%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM924+5 : TPTP v9.2.1. Released v5.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n018.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 08:41:02 AM UTC 2026 % Result : Theorem 0.36s 0.73s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM924+5 : TPTP v9.2.1. Released v5.3.0. % 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n018.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 12:32:50 EDT 2026 % 0.16/0.34 % CPUTime : % 0.29/0.52 %----Proving TF0_NAR, FOF, or CNF % 0.36/0.73 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.36/0.73 % SZS status Theorem % 0.36/0.73 % SZS output start Proof % 0.36/0.73 ( % 0.36/0.73 (declare-sort $$unsorted 0) % 0.36/0.73 (declare-const tptp.ring_char_0 (-> $$unsorted Bool)) % 0.36/0.73 (declare-const tptp.linord581940658strict (-> $$unsorted Bool)) % 0.36/0.73 (declare-const tptp.ti (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.73 (declare-const tptp.zero_zero (-> $$unsorted $$unsorted)) % 0.36/0.73 (declare-const tptp.bit1 (-> $$unsorted $$unsorted)) % 0.36/0.73 (declare-const tptp.number (-> $$unsorted Bool)) % 0.36/0.73 (declare-const tptp.bit0 (-> $$unsorted $$unsorted)) % 0.36/0.73 (declare-const tptp.undefined (-> $$unsorted $$unsorted)) % 0.36/0.73 (declare-const tptp.pls $$unsorted) % 0.36/0.73 (declare-const tptp.linordered_idom (-> $$unsorted Bool)) % 0.36/0.73 (declare-const tptp.number_semiring (-> $$unsorted Bool)) % 0.36/0.73 (declare-const tptp.plus_plus (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.36/0.73 (declare-const tptp.times_times (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.36/0.73 (declare-const tptp.linordered_ring (-> $$unsorted Bool)) % 0.36/0.73 (declare-const tptp.semiring_1 (-> $$unsorted Bool)) % 0.36/0.73 (declare-const tptp.zprime (-> $$unsorted Bool)) % 0.36/0.73 (declare-const tptp.int $$unsorted) % 0.36/0.73 (declare-const tptp.ord_less_eq (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.36/0.73 (declare-const tptp.one_one (-> $$unsorted $$unsorted)) % 0.36/0.73 (declare-const tptp.number_number_of (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.73 (declare-const tptp.linorder (-> $$unsorted Bool)) % 0.36/0.73 (declare-const tptp.s $$unsorted) % 0.36/0.73 (declare-const tptp.power_power (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.36/0.73 (declare-const tptp.nat $$unsorted) % 0.36/0.73 (declare-const tptp.number_ring (-> $$unsorted Bool)) % 0.36/0.73 (declare-const tptp.twoSqu33214720sum2sq (-> $$unsorted Bool)) % 0.36/0.73 (declare-const tptp.semiring (-> $$unsorted Bool)) % 0.36/0.73 (declare-const tptp.m $$unsorted) % 0.36/0.73 (declare-const tptp.ord_less (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.36/0.73 (declare-const tptp.t $$unsorted) % 0.36/0.73 (declare-const tptp.ring_11004092258visors (-> $$unsorted Bool)) % 0.36/0.73 (define @t1 () (@var "X_a" $$unsorted)) % 0.36/0.73 (define @t2 () (tptp.one_one @t1)) % 0.36/0.73 (define @t3 () (tptp.semiring_1 @t1)) % 0.36/0.73 (define @t4 () (@list @t1)) % 0.36/0.73 (define @t5 () (@var "B_2" $$unsorted)) % 0.36/0.73 (define @t6 () (@var "B_1" $$unsorted)) % 0.36/0.73 (define @t7 () (@var "X_b" $$unsorted)) % 0.36/0.73 (define @t8 () (tptp.plus_plus @t7 @t6 @t5)) % 0.36/0.73 (define @t9 () (tptp.ti @t7 @t6)) % 0.36/0.73 (define @t10 () (and (tptp.number @t7) (tptp.semiring @t7))) % 0.36/0.73 (define @t11 () (@list @t6 @t5 @t7)) % 0.36/0.73 (define @t12 () (tptp.ti @t7 @t5)) % 0.36/0.73 (define @t13 () (tptp.plus_plus @t1 @t6 @t5)) % 0.36/0.73 (define @t14 () (tptp.ti @t1 @t6)) % 0.36/0.73 (define @t15 () (tptp.linordered_ring @t1)) % 0.36/0.73 (define @t16 () (@list @t6 @t5 @t1)) % 0.36/0.73 (define @t17 () (tptp.ti @t1 @t5)) % 0.36/0.73 (define @t18 () (tptp.times_times @t7 @t6 @t5)) % 0.36/0.73 (define @t19 () (tptp.times_times @t1 @t6 @t5)) % 0.36/0.73 (define @t20 () (tptp.zero_zero @t1)) % 0.36/0.73 (define @t21 () (= (tptp.ti @t1 @t20) @t20)) % 0.36/0.73 (define @t22 () (tptp.undefined @t1)) % 0.36/0.73 (define @t23 () (tptp.ti tptp.int @t6)) % 0.36/0.73 (define @t24 () (@list @t6)) % 0.36/0.73 (define @t25 () (tptp.bit0 @t6)) % 0.36/0.73 (define @t26 () (tptp.bit1 @t6)) % 0.36/0.73 (define @t27 () (tptp.number_number_of @t1 @t6)) % 0.36/0.73 (define @t28 () (tptp.number @t1)) % 0.36/0.73 (define @t29 () (@list @t6 @t1)) % 0.36/0.73 (define @t30 () (tptp.ord_less @t1 @t6 @t5)) % 0.36/0.73 (define @t31 () (= (tptp.ord_less @t1 @t14 @t5) @t30)) % 0.36/0.73 (define @t32 () (and @t28 (tptp.linorder @t1))) % 0.36/0.73 (define @t33 () (= (tptp.ord_less @t1 @t6 @t17) @t30)) % 0.36/0.73 (define @t34 () (tptp.linordered_idom @t1)) % 0.36/0.73 (define @t35 () (tptp.ord_less_eq @t1 @t6 @t5)) % 0.36/0.73 (define @t36 () (= (tptp.ord_less_eq @t1 @t14 @t5) @t35)) % 0.36/0.73 (define @t37 () (= (tptp.ord_less_eq @t1 @t6 @t17) @t35)) % 0.36/0.73 (define @t38 () (tptp.power_power @t1 @t6 @t5)) % 0.36/0.73 (define @t39 () (tptp.zero_zero tptp.int)) % 0.36/0.73 (define @t40 () (tptp.one_one tptp.int)) % 0.36/0.73 (define @t41 () (tptp.bit1 tptp.pls)) % 0.36/0.73 (define @t42 () (tptp.bit0 @t41)) % 0.36/0.73 (define @t43 () (tptp.plus_plus tptp.int (tptp.times_times tptp.int (tptp.number_number_of tptp.int (tptp.bit0 @t42)) tptp.m) @t40)) % 0.36/0.73 (define @t44 () (tptp.times_times tptp.int @t43 @t39)) % 0.36/0.73 (define @t45 () (tptp.times_times tptp.int @t43 tptp.t)) % 0.36/0.73 (define @t46 () (tptp.ord_less tptp.int @t45 @t44)) % 0.36/0.73 (define @t47 () (tptp.number_number_of tptp.nat @t42)) % 0.36/0.73 (define @t48 () (tptp.plus_plus tptp.int (tptp.power_power tptp.int tptp.s @t47) @t40)) % 0.36/0.73 (define @t49 () (@var "Y" $$unsorted)) % 0.36/0.73 (define @t50 () (@var "X" $$unsorted)) % 0.36/0.73 (define @t51 () (@list @t50 @t49)) % 0.36/0.73 (define @t52 () (@var "Y_1" $$unsorted)) % 0.36/0.73 (define @t53 () (= (tptp.ti @t1 @t52) @t20)) % 0.36/0.73 (define @t54 () (@var "X_1" $$unsorted)) % 0.36/0.73 (define @t55 () (tptp.ti @t1 @t54)) % 0.36/0.73 (define @t56 () (= @t55 @t20)) % 0.36/0.73 (define @t57 () (tptp.plus_plus @t1 (tptp.power_power @t1 @t54 @t47) (tptp.power_power @t1 @t52 @t47))) % 0.36/0.73 (define @t58 () (@list @t54 @t52)) % 0.36/0.73 (define @t59 () (and @t56 @t53)) % 0.36/0.73 (define @t60 () (@var "A_1" $$unsorted)) % 0.36/0.73 (define @t61 () (@var "A_2" $$unsorted)) % 0.36/0.73 (define @t62 () (= (tptp.ti @t1 @t61) @t20)) % 0.36/0.73 (define @t63 () (tptp.power_power @t1 @t61 @t47)) % 0.36/0.73 (define @t64 () (@list @t61)) % 0.36/0.73 (define @t65 () (@var "W" $$unsorted)) % 0.36/0.73 (define @t66 () (tptp.number_number_of @t1 @t65)) % 0.36/0.73 (define @t67 () (@list @t65)) % 0.36/0.73 (define @t68 () (tptp.number_ring @t1)) % 0.36/0.73 (define @t69 () (@var "V" $$unsorted)) % 0.36/0.73 (define @t70 () (tptp.number_number_of @t1 @t69)) % 0.36/0.73 (define @t71 () (@var "T_1" $$unsorted)) % 0.36/0.73 (define @t72 () (@var "K_1" $$unsorted)) % 0.36/0.73 (define @t73 () (tptp.number_number_of tptp.int @t72)) % 0.36/0.73 (define @t74 () (forall (@list @t72) (= @t73 @t72))) % 0.36/0.73 (define @t75 () (@var "Z" $$unsorted)) % 0.36/0.73 (define @t76 () (@list @t75 @t65)) % 0.36/0.73 (define @t77 () (tptp.ord_less_eq tptp.int @t65 @t75)) % 0.36/0.73 (define @t78 () (tptp.ord_less_eq tptp.int @t75 @t65)) % 0.36/0.73 (define @t79 () (tptp.times_times tptp.int @t69 @t65)) % 0.36/0.73 (define @t80 () (tptp.number_number_of tptp.int @t65)) % 0.36/0.73 (define @t81 () (tptp.number_number_of tptp.int @t69)) % 0.36/0.73 (define @t82 () (@list @t69 @t65)) % 0.36/0.73 (define @t83 () (@var "L" $$unsorted)) % 0.36/0.73 (define @t84 () (@var "K" $$unsorted)) % 0.36/0.73 (define @t85 () (tptp.ord_less_eq tptp.int @t84 @t83)) % 0.36/0.73 (define @t86 () (tptp.number_number_of tptp.int @t83)) % 0.36/0.73 (define @t87 () (tptp.number_number_of tptp.int @t84)) % 0.36/0.73 (define @t88 () (@list @t84 @t83)) % 0.36/0.73 (define @t89 () (tptp.number_number_of @t1 @t52)) % 0.36/0.73 (define @t90 () (tptp.number_number_of @t1 @t54)) % 0.36/0.73 (define @t91 () (and @t68 @t34)) % 0.36/0.73 (define @t92 () (@var "Z3" $$unsorted)) % 0.36/0.73 (define @t93 () (@var "Z2" $$unsorted)) % 0.36/0.73 (define @t94 () (@var "Z1" $$unsorted)) % 0.36/0.73 (define @t95 () (@list @t94 @t93 @t92)) % 0.36/0.73 (define @t96 () (@var "I" $$unsorted)) % 0.36/0.73 (define @t97 () (@var "J" $$unsorted)) % 0.36/0.73 (define @t98 () (tptp.ord_less_eq tptp.int @t96 @t97)) % 0.36/0.73 (define @t99 () (@list @t72 @t96 @t97)) % 0.36/0.73 (define @t100 () (@list @t50 @t49 @t75)) % 0.36/0.73 (define @t101 () (@var "K2" $$unsorted)) % 0.36/0.73 (define @t102 () (@var "K1" $$unsorted)) % 0.36/0.73 (define @t103 () (tptp.ord_less_eq tptp.int @t102 @t101)) % 0.36/0.73 (define @t104 () (tptp.bit1 @t101)) % 0.36/0.73 (define @t105 () (tptp.bit1 @t102)) % 0.36/0.73 (define @t106 () (@list @t102 @t101)) % 0.36/0.73 (define @t107 () (tptp.bit1 @t83)) % 0.36/0.73 (define @t108 () (tptp.bit1 @t84)) % 0.36/0.73 (define @t109 () (tptp.bit0 @t101)) % 0.36/0.73 (define @t110 () (tptp.bit0 @t102)) % 0.36/0.73 (define @t111 () (tptp.bit0 @t83)) % 0.36/0.73 (define @t112 () (tptp.bit0 @t84)) % 0.36/0.73 (define @t113 () (@var "W_1" $$unsorted)) % 0.36/0.73 (define @t114 () (@var "Z_1" $$unsorted)) % 0.36/0.73 (define @t115 () (@var "V_3" $$unsorted)) % 0.36/0.73 (define @t116 () (tptp.ord_less_eq tptp.int @t115 tptp.pls)) % 0.36/0.73 (define @t117 () (tptp.zero_zero tptp.nat)) % 0.36/0.73 (define @t118 () (tptp.number_number_of tptp.nat @t115)) % 0.36/0.73 (define @t119 () (@list @t115)) % 0.36/0.73 (define @t120 () (@var "V_1" $$unsorted)) % 0.36/0.73 (define @t121 () (tptp.number_number_of @t1 @t120)) % 0.36/0.73 (define @t122 () (tptp.ord_less_eq tptp.int tptp.pls @t120)) % 0.36/0.73 (define @t123 () (tptp.ord_less_eq tptp.int tptp.pls @t69)) % 0.36/0.73 (define @t124 () (@list @t120 @t69)) % 0.36/0.73 (define @t125 () (tptp.number_semiring @t1)) % 0.36/0.73 (define @t126 () (tptp.number_number_of @t1 @t79)) % 0.36/0.73 (define @t127 () (tptp.times_times @t1 @t70 @t66)) % 0.36/0.73 (define @t128 () (tptp.plus_plus @t1 (tptp.times_times @t1 @t54 @t54) (tptp.times_times @t1 @t52 @t52))) % 0.36/0.73 (define @t129 () (tptp.linord581940658strict @t1)) % 0.36/0.73 (define @t130 () (@list @t54)) % 0.36/0.73 (define @t131 () (@list @t52)) % 0.36/0.73 (define @t132 () (tptp.number_number_of @t1 @t115)) % 0.36/0.73 (define @t133 () (tptp.number_number_of @t1 @t113)) % 0.36/0.73 (define @t134 () (tptp.ord_less_eq tptp.int tptp.pls @t84)) % 0.36/0.73 (define @t135 () (@list @t84)) % 0.36/0.73 (define @t136 () (tptp.plus_plus tptp.int @t65 @t75)) % 0.36/0.73 (define @t137 () (@var "Z_2" $$unsorted)) % 0.36/0.73 (define @t138 () (@var "W_2" $$unsorted)) % 0.36/0.73 (define @t139 () (tptp.number_number_of tptp.nat tptp.pls)) % 0.36/0.73 (define @t140 () (tptp.one_one tptp.nat)) % 0.36/0.73 (define @t141 () (tptp.times_times tptp.int tptp.pls @t65)) % 0.36/0.73 (define @t142 () (forall @t67 (= @t141 tptp.pls))) % 0.36/0.73 (define @t143 () (@var "L_1" $$unsorted)) % 0.36/0.73 (define @t144 () (tptp.ord_less tptp.int @t84 @t83)) % 0.36/0.73 (define @t145 () (@list @t75)) % 0.36/0.73 (define @t146 () (tptp.plus_plus tptp.int @t94 @t93)) % 0.36/0.73 (define @t147 () (@var "V_2" $$unsorted)) % 0.36/0.73 (define @t148 () (tptp.ord_less tptp.int @t115 @t147)) % 0.36/0.73 (define @t149 () (tptp.number_number_of tptp.nat @t41)) % 0.36/0.73 (define @t150 () (tptp.ord_less_eq tptp.int (tptp.plus_plus tptp.int @t65 @t40) @t75)) % 0.36/0.73 (define @t151 () (tptp.ord_less tptp.int @t65 @t75)) % 0.36/0.73 (define @t152 () (forall (@list @t65 @t75) (=> @t151 @t150))) % 0.36/0.73 (define @t153 () (@list @t113 @t114)) % 0.36/0.73 (define @t154 () (forall @t153 (= (tptp.ord_less_eq tptp.int (tptp.plus_plus tptp.int @t113 @t40) @t114) (tptp.ord_less tptp.int @t113 @t114)))) % 0.36/0.73 (define @t155 () (tptp.plus_plus tptp.int @t69 @t120)) % 0.36/0.73 (define @t156 () (tptp.number_number_of tptp.nat @t120)) % 0.36/0.73 (define @t157 () (tptp.number_number_of tptp.nat @t69)) % 0.36/0.73 (define @t158 () (tptp.plus_plus tptp.nat @t157 @t156)) % 0.36/0.73 (define @t159 () (tptp.ord_less tptp.int @t120 tptp.pls)) % 0.36/0.73 (define @t160 () (tptp.ord_less tptp.int @t69 tptp.pls)) % 0.36/0.73 (define @t161 () (= @t84 @t83)) % 0.36/0.73 (define @t162 () (tptp.number_number_of @t7 @t69)) % 0.36/0.73 (define @t163 () (@var "B" $$unsorted)) % 0.36/0.73 (define @t164 () (@list @t7)) % 0.36/0.73 (define @t165 () (@var "C" $$unsorted)) % 0.36/0.73 (define @t166 () (@var "A" $$unsorted)) % 0.36/0.73 (define @t167 () (@var "T" $$unsorted)) % 0.36/0.73 (define @t168 () (tptp.ti @t167 @t166)) % 0.36/0.73 (define @t169 () (tptp.ord_less tptp.int @t48 @t39)) % 0.36/0.73 (define @t170 () (tptp.ord_less_eq tptp.int (tptp.plus_plus tptp.int @t45 @t40) @t44)) % 0.36/0.73 (define @t171 () (not @t46)) % 0.36/0.73 (define @t172 () (or @t171 @t170)) % 0.36/0.73 (define @t173 () (tptp.plus_plus tptp.int @t48 @t40)) % 0.36/0.73 (define @t174 () (tptp.ord_less_eq tptp.int @t173 @t39)) % 0.36/0.73 (define @t175 () (= @t174 @t169)) % 0.36/0.73 (define @t176 () (= @t169 @t174)) % 0.36/0.73 (define @t177 () (not @t174)) % 0.36/0.73 (assume @p1 (forall @t4 (=> @t3 (= (tptp.ti @t1 @t2) @t2)))) % 0.36/0.73 (assume @p2 (forall @t11 (=> @t10 (= (tptp.plus_plus @t7 @t9 @t5) @t8)))) % 0.36/0.73 (assume @p3 (forall @t11 (=> @t10 (= (tptp.plus_plus @t7 @t6 @t12) @t8)))) % 0.36/0.73 (assume @p4 (forall @t11 (=> @t10 (= (tptp.ti @t7 @t8) @t8)))) % 0.36/0.73 (assume @p5 (forall @t16 (=> @t15 (= (tptp.plus_plus @t1 @t14 @t5) @t13)))) % 0.36/0.73 (assume @p6 (forall @t16 (=> @t15 (= (tptp.plus_plus @t1 @t6 @t17) @t13)))) % 0.36/0.73 (assume @p7 (forall @t16 (=> @t15 (= (tptp.ti @t1 @t13) @t13)))) % 0.36/0.73 (assume @p8 (forall @t11 (=> @t10 (= (tptp.times_times @t7 @t9 @t5) @t18)))) % 0.36/0.73 (assume @p9 (forall @t11 (=> @t10 (= (tptp.times_times @t7 @t6 @t12) @t18)))) % 0.36/0.73 (assume @p10 (forall @t11 (=> @t10 (= (tptp.ti @t7 @t18) @t18)))) % 0.36/0.73 (assume @p11 (forall @t16 (=> @t15 (= (tptp.times_times @t1 @t14 @t5) @t19)))) % 0.36/0.73 (assume @p12 (forall @t16 (=> @t15 (= (tptp.times_times @t1 @t6 @t17) @t19)))) % 0.36/0.73 (assume @p13 (forall @t16 (=> @t15 (= (tptp.ti @t1 @t19) @t19)))) % 0.36/0.73 (assume @p14 (forall @t4 (=> @t15 @t21))) % 0.36/0.73 (assume @p15 (forall @t4 (=> @t3 @t21))) % 0.36/0.73 (assume @p16 (forall @t4 (= (tptp.ti @t1 @t22) @t22))) % 0.36/0.73 (assume @p17 (forall @t24 (= (tptp.zprime @t23) (tptp.zprime @t6)))) % 0.36/0.73 (assume @p18 (forall @t24 (= (tptp.bit0 @t23) @t25))) % 0.36/0.73 (assume @p19 (forall @t24 (= (tptp.ti tptp.int @t25) @t25))) % 0.36/0.73 (assume @p20 (forall @t24 (= (tptp.bit1 @t23) @t26))) % 0.36/0.73 (assume @p21 (forall @t24 (= (tptp.ti tptp.int @t26) @t26))) % 0.36/0.73 (assume @p22 (= (tptp.ti tptp.int tptp.pls) tptp.pls)) % 0.36/0.73 (assume @p23 (forall @t29 (=> @t28 (= (tptp.number_number_of @t1 @t23) @t27)))) % 0.36/0.73 (assume @p24 (forall @t29 (=> @t28 (= (tptp.ti @t1 @t27) @t27)))) % 0.36/0.73 (assume @p25 (forall @t16 (=> @t32 @t31))) % 0.36/0.73 (assume @p26 (forall @t16 (=> @t32 @t33))) % 0.36/0.73 (assume @p27 (forall @t16 (=> @t34 @t31))) % 0.36/0.73 (assume @p28 (forall @t16 (=> @t34 @t33))) % 0.36/0.73 (assume @p29 (forall @t16 (=> @t32 @t36))) % 0.36/0.73 (assume @p30 (forall @t16 (=> @t32 @t37))) % 0.36/0.73 (assume @p31 (forall @t16 (=> @t15 @t36))) % 0.36/0.73 (assume @p32 (forall @t16 (=> @t15 @t37))) % 0.36/0.73 (assume @p33 (forall @t16 (=> @t3 (= (tptp.power_power @t1 @t14 @t5) @t38)))) % 0.36/0.73 (assume @p34 (forall @t16 (=> @t3 (= (tptp.power_power @t1 @t6 (tptp.ti tptp.nat @t5)) @t38)))) % 0.36/0.73 (assume @p35 (forall @t16 (=> @t3 (= (tptp.ti @t1 @t38) @t38)))) % 0.36/0.73 (assume @p36 (forall @t24 (= (tptp.twoSqu33214720sum2sq @t23) (tptp.twoSqu33214720sum2sq @t6)))) % 0.36/0.73 (assume @p37 (= (tptp.ti tptp.int tptp.m) tptp.m)) % 0.36/0.73 (assume @p38 (= (tptp.ti tptp.int tptp.s) tptp.s)) % 0.36/0.73 (assume @p39 (= (tptp.ti tptp.int tptp.t) tptp.t)) % 0.36/0.73 (assume @p40 (tptp.ord_less tptp.int tptp.t @t39)) % 0.36/0.73 (assume @p41 (tptp.ord_less tptp.int tptp.t @t40)) % 0.36/0.73 (assume @p42 @t46) % 0.36/0.73 (assume @p43 (= @t48 @t45)) % 0.36/0.73 (assume @p44 (=> (= tptp.t @t39) (= @t48 @t39))) % 0.36/0.73 (assume @p45 (not (tptp.ord_less_eq tptp.int @t40 tptp.t))) % 0.36/0.73 (assume @p46 (tptp.ord_less tptp.int @t39 @t43)) % 0.36/0.73 (assume @p47 (forall @t4 (=> @t34 (forall @t51 (not (tptp.ord_less @t1 (tptp.plus_plus @t1 (tptp.power_power @t1 @t50 @t47) (tptp.power_power @t1 @t49 @t47)) @t20)))))) % 0.36/0.73 (assume @p48 (forall @t4 (=> @t34 (forall @t58 (= (tptp.ord_less @t1 @t20 @t57) (or (not @t56) (not @t53))))))) % 0.36/0.73 (assume @p49 (forall @t4 (=> @t34 (forall @t58 (= (= @t57 @t20) @t59))))) % 0.36/0.73 (assume @p50 (forall @t4 (=> @t34 (forall (@list @t60) (not (tptp.ord_less @t1 (tptp.power_power @t1 @t60 @t47) @t20)))))) % 0.36/0.73 (assume @p51 (forall @t4 (=> @t34 (forall @t64 (= (tptp.ord_less @t1 @t20 @t63) (not @t62)))))) % 0.36/0.73 (assume @p52 (forall @t4 (=> @t3 (= (tptp.power_power @t1 @t2 @t47) @t2)))) % 0.36/0.73 (assume @p53 (forall @t4 (=> @t3 (= (tptp.power_power @t1 @t20 @t47) @t20)))) % 0.36/0.73 (assume @p54 (forall @t4 (=> (tptp.ring_11004092258visors @t1) (forall @t64 (= (= @t63 @t20) @t62))))) % 0.36/0.73 (assume @p55 (forall @t4 (=> @t68 (forall @t67 (= (tptp.plus_plus @t1 @t2 @t66) (tptp.number_number_of @t1 (tptp.plus_plus tptp.int @t41 @t65))))))) % 0.36/0.73 (assume @p56 (forall @t4 (=> @t68 (forall (@list @t69) (= (tptp.plus_plus @t1 @t70 @t2) (tptp.number_number_of @t1 (tptp.plus_plus tptp.int @t69 @t41))))))) % 0.36/0.73 (assume @p57 (tptp.ord_less tptp.int tptp.t @t43)) % 0.36/0.73 (assume @p58 (not (forall (@list @t71) (not (= @t48 (tptp.times_times tptp.int @t43 @t71)))))) % 0.36/0.73 (assume @p59 (tptp.zprime @t43)) % 0.36/0.73 (assume @p60 (tptp.twoSqu33214720sum2sq @t45)) % 0.36/0.73 (assume @p61 (forall @t67 (tptp.ord_less_eq tptp.int @t65 @t65))) % 0.36/0.73 (assume @p62 @t74) % 0.36/0.73 (assume @p63 (forall @t76 (= (tptp.times_times tptp.int @t75 @t65) (tptp.times_times tptp.int @t65 @t75)))) % 0.36/0.73 (assume @p64 (forall @t76 (or @t78 @t77))) % 0.36/0.73 (assume @p65 (forall @t82 (= (tptp.times_times tptp.int @t81 @t80) (tptp.number_number_of tptp.int @t79)))) % 0.36/0.73 (assume @p66 (forall @t88 (= (tptp.ord_less_eq tptp.int @t87 @t86) @t85))) % 0.36/0.73 (assume @p67 (forall @t4 (=> @t91 (forall @t58 (= (tptp.ord_less_eq @t1 @t90 @t89) (tptp.ord_less_eq tptp.int @t54 @t52)))))) % 0.36/0.73 (assume @p68 (forall @t95 (= (tptp.times_times tptp.int (tptp.times_times tptp.int @t94 @t93) @t92) (tptp.times_times tptp.int @t94 (tptp.times_times tptp.int @t93 @t92))))) % 0.36/0.73 (assume @p69 (forall @t99 (=> @t98 (=> (tptp.ord_less_eq tptp.int @t97 @t72) (tptp.ord_less_eq tptp.int @t96 @t72))))) % 0.36/0.73 (assume @p70 (forall @t76 (=> @t78 (=> @t77 (= @t75 @t65))))) % 0.36/0.73 (assume @p71 (forall @t100 (= (tptp.power_power tptp.int @t50 (tptp.plus_plus tptp.nat @t49 @t75)) (tptp.times_times tptp.int (tptp.power_power tptp.int @t50 @t49) (tptp.power_power tptp.int @t50 @t75))))) % 0.36/0.73 (assume @p72 (forall @t106 (= (tptp.ord_less_eq tptp.int @t105 @t104) @t103))) % 0.36/0.74 (assume @p73 (forall @t88 (= (tptp.ord_less_eq tptp.int @t108 @t107) @t85))) % 0.36/0.74 (assume @p74 (tptp.ord_less_eq tptp.int tptp.pls tptp.pls)) % 0.36/0.74 (assume @p75 (forall @t106 (= (tptp.ord_less_eq tptp.int @t110 @t109) @t103))) % 0.36/0.74 (assume @p76 (forall @t88 (= (tptp.ord_less_eq tptp.int @t112 @t111) @t85))) % 0.36/0.74 (assume @p77 (forall (@list @t114 @t113) (= (tptp.ord_less tptp.int @t114 @t113) (and (tptp.ord_less_eq tptp.int @t114 @t113) (not (= @t114 @t113)))))) % 0.36/0.74 (assume @p78 (forall @t99 (=> @t98 (tptp.ord_less_eq tptp.int (tptp.plus_plus tptp.int @t72 @t96) (tptp.plus_plus tptp.int @t72 @t97))))) % 0.36/0.74 (assume @p79 (forall @t119 (= (= @t118 @t117) @t116))) % 0.36/0.74 (assume @p80 (forall @t119 (= (= @t117 @t118) @t116))) % 0.36/0.74 (assume @p81 (forall @t4 (=> @t125 (forall @t124 (=> @t123 (=> @t122 (= (tptp.times_times @t1 @t70 @t121) (tptp.number_number_of @t1 (tptp.times_times tptp.int @t69 @t120))))))))) % 0.36/0.74 (assume @p82 (forall @t4 (=> @t68 (forall (@list @t69 @t65 @t75) (= (tptp.times_times @t1 @t70 (tptp.times_times @t1 @t66 @t75)) (tptp.times_times @t1 @t126 @t75)))))) % 0.36/0.74 (assume @p83 (forall @t4 (=> @t68 (forall @t82 (= @t127 @t126))))) % 0.36/0.74 (assume @p84 (forall @t4 (=> @t68 (forall @t82 (= @t126 @t127))))) % 0.36/0.74 (assume @p85 (forall @t4 (=> @t129 (forall @t58 (= (tptp.ord_less_eq @t1 @t128 @t20) @t59))))) % 0.36/0.74 (assume @p86 (forall @t4 (=> @t15 (forall @t51 (tptp.ord_less_eq @t1 @t20 (tptp.plus_plus @t1 (tptp.times_times @t1 @t50 @t50) (tptp.times_times @t1 @t49 @t49))))))) % 0.36/0.74 (assume @p87 (forall @t4 (=> @t91 (forall @t130 (= (tptp.ord_less_eq @t1 @t90 @t20) (tptp.ord_less_eq tptp.int @t54 tptp.pls)))))) % 0.36/0.74 (assume @p88 (forall @t4 (=> @t91 (forall @t131 (= (tptp.ord_less_eq @t1 @t20 @t89) (tptp.ord_less_eq tptp.int tptp.pls @t52)))))) % 0.36/0.74 (assume @p89 (forall @t119 (= (tptp.ord_less tptp.nat @t117 @t118) (tptp.ord_less tptp.int tptp.pls @t115)))) % 0.36/0.74 (assume @p90 (forall @t4 (=> @t32 (forall (@list @t115 @t113) (= (tptp.ord_less_eq @t1 @t132 @t133) (not (tptp.ord_less @t1 @t133 @t132))))))) % 0.36/0.74 (assume @p91 (forall @t135 (= (tptp.ord_less_eq tptp.int tptp.pls @t108) @t134))) % 0.36/0.74 (assume @p92 (forall @t106 (= (tptp.ord_less_eq tptp.int @t110 @t104) @t103))) % 0.36/0.74 (assume @p93 (forall @t88 (= (tptp.ord_less_eq tptp.int @t112 @t107) @t85))) % 0.36/0.74 (assume @p94 (forall @t135 (= (tptp.ord_less_eq tptp.int @t112 tptp.pls) (tptp.ord_less_eq tptp.int @t84 tptp.pls)))) % 0.36/0.74 (assume @p95 (forall @t135 (= (tptp.ord_less_eq tptp.int tptp.pls @t112) @t134))) % 0.36/0.74 (assume @p96 (forall (@list @t137 @t75 @t138 @t65) (=> (tptp.ord_less tptp.int @t138 @t65) (=> (tptp.ord_less_eq tptp.int @t137 @t75) (tptp.ord_less tptp.int (tptp.plus_plus tptp.int @t138 @t137) @t136))))) % 0.36/0.74 (assume @p97 (= @t139 @t117)) % 0.36/0.74 (assume @p98 (= @t117 @t139)) % 0.36/0.74 (assume @p99 (forall @t4 (=> @t91 (forall @t130 (= (tptp.ord_less_eq @t1 @t90 @t2) (tptp.ord_less_eq tptp.int @t54 @t41)))))) % 0.36/0.74 (assume @p100 (forall @t4 (=> @t91 (forall @t131 (= (tptp.ord_less_eq @t1 @t2 @t89) (tptp.ord_less_eq tptp.int @t41 @t52)))))) % 0.36/0.74 (assume @p101 (= (tptp.plus_plus tptp.nat @t140 @t140) @t47)) % 0.36/0.74 (assume @p102 @t142) % 0.36/0.74 (assume @p103 (forall (@list @t72 @t143) (= (tptp.times_times tptp.int (tptp.bit0 @t72) @t143) (tptp.bit0 (tptp.times_times tptp.int @t72 @t143))))) % 0.36/0.74 (assume @p104 (forall @t88 (= (tptp.ord_less tptp.int @t87 @t86) @t144))) % 0.36/0.74 (assume @p105 (forall @t145 (= (tptp.times_times tptp.int @t75 @t40) @t75))) % 0.36/0.74 (assume @p106 (forall @t145 (= (tptp.times_times tptp.int @t40 @t75) @t75))) % 0.36/0.74 (assume @p107 (forall @t82 (= (tptp.plus_plus tptp.int @t81 @t80) (tptp.number_number_of tptp.int (tptp.plus_plus tptp.int @t69 @t65))))) % 0.36/0.74 (assume @p108 (forall (@list @t94 @t93 @t65) (= (tptp.times_times tptp.int @t146 @t65) (tptp.plus_plus tptp.int (tptp.times_times tptp.int @t94 @t65) (tptp.times_times tptp.int @t93 @t65))))) % 0.36/0.74 (assume @p109 (forall (@list @t65 @t94 @t93) (= (tptp.times_times tptp.int @t65 @t146) (tptp.plus_plus tptp.int (tptp.times_times tptp.int @t65 @t94) (tptp.times_times tptp.int @t65 @t93))))) % 0.36/0.74 (assume @p110 (forall @t135 (= (tptp.ord_less_eq tptp.int @t108 tptp.pls) (tptp.ord_less tptp.int @t84 tptp.pls)))) % 0.36/0.74 (assume @p111 (forall @t135 (= (tptp.ord_less tptp.int tptp.pls @t108) @t134))) % 0.36/0.74 (assume @p112 (forall @t106 (= (tptp.ord_less_eq tptp.int @t105 @t109) (tptp.ord_less tptp.int @t102 @t101)))) % 0.36/0.74 (assume @p113 (forall @t88 (= (tptp.ord_less_eq tptp.int @t108 @t111) @t144))) % 0.36/0.74 (assume @p114 (forall @t106 (= (tptp.ord_less tptp.int @t110 @t104) @t103))) % 0.36/0.74 (assume @p115 (forall @t88 (= (tptp.ord_less tptp.int @t112 @t107) @t85))) % 0.36/0.74 (assume @p116 (forall (@list @t115 @t147) (= (tptp.ord_less tptp.nat @t118 (tptp.number_number_of tptp.nat @t147)) (and (=> @t148 (tptp.ord_less tptp.int tptp.pls @t147)) @t148)))) % 0.36/0.74 (assume @p117 (forall (@list @t114) (= (tptp.ord_less_eq tptp.int @t40 @t114) (tptp.ord_less tptp.int @t39 @t114)))) % 0.36/0.74 (assume @p118 (= @t149 @t140)) % 0.36/0.74 (assume @p119 (= @t140 @t149)) % 0.36/0.74 (assume @p120 @t152) % 0.36/0.74 (assume @p121 @t154) % 0.36/0.74 (assume @p122 (forall @t153 (= (tptp.ord_less tptp.int @t113 (tptp.plus_plus tptp.int @t114 @t40)) (tptp.ord_less_eq tptp.int @t113 @t114)))) % 0.36/0.74 (assume @p123 (forall @t4 (=> @t125 (forall @t124 (=> @t123 (=> @t122 (= (tptp.plus_plus @t1 @t70 @t121) (tptp.number_number_of @t1 @t155)))))))) % 0.36/0.74 (assume @p124 (forall @t124 (and (=> @t160 (= @t158 @t156)) (=> (not @t160) (and (=> @t159 (= @t158 @t157)) (=> (not @t159) (= @t158 (tptp.number_number_of tptp.nat @t155)))))))) % 0.36/0.74 (assume @p125 (forall @t145 (=> (tptp.ord_less_eq tptp.int @t39 @t75) (tptp.ord_less tptp.int @t39 (tptp.plus_plus tptp.int @t40 @t75))))) % 0.36/0.74 (assume @p126 (forall @t4 (=> (and @t68 (tptp.ring_char_0 @t1)) (forall @t58 (= (= @t90 @t89) (= @t54 @t52)))))) % 0.36/0.74 (assume @p127 (forall @t4 (=> @t28 (forall (@list @t113 @t54) (= (= @t133 @t55) (= @t55 @t133)))))) % 0.36/0.74 (assume @p128 (forall @t88 (= (= @t108 @t107) @t161))) % 0.36/0.74 (assume @p129 (forall @t88 (= (= @t112 @t111) @t161))) % 0.36/0.74 (assume @p130 (forall @t51 (or (tptp.ord_less tptp.int @t50 @t49) (= @t50 @t49) (tptp.ord_less tptp.int @t49 @t50)))) % 0.36/0.74 (assume @p131 (forall @t4 (=> @t129 (forall @t58 (= (= @t128 @t20) @t59))))) % 0.36/0.74 (assume @p132 (forall @t164 (=> @t10 (forall (@list @t60 @t163 @t69) (= (tptp.times_times @t7 (tptp.plus_plus @t7 @t60 @t163) @t162) (tptp.plus_plus @t7 (tptp.times_times @t7 @t60 @t162) (tptp.times_times @t7 @t163 @t162))))))) % 0.36/0.74 (assume @p133 (forall @t164 (=> @t10 (forall (@list @t69 @t163 @t165) (= (tptp.times_times @t7 @t162 (tptp.plus_plus @t7 @t163 @t165)) (tptp.plus_plus @t7 (tptp.times_times @t7 @t162 @t163) (tptp.times_times @t7 @t162 @t165))))))) % 0.36/0.74 (assume @p134 (forall @t95 (= (tptp.plus_plus tptp.int @t146 @t92) (tptp.plus_plus tptp.int @t94 (tptp.plus_plus tptp.int @t93 @t92))))) % 0.36/0.74 (assume @p135 (forall @t100 (= (tptp.plus_plus tptp.int @t50 (tptp.plus_plus tptp.int @t49 @t75)) (tptp.plus_plus tptp.int @t49 (tptp.plus_plus tptp.int @t50 @t75))))) % 0.36/0.74 (assume @p136 (forall @t76 (= (tptp.plus_plus tptp.int @t75 @t65) @t136))) % 0.36/0.74 (assume @p137 (= @t39 (tptp.number_number_of tptp.int tptp.pls))) % 0.36/0.74 (assume @p138 (tptp.ring_11004092258visors tptp.int)) % 0.36/0.74 (assume @p139 (tptp.linord581940658strict tptp.int)) % 0.36/0.74 (assume @p140 (tptp.linordered_ring tptp.int)) % 0.36/0.74 (assume @p141 (tptp.linordered_idom tptp.int)) % 0.36/0.74 (assume @p142 (tptp.number_semiring tptp.int)) % 0.36/0.74 (assume @p143 (tptp.linorder tptp.int)) % 0.36/0.74 (assume @p144 (tptp.semiring_1 tptp.int)) % 0.36/0.74 (assume @p145 (tptp.ring_char_0 tptp.int)) % 0.36/0.74 (assume @p146 (tptp.number_ring tptp.int)) % 0.36/0.74 (assume @p147 (tptp.semiring tptp.int)) % 0.36/0.74 (assume @p148 (tptp.number tptp.int)) % 0.36/0.74 (assume @p149 (tptp.number_semiring tptp.nat)) % 0.36/0.74 (assume @p150 (tptp.linorder tptp.nat)) % 0.36/0.74 (assume @p151 (tptp.semiring_1 tptp.nat)) % 0.36/0.74 (assume @p152 (tptp.semiring tptp.nat)) % 0.36/0.74 (assume @p153 (tptp.number tptp.nat)) % 0.36/0.74 (assume @p154 (forall (@list @t167 @t166) (= (tptp.ti @t167 @t168) @t168))) % 0.36/0.74 (assume @p155 (not @t169)) % 0.36/0.74 (assume @p156 true) % 0.36/0.74 (step @p157 :rule evaluate :args ((= false true))) % 0.36/0.74 (step @p158 :rule bool-impl-elim :args (@t151 @t150)) % 0.36/0.74 (step @p159 :rule cong :premises (@p158) :args (@t152)) % 0.36/0.74 (step @p160 :rule eq_resolve :premises (@p120 @p159)) % 0.36/0.74 (step @p161 :rule instantiate :premises (@p160) :args ((@list @t45 @t44))) % 0.36/0.74 (step @p162 :rule cnf_or_pos :args (@t172)) % 0.36/0.74 (step @p163 :rule reordering :premises (@p162) :args ((or @t171 @t170 (not @t172)))) % 0.36/0.74 (step @p164 :rule chain_m_resolution :premises (@p163 @p42 @p161) :args (@t170 (@list false false) (@list @t46 @t172))) % 0.36/0.74 (step @p165 :rule true_intro :premises (@p164)) % 0.36/0.74 (step @p166 :rule instantiate :premises (@p63) :args ((@list @t43 @t39))) % 0.36/0.74 (step @p167 :rule symm :premises (@p166)) % 0.36/0.74 (step @p168 :rule refl :args (@t43)) % 0.36/0.74 (step @p169 :rule symm :premises (@p137)) % 0.36/0.74 (step @p170 :rule eq-symm :args (@t73 @t72)) % 0.36/0.74 (step @p171 :rule cong :premises (@p170) :args (@t74)) % 0.36/0.74 (step @p172 :rule eq_resolve :premises (@p62 @p171)) % 0.36/0.74 (step @p173 :rule instantiate :premises (@p172) :args ((@list tptp.pls))) % 0.36/0.74 (step @p174 :rule trans :premises (@p173 @p169)) % 0.36/0.74 (step @p175 :rule refl :args (tptp.int)) % 0.36/0.74 (step @p176 :rule cong :premises (@p175 @p174 @p168) :args ((tptp.times_times tptp.int tptp.pls @t43))) % 0.36/0.74 (step @p177 :rule eq-symm :args (@t141 tptp.pls)) % 0.36/0.74 (step @p178 :rule cong :premises (@p177) :args (@t142)) % 0.36/0.74 (step @p179 :rule eq_resolve :premises (@p102 @p178)) % 0.36/0.74 (step @p180 :rule instantiate :premises (@p179) :args ((@list @t43))) % 0.36/0.74 (step @p181 :rule trans :premises (@p180 @p176 @p167)) % 0.36/0.74 (step @p182 :rule refl :args (@t40)) % 0.36/0.74 (step @p183 :rule cong :premises (@p175 @p43 @p182) :args (@t173)) % 0.36/0.74 (step @p184 :rule cong :premises (@p175 @p183 @p181) :args ((tptp.ord_less_eq tptp.int @t173 tptp.pls))) % 0.36/0.74 (step @p185 :rule symm :premises (@p174)) % 0.36/0.74 (step @p186 :rule refl :args (@t173)) % 0.36/0.74 (step @p187 :rule cong :premises (@p175 @p186 @p185) :args (@t174)) % 0.36/0.74 (step @p188 :rule eq-symm :args (@t174 @t169)) % 0.36/0.74 (step @p189 :rule refl :args (@t154)) % 0.36/0.74 (step @p190 :rule cong :premises (@p189 @p188) :args ((=> @t154 @t175))) % 0.36/0.74 (assume-push @p205 @t154) % 0.36/0.74 (step @p192 :rule instantiate :premises (@p121) :args ((@list @t48 @t39))) % 0.36/0.74 (step-pop @p206 :rule scope :premises (@p192)) % 0.36/0.74 (step @p193 :rule process_scope :premises (@p206) :args (@t175)) % 0.36/0.74 (step @p195 :rule eq_resolve :premises (@p193 @p190)) % 0.36/0.74 (step @p196 :rule implies_elim :premises (@p195)) % 0.36/0.74 (step @p197 :rule chain_m_resolution :premises (@p196 @p121) :args (@t176 (@list false) (@list @t154))) % 0.36/0.74 (step @p198 :rule cnf_equiv_pos2 :args (@t176)) % 0.36/0.74 (step @p199 :rule reordering :premises (@p198) :args ((or @t169 @t177 (not @t176)))) % 0.36/0.74 (step @p200 :rule chain_m_resolution :premises (@p199 @p155 @p197) :args (@t177 (@list true false) (@list @t169 @t176))) % 0.36/0.74 (step @p201 :rule false_intro :premises (@p200)) % 0.36/0.74 (step @p202 :rule symm :premises (@p201)) % 0.36/0.74 (step @p203 :rule trans :premises (@p202 @p187 @p184 @p165)) % 0.36/0.74 (step @p204 false :rule eq_resolve :premises (@p203 @p157)) % 0.36/0.74 ) % 0.36/0.74 % SZS output end Proof % 0.36/0.74 % cvc5 exiting %------------------------------------------------------------------------------