (define @t205 () (@var "Z" $$unsorted)) % 0.39/1.02 (define @t206 () (tptp.hBOOL (tptp.hAPP @t17 tptp.bool (tptp.hAPP @t2 @t152 @t174 @t165) @t50))) % 0.39/1.02 (define @t207 () (tptp.hAPP @t3 @t2 @t65 @t81)) % 0.39/1.02 (define @t208 () (tptp.hBOOL (tptp.hAPP @t17 tptp.bool (tptp.hAPP @t2 @t152 @t174 @t207) @t67))) % 0.39/1.02 (define @t209 () (@list @t2 @t3 @t65 @t81 @t50)) % 0.39/1.02 (define @t210 () (forall @t209 (=> @t87 @t208))) % 0.39/1.02 (define @t211 () (@var "Xa" $$unsorted)) % 0.39/1.02 (define @t212 () (@var "X_d" $$unsorted)) % 0.39/1.02 (define @t213 () (tptp.fun @t212 @t3)) % 0.39/1.02 (define @t214 () (tptp.fun @t212 @t2)) % 0.39/1.02 (define @t215 () (tptp.fun @t212 tptp.bool)) % 0.39/1.02 (define @t216 () (@var "Y_1" $$unsorted)) % 0.39/1.02 (define @t217 () (@var "D" $$unsorted)) % 0.39/1.02 (define @t218 () (tptp.insert @t2)) % 0.39/1.02 (define @t219 () (tptp.fun @t17 @t17)) % 0.39/1.02 (define @t220 () (@var "AA" $$unsorted)) % 0.39/1.02 (define @t221 () (tptp.hAPP @t17 @t152 @t151 @t67)) % 0.39/1.02 (define @t222 () (@var "I" $$unsorted)) % 0.39/1.02 (define @t223 () (@var "M" $$unsorted)) % 0.39/1.02 (define @t224 () (@var "M_1" $$unsorted)) % 0.39/1.02 (define @t225 () (@list @t223)) % 0.39/1.02 (define @t226 () (@var "N" $$unsorted)) % 0.39/1.02 (define @t227 () (@var "T_1" $$unsorted)) % 0.39/1.02 (define @t228 () (@var "T_2" $$unsorted)) % 0.39/1.02 (define @t229 () (tptp.fun @t228 @t227)) % 0.39/1.02 (define @t230 () (@list @t228 @t227)) % 0.39/1.02 (define @t231 () (@var "A" $$unsorted)) % 0.39/1.02 (define @t232 () (@var "T" $$unsorted)) % 0.39/1.02 (define @t233 () (tptp.ti @t232 @t231)) % 0.39/1.02 (define @t234 () (@var "P" $$unsorted)) % 0.39/1.02 (define @t235 () (tptp.hBOOL @t234)) % 0.39/1.02 (define @t236 () (not @t235)) % 0.39/1.02 (define @t237 () (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool tptp.fNot @t234))) % 0.39/1.02 (define @t238 () (@list @t234)) % 0.39/1.02 (define @t239 () (@var "R" $$unsorted)) % 0.39/1.02 (define @t240 () (@var "Q" $$unsorted)) % 0.39/1.02 (define @t241 () (tptp.hAPP @t1 @t3 @t240 @t239)) % 0.39/1.02 (define @t242 () (@list @t1 @t2 @t3 @t234 @t240 @t239)) % 0.39/1.02 (define @t243 () (tptp.hAPP @t1 @t8 @t234 @t239)) % 0.39/1.02 (define @t244 () (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool @t34 tptp.fconj @t234) @t240))) % 0.39/1.02 (define @t245 () (tptp.hBOOL @t240)) % 0.39/1.02 (define @t246 () (not @t245)) % 0.39/1.02 (define @t247 () (@list @t240 @t234)) % 0.39/1.02 (define @t248 () (not @t244)) % 0.39/1.02 (define @t249 () (@list @t234 @t240)) % 0.39/1.02 (define @t250 () (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool @t34 tptp.fdisj @t234) @t240))) % 0.39/1.02 (define @t251 () (= (tptp.ti @t1 @t117) (tptp.ti @t1 @t116))) % 0.39/1.02 (define @t252 () (tptp.hBOOL (tptp.hAPP @t1 tptp.bool (tptp.hAPP @t1 @t26 @t36 @t117) @t116))) % 0.39/1.02 (define @t253 () (@list @t1 @t117 @t116)) % 0.39/1.02 (define @t254 () (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool @t34 tptp.fimplies @t234) @t240))) % 0.39/1.02 (define @t255 () (tptp.hAPP @t45 @t43 (tptp.hAPP @t46 (tptp.fun @t45 @t43) (tptp.image tptp.pname tptp.x_a) tptp.mgt_call) tptp.u)) % 0.39/1.02 (define @t256 () (tptp.hBOOL (tptp.hAPP @t43 tptp.bool (tptp.hAPP @t43 @t44 @t49 tptp.g) @t255))) % 0.39/1.02 (define @t257 () (tptp.finite_card tptp.x_a)) % 0.39/1.02 (define @t258 () (tptp.hAPP @t43 tptp.nat @t257 @t255)) % 0.39/1.02 (define @t259 () (tptp.hAPP tptp.nat tptp.nat tptp.suc tptp.na)) % 0.39/1.02 (define @t260 () (tptp.hBOOL (tptp.hAPP @t45 tptp.bool (tptp.hAPP tptp.pname (tptp.fun @t45 tptp.bool) (tptp.member tptp.pname) tptp.pn) tptp.u))) % 0.39/1.02 (define @t261 () (tptp.hAPP tptp.pname tptp.x_a tptp.mgt_call tptp.pn)) % 0.39/1.02 (define @t262 () (tptp.hAPP tptp.x_a @t44 (tptp.member tptp.x_a) @t261)) % 0.39/1.02 (define @t263 () (tptp.hBOOL (tptp.hAPP @t43 tptp.bool (tptp.hAPP @t43 @t44 @t49 (tptp.hAPP @t43 @t43 (tptp.hAPP tptp.x_a (tptp.fun @t43 @t43) (tptp.insert tptp.x_a) @t261) tptp.g)) @t255))) % 0.39/1.02 (define @t264 () (tptp.hBOOL (tptp.hAPP @t43 tptp.bool @t262 @t255))) % 0.39/1.02 (define @t265 () (and @t264 @t256)) % 0.39/1.02 (define @t266 () (= @t263 @t265)) % 0.39/1.02 (define @t267 () (not @t265)) % 0.39/1.02 (define @t268 () (@list true false)) % 0.39/1.02 (define @t269 () (not @t264)) % 0.39/1.02 (define @t270 () (@list false true)) % 0.39/1.02 (define @t271 () (not @t260)) % 0.39/1.02 (define @t272 () (or @t271 @t264)) % 0.39/1.02 (define @t273 () (not @t272)) % 0.39/1.02 (define @t274 () (forall @t209 (or @t88 @t208))) % 0.39/1.02 (assume @p1 (forall (@list @t3 @t2 @t1) (= (tptp.ti (tptp.fun @t8 @t7) @t4) @t4))) % 0.39/1.02 (assume @p2 (forall @t12 (= (tptp.ti (tptp.fun @t11 @t10) @t9) @t9))) % 0.39/1.02 (assume @p3 (forall @t14 (= (tptp.ti (tptp.fun @t1 @t1) @t13) @t13))) % 0.39/1.02 (assume @p4 (forall @t12 (= (tptp.ti (tptp.fun @t11 @t7) @t15) @t15))) % 0.39/1.02 (assume @p5 (forall (@list @t2) (= (tptp.ti (tptp.fun @t17 tptp.nat) @t16) @t16))) % 0.39/1.02 (assume @p6 (forall @t21 (= (tptp.ti @t20 @t18) @t18))) % 0.39/1.02 (assume @p7 (= (tptp.ti (tptp.fun tptp.nat @t23) @t22) @t22)) % 0.39/1.02 (assume @p8 (forall @t14 (= (tptp.ti @t1 @t24) @t24))) % 0.39/1.02 (assume @p9 (= (tptp.ti @t23 tptp.suc) tptp.suc)) % 0.39/1.02 (assume @p10 (forall @t14 (=> @t28 (= (tptp.ti @t27 @t25) @t25)))) % 0.39/1.02 (assume @p11 (forall @t21 (= (tptp.ti @t30 @t29) @t29))) % 0.39/1.02 (assume @p12 (forall (@list @t3 @t2) (= (tptp.ti (tptp.fun @t8 @t32) @t31) @t31))) % 0.39/1.02 (assume @p13 (forall @t21 (= (tptp.ti (tptp.fun @t3 @t30) @t33) @t33))) % 0.39/1.02 (assume @p14 (= (tptp.ti @t34 tptp.fNot) tptp.fNot)) % 0.39/1.02 (assume @p15 (= (tptp.ti @t35 tptp.fconj) tptp.fconj)) % 0.39/1.02 (assume @p16 (= (tptp.ti @t35 tptp.fdisj) tptp.fdisj)) % 0.39/1.02 (assume @p17 (forall @t14 (= (tptp.ti @t27 @t36) @t36))) % 0.39/1.02 (assume @p18 (= (tptp.ti @t35 tptp.fimplies) tptp.fimplies)) % 0.39/1.02 (assume @p19 (forall @t40 (= (tptp.hAPP @t1 @t2 (tptp.ti @t5 @t38) @t37) @t39))) % 0.39/1.02 (assume @p20 (forall @t40 (= (tptp.hAPP @t1 @t2 @t38 (tptp.ti @t1 @t37)) @t39))) % 0.39/1.02 (assume @p21 (forall (@list @t2 @t1 @t38 @t37) (= (tptp.ti @t2 @t39) @t39))) % 0.39/1.02 (assume @p22 (forall (@list @t38) (= (tptp.hBOOL (tptp.ti tptp.bool @t38)) (tptp.hBOOL @t38)))) % 0.39/1.02 (assume @p23 (forall @t21 (= (tptp.ti @t42 @t41) @t41))) % 0.39/1.02 (assume @p24 (= (tptp.ti @t43 tptp.g) tptp.g)) % 0.39/1.02 (assume @p25 (= (tptp.ti (tptp.fun @t43 @t44) tptp.p) tptp.p)) % 0.39/1.02 (assume @p26 (= (tptp.ti @t45 tptp.u) tptp.u)) % 0.39/1.02 (assume @p27 (= (tptp.ti @t46 tptp.mgt_call) tptp.mgt_call)) % 0.39/1.02 (assume @p28 (= (tptp.ti tptp.nat tptp.na) tptp.na)) % 0.39/1.02 (assume @p29 (= (tptp.ti tptp.pname tptp.pn) tptp.pn)) % 0.39/1.02 (assume @p30 (forall (@list @t47 @t48) (=> (tptp.hBOOL (tptp.hAPP @t43 tptp.bool (tptp.hAPP @t43 @t44 @t49 @t47) @t48)) (tptp.hBOOL (tptp.hAPP @t43 tptp.bool (tptp.hAPP @t43 @t44 tptp.p @t48) @t47))))) % 0.39/1.02 (assume @p31 (forall @t54 (=> @t53 (tptp.hBOOL (tptp.hAPP @t20 tptp.bool (tptp.finite_finite @t19) (tptp.hAPP @t20 @t20 (tptp.collect @t19) (tptp.hAPP @t19 @t20 (tptp.hAPP @t52 @t52 (tptp.combc @t19 @t19 tptp.bool) @t51) @t50))))))) % 0.39/1.02 (assume @p32 (forall (@list @t2 @t3 @t56 @t55) (=> (tptp.hBOOL (tptp.hAPP @t19 tptp.bool @t18 @t55)) (tptp.hBOOL (tptp.hAPP @t17 tptp.bool @t57 (tptp.hAPP @t19 @t17 (tptp.hAPP @t8 @t32 @t31 @t56) @t55)))))) % 0.39/1.02 (assume @p33 (forall @t62 (=> @t53 @t61))) % 0.39/1.02 (assume @p34 (forall @t70 (=> @t53 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat @t69 @t68 (tptp.hAPP @t17 tptp.nat @t16 @t67)) @t64))))) % 0.39/1.02 (assume @p35 (forall @t77 (=> @t76 (=> @t75 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool @t73 @t72)))))) % 0.39/1.02 (assume @p36 (forall @t77 (=> @t76 (=> @t75 (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat @t69 @t68 @t72) @t64)) @t80))))) % 0.39/1.02 (assume @p37 (forall @t85 (=> @t53 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool @t73 @t84))))) % 0.39/1.02 (assume @p38 (forall @t85 (=> @t53 (and (=> @t87 (= @t84 @t64)) @t89)))) % 0.39/1.02 (assume @p39 (forall @t85 (=> @t53 @t89))) % 0.39/1.02 (assume @p40 (forall (@list @t3 @t90 @t91) (=> (or @t99 @t97) (tptp.hBOOL (tptp.hAPP @t19 tptp.bool @t18 (tptp.hAPP @t19 @t19 @t29 (tptp.hAPP @t19 @t19 (tptp.hAPP @t93 @t30 @t96 (tptp.hAPP @t19 @t93 @t95 @t91)) @t90))))))) % 0.39/1.02 (assume @p41 (forall (@list @t100 @t101) (=> @t108 (= @t106 (tptp.hAPP tptp.nat tptp.nat tptp.suc @t103))))) % 0.39/1.02 (assume @p42 (forall (@list @t109) (tptp.hBOOL (tptp.hAPP @t69 tptp.bool @t113 (tptp.hAPP @t69 @t69 @t112 (tptp.hAPP tptp.nat @t69 @t111 @t109)))))) % 0.39/1.02 (assume @p43 (forall (@list @t114) (= (tptp.hAPP @t69 tptp.nat (tptp.finite_card tptp.nat) (tptp.hAPP @t69 @t69 @t112 (tptp.hAPP tptp.nat @t69 @t111 @t114))) @t115))) % 0.39/1.02 (assume @p44 (forall @t21 (=> (tptp.finite_finite_1 @t3) (forall (@list @t50) @t53)))) % 0.39/1.02 (assume @p45 (forall (@list @t117 @t116) (=> (= (tptp.hAPP tptp.nat tptp.nat tptp.suc @t117) (tptp.hAPP tptp.nat tptp.nat tptp.suc @t116)) (= @t117 @t116)))) % 0.39/1.02 (assume @p46 (forall (@list @t119 @t118) (= (= (tptp.hAPP tptp.nat tptp.nat tptp.suc @t119) (tptp.hAPP tptp.nat tptp.nat tptp.suc @t118)) (= @t119 @t118)))) % 0.39/1.02 (assume @p47 (forall @t121 (not (= @t120 @t100)))) % 0.39/1.02 (assume @p48 (forall @t121 (not (= @t100 @t120)))) % 0.39/1.02 (assume @p49 (forall @t125 (=> @t124 (=> @t108 @t122)))) % 0.39/1.02 (assume @p50 (forall (@list @t126 @t127 @t129) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool @t128 @t129)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat @t69 @t68 @t129) @t126)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool @t128 @t126)))))) % 0.39/1.02 (assume @p51 (forall @t125 (=> @t122 @t124))) % 0.39/1.02 (assume @p52 (forall @t125 (or @t124 @t108))) % 0.39/1.02 (assume @p53 (forall @t121 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool @t107 @t100)))) % 0.39/1.02 (assume @p54 (forall (@list @t127 @t129 @t126) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat @t23 @t22 (tptp.hAPP tptp.nat tptp.nat @t130 @t129)) @t126) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat @t23 @t22 (tptp.hAPP tptp.nat tptp.nat @t130 @t126)) @t129)))) % 0.39/1.02 (assume @p55 (forall (@list @t3 @t91 @t90) (= (tptp.hBOOL (tptp.hAPP @t19 tptp.bool @t18 (tptp.hAPP @t19 @t19 @t29 (tptp.hAPP @t19 @t19 (tptp.hAPP @t93 @t30 @t96 (tptp.hAPP @t19 @t93 @t131 @t91)) @t90)))) (and @t99 @t97)))) % 0.39/1.02 (assume @p56 (forall @t62 (= @t61 @t53))) % 0.39/1.02 (assume @p57 (forall @t77 (=> @t75 (=> @t76 @t53)))) % 0.39/1.02 (assume @p58 (forall @t77 (=> @t76 (=> @t75 @t53)))) % 0.39/1.02 (assume @p59 (forall @t125 (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat @t69 @t68 @t104) @t100)) @t124))) % 0.39/1.02 (assume @p60 (forall @t125 (=> @t132 (=> (not @t124) (= @t101 @t120))))) % 0.39/1.02 (assume @p61 (forall @t125 (=> @t124 @t132))) % 0.39/1.02 (assume @p62 (forall (@list @t114 @t133) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool @t135 (tptp.hAPP tptp.nat tptp.nat tptp.suc @t133))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool @t134 @t133))))) % 0.39/1.02 (assume @p63 (forall @t138 (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool @t136 @t115)) (or @t137 (= @t133 @t115))))) % 0.39/1.02 (assume @p64 (forall @t138 (= (not @t137) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool @t135 @t133))))) % 0.39/1.02 (assume @p65 (forall @t121 (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool @t139 @t100))))) % 0.39/1.02 (assume @p66 (forall (@list @t101 @t100 @t126) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat @t23 @t22 @t106) (tptp.hAPP tptp.nat tptp.nat tptp.suc @t126)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat @t23 @t22 @t103) @t126)))) % 0.39/1.02 (assume @p67 (forall @t125 (= (tptp.hAPP tptp.nat tptp.nat @t105 @t120) @t103))) % 0.39/1.02 (assume @p68 (forall @t145 (=> @t144 (=> @t143 (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat @t69 @t68 @t141) @t140)) @t137))))) % 0.39/1.02 (assume @p69 (forall (@list @t100 @t126 @t101) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool @t147 @t101)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool @t147 @t100)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat @t23 @t22 (tptp.hAPP tptp.nat tptp.nat @t102 @t126)) (tptp.hAPP tptp.nat tptp.nat @t146 @t126)) @t103))))) % 0.39/1.02 (assume @p70 (forall @t145 (=> @t144 (=> @t143 (= (= @t141 @t140) (= @t133 @t114)))))) % 0.39/1.02 (assume @p71 (forall (@list @t127 @t100) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool @t128 @t100)) (= (tptp.hAPP tptp.nat tptp.nat @t146 (tptp.hAPP tptp.nat tptp.nat @t146 @t127)) @t127)))) % 0.39/1.02 (assume @p72 (forall @t149 (=> @t124 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat @t69 @t68 (tptp.hAPP tptp.nat tptp.nat @t102 @t148)) (tptp.hAPP tptp.nat tptp.nat @t146 @t148)))))) % 0.39/1.02 (assume @p73 (forall @t149 (=> @t124 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat @t69 @t68 (tptp.hAPP tptp.nat tptp.nat @t150 @t100)) (tptp.hAPP tptp.nat tptp.nat @t150 @t101)))))) % 0.39/1.02 (assume @p74 (forall @t125 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat @t69 @t68 @t103) @t101)))) % 0.39/1.02 (assume @p75 (forall (@list @t2 @t3 @t71 @t65 @t50) (=> @t53 (=> (tptp.hBOOL (tptp.hAPP @t17 tptp.bool (tptp.hAPP @t17 @t152 @t151 @t71) @t67)) (tptp.hBOOL (tptp.hAPP @t17 tptp.bool @t57 @t71)))))) % 0.39/1.02 (assume @p76 (forall @t159 (=> @t76 (=> @t158 (exists (@list @t153) (and (tptp.hBOOL (tptp.hAPP @t17 tptp.bool (tptp.hAPP @t17 @t152 @t151 @t153) @t50)) (tptp.hBOOL (tptp.hAPP @t17 tptp.bool @t57 @t153)) (= @t78 (tptp.hAPP @t17 @t19 @t155 @t153)))))))) % 0.39/1.02 (assume @p77 (forall @t21 (=> (tptp.order @t3) (forall (@list @t114 @t160 @t65) (=> (forall @t164 (tptp.hBOOL (tptp.hAPP @t3 tptp.bool (tptp.hAPP @t3 @t19 @t161 (tptp.hAPP tptp.nat @t3 @t65 @t162)) (tptp.hAPP tptp.nat @t3 @t65 @t163)))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool @t134 @t160)) (tptp.hBOOL (tptp.hAPP @t3 tptp.bool (tptp.hAPP @t3 @t19 @t161 (tptp.hAPP tptp.nat @t3 @t65 @t114)) (tptp.hAPP tptp.nat @t3 @t65 @t160))))))))) % 0.39/1.02 (assume @p78 (forall @t70 (=> (not @t53) (=> (tptp.hBOOL (tptp.hAPP @t17 tptp.bool @t57 @t67)) (exists @t171 (and @t170 (not (tptp.hBOOL (tptp.hAPP @t19 tptp.bool @t18 (tptp.hAPP @t19 @t19 @t29 (tptp.hAPP @t19 @t19 (tptp.hAPP @t93 @t30 @t96 (tptp.hAPP @t19 @t93 @t95 (tptp.hAPP @t19 @t19 @t168 @t50))) (tptp.hAPP @t2 @t19 (tptp.hAPP @t167 (tptp.fun @t2 @t19) (tptp.combc @t3 @t2 tptp.bool) (tptp.hAPP @t8 @t167 (tptp.hAPP (tptp.fun @t2 @t17) (tptp.fun @t8 @t167) (tptp.combb @t2 @t17 @t3) (tptp.fequal @t2)) @t65)) @t166)))))))))))) % 0.39/1.03 (assume @p79 (forall (@list @t3 @t2 @t50 @t172 @t65 @t81) (=> (= @t175 (tptp.hAPP @t2 @t3 @t65 @t81)) (=> (tptp.hBOOL (tptp.hAPP @t17 tptp.bool (tptp.hAPP @t2 @t152 @t174 @t81) @t50)) @t173)))) % 0.39/1.03 (assume @p80 (forall @t77 (=> @t75 (=> @t176 @t80)))) % 0.39/1.03 (assume @p81 (forall (@list @t3 @t177 @t50 @t71) (=> @t75 (=> (tptp.hBOOL (tptp.hAPP @t19 tptp.bool @t178 @t50)) (tptp.hBOOL (tptp.hAPP @t19 tptp.bool @t178 @t71)))))) % 0.39/1.03 (assume @p82 (forall @t185 (=> (=> (not @t184) @t183) @t182))) % 0.39/1.03 (assume @p83 (forall @t188 (=> @t187 (=> (not @t183) @t186)))) % 0.39/1.03 (assume @p84 (forall @t190 (tptp.hBOOL (tptp.hAPP @t19 tptp.bool @t181 @t189)))) % 0.39/1.03 (assume @p85 (forall @t190 (= @t189 (tptp.hAPP @t19 @t19 @t29 (tptp.hAPP @t19 @t19 (tptp.hAPP @t93 @t30 @t96 (tptp.hAPP @t19 @t93 @t131 @t193)) (tptp.hAPP @t19 @t19 @t168 @t71)))))) % 0.39/1.03 (assume @p86 (forall (@list @t3 @t58 @t91) (= (tptp.hAPP @t19 @t19 @t59 @t98) (tptp.hAPP @t19 @t19 @t29 (tptp.hAPP @t19 @t19 (tptp.hAPP @t93 @t30 @t96 (tptp.hAPP @t19 @t93 (tptp.hAPP @t35 @t94 @t92 tptp.fimplies) (tptp.hAPP @t19 @t19 (tptp.hAPP @t34 @t30 (tptp.combb tptp.bool tptp.bool @t3) tptp.fNot) @t193))) @t91))))) % 0.39/1.03 (assume @p87 (forall @t85 (= (tptp.hAPP @t19 @t19 @t82 @t83) @t83))) % 0.39/1.03 (assume @p88 (forall (@list @t3 @t81 @t194 @t50) (= (tptp.hAPP @t19 @t19 @t82 @t196) (tptp.hAPP @t19 @t19 @t195 @t83)))) % 0.39/1.03 (assume @p89 (forall @t188 (= @t187 (or @t183 @t186)))) % 0.39/1.03 (assume @p90 (forall (@list @t3 @t194 @t50 @t81) (= (tptp.hBOOL (tptp.hAPP @t3 tptp.bool @t196 @t81)) (or (= (tptp.ti @t3 @t194) (tptp.ti @t3 @t81)) @t197)))) % 0.39/1.03 (assume @p91 (forall @t200 (=> @t88 (=> (not @t199) (= (= @t83 @t198) @t80))))) % 0.39/1.03 (assume @p92 (forall @t185 (=> @t184 @t182))) % 0.39/1.03 (assume @p93 (forall @t62 (=> @t186 (= @t60 @t79)))) % 0.39/1.03 (assume @p94 (forall @t54 (tptp.hBOOL (tptp.hAPP @t19 tptp.bool @t74 @t50)))) % 0.39/1.03 (assume @p95 (forall @t77 (= @t80 (and @t75 @t176)))) % 0.39/1.03 (assume @p96 (forall @t77 (=> @t80 @t75))) % 0.39/1.03 (assume @p97 (forall @t77 (=> @t80 @t176))) % 0.39/1.03 (assume @p98 (forall @t201 (=> @t75 (=> @t87 @t199)))) % 0.39/1.03 (assume @p99 (forall @t200 (=> @t87 (=> @t75 @t199)))) % 0.39/1.03 (assume @p100 (forall (@list @t3 @t202 @t50 @t71) (=> @t75 (=> (tptp.hBOOL (tptp.hAPP @t19 tptp.bool @t157 @t202)) (tptp.hBOOL (tptp.hAPP @t19 tptp.bool @t74 @t202)))))) % 0.39/1.03 (assume @p101 (forall @t77 (=> @t80 (not (=> @t75 (not @t176)))))) % 0.39/1.03 (assume @p102 (forall (@list @t3 @t2 @t65 @t203) (=> (forall @t171 (= @t166 (tptp.hAPP @t3 @t2 @t203 @t165))) (= (tptp.ti @t8 @t65) (tptp.ti @t8 @t203))))) % 0.39/1.03 (assume @p103 (forall @t85 (= @t87 @t197))) % 0.39/1.03 (assume @p104 (forall (@list @t3 @t91) (= @t98 (tptp.ti @t19 @t91)))) % 0.39/1.03 (assume @p105 (forall (@list @t3 @t2 @t205 @t65 @t50) (= (tptp.hBOOL (tptp.hAPP @t19 tptp.bool (tptp.hAPP @t3 @t20 @t41 @t205) @t156)) (exists @t171 (and @t206 (= (tptp.ti @t3 @t205) @t204)))))) % 0.39/1.03 (assume @p106 @t210) % 0.39/1.03 (assume @p107 (forall (@list @t2 @t3 @t172 @t65 @t81 @t50) (=> @t87 (=> (= (tptp.ti @t2 @t172) @t207) (tptp.hBOOL (tptp.hAPP @t17 tptp.bool (tptp.hAPP @t2 @t152 @t174 @t172) @t67)))))) % 0.39/1.03 (assume @p108 (forall (@list @t3 @t165 @t211) (= (tptp.hAPP @t19 @t19 (tptp.hAPP @t3 @t30 @t33 @t165) @t211) (tptp.hAPP @t19 @t19 @t29 (tptp.hAPP @t19 @t19 (tptp.hAPP @t93 @t30 @t96 (tptp.hAPP @t19 @t93 @t131 (tptp.hAPP @t3 @t19 @t192 @t165))) (tptp.hAPP @t19 @t19 @t168 @t211)))))) % 0.39/1.03 (assume @p109 (forall (@list @t2 @t3 @t212 @t65 @t203 @t50) (= (tptp.hAPP @t17 @t19 @t155 (tptp.hAPP @t215 @t17 (tptp.hAPP @t214 (tptp.fun @t215 @t17) (tptp.image @t212 @t2) @t203) @t50)) (tptp.hAPP @t215 @t19 (tptp.hAPP @t213 (tptp.fun @t215 @t19) (tptp.image @t212 @t3) (tptp.hAPP @t214 @t213 (tptp.hAPP @t154 (tptp.fun @t214 @t213) (tptp.combb @t2 @t3 @t212) @t65) @t203)) @t50)))) % 0.39/1.03 (assume @p110 (forall (@list @t3 @t216) (= (tptp.hAPP @t19 @t19 (tptp.hAPP (tptp.fun @t3 @t3) @t30 (tptp.image @t3 @t3) (tptp.combi @t3)) @t216) (tptp.ti @t19 @t216)))) % 0.39/1.03 (assume @p111 (forall (@list @t3 @t71 @t58) (tptp.hBOOL (tptp.hAPP @t19 tptp.bool @t157 @t189)))) % 0.39/1.03 (assume @p112 (forall @t201 (= (tptp.hBOOL (tptp.hAPP @t19 tptp.bool (tptp.hAPP @t19 @t20 @t51 @t83) @t71)) (and @t199 @t75)))) % 0.39/1.03 (assume @p113 (forall @t200 (=> @t88 (= (tptp.hBOOL (tptp.hAPP @t19 tptp.bool @t74 @t198)) @t75)))) % 0.39/1.03 (assume @p114 (forall (@list @t3 @t172 @t50 @t71) (=> @t75 (tptp.hBOOL (tptp.hAPP @t19 tptp.bool @t74 @t180))))) % 0.39/1.03 (assume @p115 (forall (@list @t3 @t58 @t202 @t217) (=> (tptp.hBOOL (tptp.hAPP @t19 tptp.bool (tptp.hAPP @t19 @t20 @t51 @t202) @t217)) (tptp.hBOOL (tptp.hAPP @t19 tptp.bool (tptp.hAPP @t19 @t20 @t51 (tptp.hAPP @t19 @t19 @t59 @t202)) (tptp.hAPP @t19 @t19 @t59 @t217)))))) % 0.39/1.03 (assume @p116 (forall (@list @t2 @t3 @t65 @t58 @t71) (= (tptp.hAPP @t17 @t19 @t155 (tptp.hAPP @t17 @t17 (tptp.hAPP @t2 @t219 @t218 @t58) @t71)) (tptp.hAPP @t19 @t19 (tptp.hAPP @t3 @t30 @t33 (tptp.hAPP @t2 @t3 @t65 @t58)) (tptp.hAPP @t17 @t19 @t155 @t71))))) % 0.39/1.03 (assume @p117 (forall @t209 (=> @t87 (= (tptp.hAPP @t17 @t17 (tptp.hAPP @t2 @t219 @t218 @t207) @t67) @t67)))) % 0.39/1.03 (assume @p118 (forall (@list @t3 @t2 @t71 @t65 @t50) (= @t158 (exists (@list @t220) (and (tptp.hBOOL (tptp.hAPP @t17 tptp.bool (tptp.hAPP @t17 @t152 @t151 @t220) @t50)) (= @t78 (tptp.hAPP @t17 @t19 @t155 @t220))))))) % 0.39/1.03 (assume @p119 (forall @t159 (=> @t75 (tptp.hBOOL (tptp.hAPP @t17 tptp.bool @t221 (tptp.hAPP @t19 @t17 @t66 @t71)))))) % 0.39/1.03 (assume @p120 (forall (@list @t3 @t2 @t172 @t65 @t50) (=> @t173 (not (forall @t171 (=> (= @t175 @t204) (not @t206))))))) % 0.39/1.03 (assume @p121 (forall (@list @t3 @t71 @t50) (=> (forall @t171 (=> @t170 (tptp.hBOOL (tptp.hAPP @t19 tptp.bool @t169 @t71)))) @t75))) % 0.39/1.03 (assume @p122 (forall (@list @t222 @t91 @t109) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool @t91 @t109)) (=> (forall @t164 (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool @t91 @t163)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool @t91 @t162)))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool @t91 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat @t23 @t22 @t109) @t222))))))) % 0.39/1.03 (assume @p123 (forall (@list @t100 @t224) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool @t139 @t224)) (exists @t225 (= @t224 (tptp.hAPP tptp.nat tptp.nat tptp.suc @t223)))))) % 0.39/1.03 (assume @p124 (forall (@list @t2 @t3 @t65 @t71 @t50) (=> (forall @t171 (=> @t170 (tptp.hBOOL (tptp.hAPP @t17 tptp.bool (tptp.hAPP @t2 @t152 @t174 @t166) @t71)))) (tptp.hBOOL (tptp.hAPP @t17 tptp.bool @t221 @t71))))) % 0.39/1.03 (assume @p125 (forall @t14 (=> @t28 (forall (@list @t117) (tptp.hBOOL (tptp.hAPP @t1 tptp.bool (tptp.hAPP @t1 @t26 @t25 @t117) @t117)))))) % 0.39/1.03 (assume @p126 (forall (@list @t226) (= (tptp.hBOOL (tptp.hAPP @t69 tptp.bool @t113 @t226)) (exists @t225 (forall @t171 (=> (tptp.hBOOL (tptp.hAPP @t69 tptp.bool (tptp.hAPP tptp.nat (tptp.fun @t69 tptp.bool) (tptp.member tptp.nat) @t165) @t226)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat @t69 @t68 @t165) @t223)))))))) % 0.39/1.03 (assume @p127 (forall @t230 (=> (tptp.preorder @t227) (tptp.preorder @t229)))) % 0.39/1.03 (assume @p128 (forall @t230 (=> (and (tptp.finite_finite_1 @t227) (tptp.finite_finite_1 @t228)) (tptp.finite_finite_1 @t229)))) % 0.39/1.03 (assume @p129 (forall @t230 (=> (tptp.order @t227) (tptp.order @t229)))) % 0.39/1.03 (assume @p130 (tptp.preorder tptp.nat)) % 0.39/1.03 (assume @p131 (tptp.order tptp.nat)) % 0.39/1.03 (assume @p132 (tptp.preorder tptp.bool)) % 0.39/1.03 (assume @p133 (tptp.finite_finite_1 tptp.bool)) % 0.39/1.03 (assume @p134 (tptp.order tptp.bool)) % 0.39/1.03 (assume @p135 (forall (@list @t232 @t231) (= (tptp.ti @t232 @t233) @t233))) % 0.39/1.03 (assume @p136 (forall @t238 (or (not @t237) @t236))) % 0.39/1.03 (assume @p137 (forall @t238 (or @t235 @t237))) % 0.39/1.03 (assume @p138 (forall @t242 (= (tptp.hAPP @t1 @t2 (tptp.hAPP @t6 @t5 (tptp.hAPP @t8 @t7 @t4 @t234) @t240) @t239) (tptp.hAPP @t3 @t2 @t234 @t241)))) % 0.39/1.03 (assume @p139 (forall @t242 (= (tptp.hAPP @t1 @t2 (tptp.hAPP @t3 @t5 (tptp.hAPP @t11 @t10 @t9 @t234) @t240) @t239) (tptp.hAPP @t3 @t2 @t243 @t240)))) % 0.39/1.03 (assume @p140 (forall (@list @t1 @t234) (= (tptp.hAPP @t1 @t1 @t13 @t234) (tptp.ti @t1 @t234)))) % 0.39/1.03 (assume @p141 (forall @t242 (= (tptp.hAPP @t1 @t2 (tptp.hAPP @t6 @t5 (tptp.hAPP @t11 @t7 @t15 @t234) @t240) @t239) (tptp.hAPP @t3 @t2 @t243 @t241)))) % 0.83/1.03 (assume @p142 (forall @t247 (or @t236 @t246 @t244))) % 0.83/1.03 (assume @p143 (forall @t249 (or @t248 @t235))) % 0.83/1.03 (assume @p144 (forall @t249 (or @t248 @t245))) % 0.83/1.03 (assume @p145 (forall @t247 (or @t236 @t250))) % 0.83/1.03 (assume @p146 (forall @t249 (or @t246 @t250))) % 0.83/1.03 (assume @p147 (forall @t249 (or (not @t250) @t235 @t245))) % 0.83/1.03 (assume @p148 (forall @t253 (or (not @t252) @t251))) % 0.83/1.03 (assume @p149 (forall @t253 (or (not @t251) @t252))) % 0.83/1.03 (assume @p150 (forall @t247 (or @t235 @t254))) % 0.83/1.03 (assume @p151 (forall @t249 (or @t246 @t254))) % 0.83/1.03 (assume @p152 (forall @t249 (or (not @t254) @t236 @t245))) % 0.83/1.03 (assume @p153 (tptp.hBOOL (tptp.hAPP @t45 tptp.bool (tptp.finite_finite tptp.pname) tptp.u))) % 0.83/1.03 (assume @p154 @t256) % 0.83/1.03 (assume @p155 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat @t69 @t68 @t259) @t258))) % 0.83/1.03 (assume @p156 (= (tptp.hAPP @t43 tptp.nat @t257 tptp.g) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat @t23 @t22 @t258) @t259))) % 0.83/1.03 (assume @p157 @t260) % 0.83/1.03 (assume @p158 (not (tptp.hBOOL (tptp.hAPP @t43 tptp.bool @t262 tptp.g)))) % 0.83/1.03 (assume @p159 (not @t263)) % 0.83/1.03 (assume @p160 true) % 0.83/1.03 (step @p161 :rule bool-impl-elim :args (@t87 @t208)) % 0.83/1.03 (step @p162 :rule cong :premises (@p161) :args (@t210)) % 0.83/1.03 (step @p163 :rule eq_resolve :premises (@p106 @p162)) % 0.83/1.03 (step @p164 :rule instantiate :premises (@p112) :args ((@list tptp.x_a @t261 tptp.g @t255))) % 0.83/1.03 (step @p165 :rule cnf_equiv_pos2 :args (@t266)) % 0.83/1.03 (step @p166 :rule reordering :premises (@p165) :args ((or @t263 @t267 (not @t266)))) % 0.83/1.03 (step @p167 :rule chain_m_resolution :premises (@p166 @p159 @p164) :args (@t267 @t268 (@list @t263 @t266))) % 0.83/1.03 (step @p168 :rule cnf_and_neg :args (@t265)) % 0.83/1.03 (step @p169 :rule reordering :premises (@p168) :args ((or (not @t256) @t265 @t269))) % 0.83/1.03 (step @p170 :rule chain_m_resolution :premises (@p169 @p154 @p167) :args (@t269 @t270 (@list @t256 @t265))) % 0.83/1.03 (step @p171 :rule cnf_or_pos :args (@t272)) % 0.83/1.03 (step @p172 :rule reordering :premises (@p171) :args ((or @t271 @t264 @t273))) % 0.83/1.03 (step @p173 :rule chain_m_resolution :premises (@p172 @p157 @p170) :args (@t273 @t270 (@list @t260 @t264))) % 0.83/1.03 (assume-push @p180 @t274) % 0.83/1.03 (step @p175 :rule instantiate :premises (@p163) :args ((@list tptp.x_a tptp.pname tptp.mgt_call tptp.pn tptp.u))) % 0.83/1.03 (step-pop @p181 :rule scope :premises (@p175)) % 0.83/1.03 (step @p176 :rule process_scope :premises (@p181) :args (@t272)) % 0.83/1.03 (step @p178 :rule implies_elim :premises (@p176)) % 0.83/1.03 (step @p179 false :rule chain_m_resolution :premises (@p178 @p173 @p163) :args (false @t268 (@list @t272 @t274))) % 0.83/1.03 ) % 0.83/1.03 % SZS output end Proof % 0.83/1.03 % cvc5 exiting %------------------------------------------------------------------------------