%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWX100_1 : TPTP v9.2.1. Released v9.1.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n001.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 09:07:07 AM UTC 2026 % Result : Theorem 45.66s 45.97s % Output : Proof 45.66s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWX100_1 : TPTP v9.2.1. Released v9.1.0. % 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 : n001.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 22:56:50 EDT 2026 % 0.16/0.35 % CPUTime : % 0.29/0.51 %----Proving TF0_ARI % 45.66/45.97 --- Run --finite-model-find --decision=internal at 45... % 45.66/45.97 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 60... % 45.66/45.97 % SZS status Theorem % 45.66/45.97 % SZS output start Proof % 45.66/45.97 ( % 45.66/45.97 (declare-sort tptp.symbol 0) % 45.66/45.97 (declare-sort tptp.general 0) % 45.66/45.97 (declare-const tptp.composite_p (-> tptp.general Bool)) % 45.66/45.97 (declare-const tptp.f__integer__ (-> Int tptp.general)) % 45.66/45.97 (declare-const tptp.f__symbolic__ (-> tptp.symbol tptp.general)) % 45.66/45.97 (declare-const tptp.sqrtb (-> tptp.general Bool)) % 45.66/45.97 (declare-const tptp.p__is_symbolic__ (-> tptp.general Bool)) % 45.66/45.97 (declare-const tptp.c__supremum__ tptp.general) % 45.66/45.97 (declare-const tptp.c__infimum__ tptp.general) % 45.66/45.97 (declare-const tptp.p__is_integer__ (-> tptp.general Bool)) % 45.66/45.97 (declare-const tptp.composite (-> tptp.general Bool)) % 45.66/45.97 (declare-const tptp.prime (-> tptp.general Bool)) % 45.66/45.97 (declare-const tptp.p__less_equal__ (-> tptp.general tptp.general Bool)) % 45.66/45.97 (declare-const tptp.sqrt (-> tptp.general tptp.general Bool)) % 45.66/45.97 (declare-const tptp.p__less__ (-> tptp.general tptp.general Bool)) % 45.66/45.97 (declare-const tptp.b_i Int) % 45.66/45.97 (declare-const tptp.p__greater__ (-> tptp.general tptp.general Bool)) % 45.66/45.97 (declare-const tptp.p__greater_equal__ (-> tptp.general tptp.general Bool)) % 45.66/45.97 (declare-const tptp.a_i Int) % 45.66/45.97 (define @t1 () (@var "N" Int)) % 45.66/45.97 (define @t2 () (tptp.f__integer__ @t1)) % 45.66/45.97 (define @t3 () (@var "X" tptp.general)) % 45.66/45.97 (define @t4 () (@list @t1)) % 45.66/45.97 (define @t5 () (tptp.p__is_integer__ @t3)) % 45.66/45.97 (define @t6 () (@list @t3)) % 45.66/45.97 (define @t7 () (@var "X2" tptp.symbol)) % 45.66/45.97 (define @t8 () (@var "X1" tptp.general)) % 45.66/45.97 (define @t9 () (@var "N2" Int)) % 45.66/45.97 (define @t10 () (@var "N1" Int)) % 45.66/45.97 (define @t11 () (tptp.f__integer__ @t9)) % 45.66/45.97 (define @t12 () (tptp.f__integer__ @t10)) % 45.66/45.97 (define @t13 () (@list @t10 @t9)) % 45.66/45.97 (define @t14 () (@var "S2" tptp.symbol)) % 45.66/45.97 (define @t15 () (@var "S1" tptp.symbol)) % 45.66/45.97 (define @t16 () (@var "X2" tptp.general)) % 45.66/45.97 (define @t17 () (= @t8 @t16)) % 45.66/45.97 (define @t18 () (tptp.p__less_equal__ @t16 @t8)) % 45.66/45.97 (define @t19 () (tptp.p__less_equal__ @t8 @t16)) % 45.66/45.97 (define @t20 () (@list @t8 @t16)) % 45.66/45.97 (define @t21 () (@var "X3" tptp.general)) % 45.66/45.97 (define @t22 () (not @t17)) % 45.66/45.97 (define @t23 () (@var "S" tptp.symbol)) % 45.66/45.97 (define @t24 () (tptp.f__symbolic__ @t23)) % 45.66/45.97 (define @t25 () (@var "Z1_g" tptp.general)) % 45.66/45.97 (define @t26 () (@var "Z_g" tptp.general)) % 45.66/45.97 (define @t27 () (= @t26 @t25)) % 45.66/45.97 (define @t28 () (@var "J_i" Int)) % 45.66/45.97 (define @t29 () (@var "K_i" Int)) % 45.66/45.97 (define @t30 () (<= @t29 @t28)) % 45.66/45.97 (define @t31 () (@var "I_i" Int)) % 45.66/45.97 (define @t32 () (<= @t31 @t29)) % 45.66/45.97 (define @t33 () (= @t25 (tptp.f__integer__ @t29))) % 45.66/45.97 (define @t34 () (= @t28 tptp.b_i)) % 45.66/45.97 (define @t35 () (= @t31 2)) % 45.66/45.97 (define @t36 () (@list @t31 @t28 @t29)) % 45.66/45.97 (define @t37 () (exists @t36 (and @t35 @t34 @t33 @t32 @t30))) % 45.66/45.97 (define @t38 () (@var "J_g" tptp.general)) % 45.66/45.97 (define @t39 () (@list @t26 @t25)) % 45.66/45.97 (define @t40 () (exists @t39 (and (= @t26 @t38) @t37 @t27))) % 45.66/45.97 (define @t41 () (@var "I_g" tptp.general)) % 45.66/45.97 (define @t42 () (= @t26 @t41)) % 45.66/45.97 (define @t43 () (@var "J1_i" Int)) % 45.66/45.97 (define @t44 () (@var "I1_i" Int)) % 45.66/45.97 (define @t45 () (tptp.f__integer__ @t44)) % 45.66/45.97 (define @t46 () (@var "V1_g" tptp.general)) % 45.66/45.97 (define @t47 () (exists (@list @t44 @t43) (and (= @t46 (tptp.f__integer__ (* @t44 @t43))) (= @t45 @t41) (= (tptp.f__integer__ @t43) @t38)))) % 45.66/45.97 (define @t48 () (@list @t46)) % 45.66/45.97 (define @t49 () (= @t25 (tptp.f__integer__ tptp.b_i))) % 45.66/45.97 (define @t50 () (@var "M_g" tptp.general)) % 45.66/45.97 (define @t51 () (tptp.f__integer__ @t31)) % 45.66/45.97 (define @t52 () (= @t51 @t50)) % 45.66/45.97 (define @t53 () (= @t26 (tptp.f__integer__ (* @t31 @t28)))) % 45.66/45.97 (define @t54 () (@list @t31 @t28)) % 45.66/45.97 (define @t55 () (= (tptp.f__integer__ @t28) @t50)) % 45.66/45.97 (define @t56 () (= @t26 @t50)) % 45.66/45.97 (define @t57 () (@list @t26)) % 45.66/45.97 (define @t58 () (+ @t31 1)) % 45.66/45.97 (define @t59 () (* @t58 @t58)) % 45.66/45.97 (define @t60 () (@var "N_i" Int)) % 45.66/45.97 (define @t61 () (* @t31 @t31)) % 45.66/45.97 (define @t62 () (<= @t61 @t60)) % 45.66/45.97 (define @t63 () (>= @t31 0)) % 45.66/45.97 (define @t64 () (and @t63 @t62 (< @t60 @t59))) % 45.66/45.97 (define @t65 () (tptp.f__integer__ @t60)) % 45.66/45.97 (define @t66 () (tptp.sqrt @t51 @t65)) % 45.66/45.97 (define @t67 () (= @t66 @t64)) % 45.66/45.97 (define @t68 () (@list @t31 @t60)) % 45.66/45.97 (define @t69 () (forall @t68 @t67)) % 45.66/45.97 (define @t70 () (+ @t60 1)) % 45.66/45.97 (define @t71 () (tptp.f__integer__ @t70)) % 45.66/45.97 (define @t72 () (tptp.f__integer__ @t58)) % 45.66/45.97 (define @t73 () (tptp.sqrt @t72 @t71)) % 45.66/45.97 (define @t74 () (<= @t59 @t70)) % 45.66/45.97 (define @t75 () (and @t66 @t74)) % 45.66/45.97 (define @t76 () (=> @t75 @t73)) % 45.66/45.97 (define @t77 () (forall @t68 @t76)) % 45.66/45.97 (define @t78 () (tptp.sqrt @t51 @t71)) % 45.66/45.97 (define @t79 () (@list @t31)) % 45.66/45.97 (define @t80 () (exists @t79 @t78)) % 45.66/45.97 (define @t81 () (exists @t79 @t66)) % 45.66/45.97 (define @t82 () (>= @t60 0)) % 45.66/45.97 (define @t83 () (and @t82 @t81)) % 45.66/45.97 (define @t84 () (=> @t83 @t80)) % 45.66/45.97 (define @t85 () (@list @t60)) % 45.66/45.97 (define @t86 () (forall @t85 @t84)) % 45.66/45.97 (define @t87 () (not @t86)) % 45.66/45.97 (define @t88 () (+ 1 @t60)) % 45.66/45.97 (define @t89 () (tptp.f__integer__ @t88)) % 45.66/45.97 (define @t90 () (tptp.sqrt @t51 @t89)) % 45.66/45.97 (define @t91 () (not (forall @t79 (not @t90)))) % 45.66/45.97 (define @t92 () (@var "BOUND_VARIABLE_8631" Int)) % 45.66/45.97 (define @t93 () (not (tptp.sqrt (tptp.f__integer__ @t92) @t65))) % 45.66/45.97 (define @t94 () (not @t82)) % 45.66/45.97 (define @t95 () (or @t94 @t93 @t91)) % 45.66/45.97 (define @t96 () (forall (@list @t60 @t92) @t95)) % 45.66/45.97 (define @t97 () (@list @t92)) % 45.66/45.97 (define @t98 () (forall @t97 @t95)) % 45.66/45.97 (define @t99 () (forall @t97 @t93)) % 45.66/45.97 (define @t100 () (or @t94 @t99 @t91)) % 45.66/45.97 (define @t101 () (not @t66)) % 45.66/45.97 (define @t102 () (forall @t79 @t101)) % 45.66/45.97 (define @t103 () (or @t94 @t102 @t91)) % 45.66/45.97 (define @t104 () (not @t102)) % 45.66/45.97 (define @t105 () (and @t82 @t104)) % 45.66/45.97 (define @t106 () (@quantifiers_skolemize @t96 0)) % 45.66/45.97 (define @t107 () (+ 1 @t106)) % 45.66/45.97 (define @t108 () (tptp.f__integer__ @t107)) % 45.66/45.97 (define @t109 () (forall @t79 (not (tptp.sqrt @t51 @t108)))) % 45.66/45.97 (define @t110 () (not @t109)) % 45.66/45.97 (define @t111 () (@quantifiers_skolemize @t96 1)) % 45.66/45.97 (define @t112 () (tptp.f__integer__ @t111)) % 45.66/45.97 (define @t113 () (tptp.sqrt @t112 (tptp.f__integer__ @t106))) % 45.66/45.97 (define @t114 () (not @t113)) % 45.66/45.97 (define @t115 () (or (not (>= @t106 0)) @t114 @t110)) % 45.66/45.97 (define @t116 () (@list true)) % 45.66/45.97 (define @t117 () (@list @t115)) % 45.66/45.97 (define @t118 () (+ 1 @t31)) % 45.66/45.97 (define @t119 () (tptp.sqrt (tptp.f__integer__ @t118) @t89)) % 45.66/45.97 (define @t120 () (* @t31 @t31)) % 45.66/45.97 (define @t121 () (* 2 @t31)) % 45.66/45.97 (define @t122 () (+ @t121 (* -1 @t60) @t120)) % 45.66/45.97 (define @t123 () (>= @t122 1)) % 45.66/45.97 (define @t124 () (or @t101 @t123 @t119)) % 45.66/45.97 (define @t125 () (not @t123)) % 45.66/45.97 (define @t126 () (and @t66 @t125)) % 45.66/45.97 (define @t127 () (+ @t88 1)) % 45.66/45.97 (define @t128 () (+ 1 @t121 @t120)) % 45.66/45.97 (define @t129 () (>= @t128 @t127)) % 45.66/45.97 (define @t130 () (+ 1 @t111)) % 45.66/45.97 (define @t131 () (tptp.sqrt (tptp.f__integer__ @t130) @t108)) % 45.66/45.97 (define @t132 () (* @t111 @t111)) % 45.66/45.97 (define @t133 () (* 2 @t111)) % 45.66/45.97 (define @t134 () (* -1 @t106)) % 45.66/45.97 (define @t135 () (+ @t134 @t133 @t132)) % 45.66/45.97 (define @t136 () (* -1 @t132)) % 45.66/45.97 (define @t137 () (+ @t106 (* -2 @t111) @t136)) % 45.66/45.97 (define @t138 () (+ @t137 1)) % 45.66/45.97 (define @t139 () (* -1 (- 0 @t138))) % 45.66/45.97 (define @t140 () (>= 0 @t138)) % 45.66/45.97 (define @t141 () (+ @t133 @t134 @t132)) % 45.66/45.97 (define @t142 () (>= @t141 1)) % 45.66/45.97 (define @t143 () (or @t114 @t142 @t131)) % 45.66/45.97 (define @t144 () (forall @t68 @t124)) % 45.66/45.97 (define @t145 () (@list @t111 @t106)) % 45.66/45.97 (define @t146 () (>= @t137 0)) % 45.66/45.97 (define @t147 () (not @t146)) % 45.66/45.97 (define @t148 () (or @t114 @t147 @t131)) % 45.66/45.97 (define @t149 () (@list false)) % 45.66/45.97 (define @t150 () (>= @t122 0)) % 45.66/45.97 (define @t151 () (+ @t122 1)) % 45.66/45.97 (define @t152 () (>= @t60 @t59)) % 45.66/45.97 (define @t153 () (+ @t60 (* -1 @t120))) % 45.66/45.97 (define @t154 () (>= @t153 0)) % 45.66/45.97 (define @t155 () (>= @t141 0)) % 45.66/45.97 (define @t156 () (+ @t106 @t136)) % 45.66/45.97 (define @t157 () (>= @t156 0)) % 45.66/45.97 (define @t158 () (>= @t111 0)) % 45.66/45.97 (define @t159 () (and @t158 @t157 @t155)) % 45.66/45.97 (define @t160 () (= @t113 @t159)) % 45.66/45.97 (define @t161 () (forall @t68 (= @t66 (and @t63 @t154 @t150)))) % 45.66/45.97 (define @t162 () (and @t158 @t157 (not (>= @t137 1)))) % 45.66/45.97 (define @t163 () (= @t113 @t162)) % 45.66/45.97 (define @t164 () (@list @t161)) % 45.66/45.97 (define @t165 () (@list false false)) % 45.66/45.97 (define @t166 () (not @t162)) % 45.66/45.97 (define @t167 () (@list @t162)) % 45.66/45.97 (define @t168 () (>= @t156 -1)) % 45.66/45.97 (define @t169 () (not @t157)) % 45.66/45.97 (define @t170 () (not @t168)) % 45.66/45.97 (define @t171 () (+ -2 1)) % 45.66/45.97 (define @t172 () (>= @t156 @t171)) % 45.66/45.97 (define @t173 () (<= @t156 -2)) % 45.66/45.97 (define @t174 () (* -1 0)) % 45.66/45.97 (define @t175 () (+ -2 @t174)) % 45.66/45.97 (define @t176 () (* 0 @t106)) % 45.66/45.97 (define @t177 () (* 0 @t132)) % 45.66/45.97 (define @t178 () (+ @t177 @t176)) % 45.66/45.97 (define @t179 () (+ @t156 (* -1 @t156))) % 45.66/45.97 (define @t180 () (and @t170 @t157)) % 45.66/45.97 (define @t181 () (+ -1 @t134 @t133 @t132)) % 45.66/45.97 (define @t182 () (+ -1 @t134)) % 45.66/45.97 (define @t183 () (* -1 @t107)) % 45.66/45.97 (define @t184 () (+ @t133 @t183 @t132)) % 45.66/45.97 (define @t185 () (>= @t184 0)) % 45.66/45.97 (define @t186 () (+ 1 @t106 @t136)) % 45.66/45.97 (define @t187 () (+ @t136 @t106 1)) % 45.66/45.97 (define @t188 () (+ @t107 @t136)) % 45.66/45.97 (define @t189 () (>= @t188 0)) % 45.66/45.97 (define @t190 () (and @t158 @t189 @t185)) % 45.66/45.97 (define @t191 () (tptp.sqrt @t112 @t108)) % 45.66/45.97 (define @t192 () (= @t191 @t190)) % 45.66/45.97 (define @t193 () (and @t158 @t168 @t147)) % 45.66/45.97 (define @t194 () (= @t191 @t193)) % 45.66/45.97 (define @t195 () (not @t193)) % 45.66/45.97 (define @t196 () (not @t158)) % 45.66/45.97 (assume @p1 (forall @t6 (= @t5 (exists @t4 (= @t3 @t2))))) % 45.66/45.97 (assume @p2 (forall (@list @t8) (= (tptp.p__is_symbolic__ @t8) (exists (@list @t7) (= @t8 (tptp.f__symbolic__ @t7)))))) % 45.66/45.97 (assume @p3 (forall @t6 (or (= @t3 tptp.c__infimum__) @t5 (tptp.p__is_symbolic__ @t3) (= @t3 tptp.c__supremum__)))) % 45.66/45.97 (assume @p4 (forall @t13 (= (= @t12 @t11) (= @t10 @t9)))) % 45.66/45.97 (assume @p5 (forall (@list @t15 @t14) (= (= (tptp.f__symbolic__ @t15) (tptp.f__symbolic__ @t14)) (= @t15 @t14)))) % 45.66/45.97 (assume @p6 (forall @t13 (= (tptp.p__less_equal__ @t12 @t11) (<= @t10 @t9)))) % 45.66/45.97 (assume @p7 (forall @t20 (=> (and @t19 @t18) @t17))) % 45.66/45.97 (assume @p8 (forall (@list @t8 @t16 @t21) (=> (and @t19 (tptp.p__less_equal__ @t16 @t21)) (tptp.p__less_equal__ @t8 @t21)))) % 45.66/45.97 (assume @p9 (forall @t20 (or @t19 @t18))) % 45.66/45.97 (assume @p10 (forall @t20 (= (tptp.p__less__ @t8 @t16) (and @t19 @t22)))) % 45.66/45.97 (assume @p11 (forall @t20 (= (tptp.p__greater_equal__ @t8 @t16) @t18))) % 45.66/45.97 (assume @p12 (forall @t20 (= (tptp.p__greater__ @t8 @t16) (and @t18 @t22)))) % 45.66/45.97 (assume @p13 (forall @t4 (tptp.p__less__ tptp.c__infimum__ @t2))) % 45.66/45.97 (assume @p14 (forall (@list @t1 @t23) (tptp.p__less__ @t2 @t24))) % 45.66/45.97 (assume @p15 (forall (@list @t23) (tptp.p__less__ @t24 tptp.c__supremum__))) % 45.66/45.97 (assume @p16 (> tptp.a_i 1)) % 45.66/45.97 (assume @p17 (forall @t48 (= (tptp.composite @t46) (exists (@list @t41 @t38) (and @t47 (exists @t39 (and @t42 @t37 @t27)) @t40))))) % 45.66/45.97 (assume @p18 (forall @t48 (= (tptp.sqrtb @t46) (exists (@list @t50) (and (= @t46 @t50) (exists @t39 (and @t56 (exists @t36 (and (= @t31 1) @t34 @t33 @t32 @t30)) @t27)) (exists @t39 (and (exists @t54 (and @t53 @t52 @t55)) @t49 (tptp.p__less_equal__ @t26 @t25))) (exists @t39 (and (exists @t54 (and @t53 (exists (@list @t44 @t28) (and (= @t31 (+ @t44 @t28)) (= @t45 @t50) (= @t28 1))) (exists (@list @t31 @t43) (and (= @t28 (+ @t31 @t43)) @t52 (= @t43 1))))) @t49 (tptp.p__greater__ @t26 @t25)))))))) % 45.66/45.97 (assume @p19 (forall @t48 (= (tptp.composite_p @t46) (exists (@list @t41 @t38 @t50) (and @t47 (exists @t57 (and @t56 (tptp.sqrtb @t26))) (exists @t39 (and @t42 (exists @t36 (and @t35 @t55 @t33 @t32 @t30)) @t27)) @t40))))) % 45.66/45.97 (assume @p20 (forall @t48 (= (tptp.prime @t46) (exists (@list @t41) (and (= @t46 @t41) (exists @t39 (and @t42 (exists @t36 (and (= @t31 tptp.a_i) @t34 @t33 @t32 @t30)) @t27)) (exists @t57 (and @t42 (not (tptp.composite @t26))))))))) % 45.66/45.97 (assume @p21 @t69) % 45.66/45.97 (assume @p22 @t77) % 45.66/45.97 (assume @p23 @t87) % 45.66/45.97 (assume @p24 true) % 45.66/45.97 (step @p25 :rule quant-merge-prenex :args ((= (forall @t85 @t98) @t96))) % 45.66/45.97 (step @p26 :rule refl :args (@t91)) % 45.66/45.97 (step @p27 :rule alpha_equiv :args (@t99 (@list @t92) (@list @t31))) % 45.66/45.97 (step @p28 :rule refl :args (@t94)) % 45.66/45.97 (step @p29 :rule nary_cong :premises (@p28 @p27 @p26) :args (@t100)) % 45.66/45.97 (step @p30 :rule quant-miniscope-or :args ((= @t98 @t100))) % 45.66/45.97 (step @p31 :rule trans :premises (@p30 @p29)) % 45.66/45.97 (step @p32 :rule symm :premises (@p31)) % 45.66/45.97 (step @p33 :rule cong :premises (@p32) :args ((forall @t85 @t103))) % 45.66/45.97 (step @p34 :rule trans :premises (@p33 @p25)) % 45.66/45.97 (step @p35 :rule aci_norm :args ((= (or (or @t94 @t102) @t91) @t103))) % 45.66/45.97 (step @p36 :rule bool-double-not-elim :args (@t102)) % 45.66/45.97 (step @p37 :rule nary_cong :premises (@p28 @p36) :args ((or @t94 (not @t104)))) % 45.66/45.97 (step @p38 :rule bool-and-de-morgan :args (@t82 @t104 true)) % 45.66/45.97 (step @p39 :rule trans :premises (@p38 @p37)) % 45.66/45.97 (step @p40 :rule nary_cong :premises (@p39 @p26) :args ((or (not @t105) @t91))) % 45.66/45.97 (step @p41 :rule trans :premises (@p40 @p35)) % 45.66/45.97 (step @p42 :rule bool-impl-elim :args (@t105 @t91)) % 45.66/45.97 (step @p43 :rule trans :premises (@p42 @p41)) % 45.66/45.97 (step @p44 :rule cong :premises (@p43) :args ((forall @t85 (=> @t105 @t91)))) % 45.66/45.97 (step @p45 :rule trans :premises (@p44 @p34)) % 45.66/45.97 (step @p46 :rule exists-elim :args ((= (exists @t79 @t90) @t91))) % 45.66/45.97 (step @p47 :rule arith_poly_norm :args ((= @t70 @t88))) % 45.66/45.97 (step @p48 :rule cong :premises (@p47) :args (@t71)) % 45.66/45.97 (step @p49 :rule refl :args (@t51)) % 45.66/45.97 (step @p50 :rule cong :premises (@p49 @p48) :args (@t78)) % 45.66/45.97 (step @p51 :rule cong :premises (@p50) :args (@t80)) % 45.66/45.97 (step @p52 :rule trans :premises (@p51 @p46)) % 45.66/45.97 (step @p53 :rule exists-elim :args ((= @t81 @t104))) % 45.66/45.97 (step @p54 :rule refl :args (@t82)) % 45.66/45.97 (step @p55 :rule nary_cong :premises (@p54 @p53) :args (@t83)) % 45.66/45.97 (step @p56 :rule cong :premises (@p55 @p52) :args (@t84)) % 45.66/45.97 (step @p57 :rule cong :premises (@p56) :args (@t86)) % 45.66/45.97 (step @p58 :rule trans :premises (@p57 @p45)) % 45.66/45.97 (step @p59 :rule cong :premises (@p58) :args (@t87)) % 45.66/45.97 (step @p60 :rule eq_resolve :premises (@p23 @p59)) % 45.66/45.97 (step @p61 :rule skolemize :premises (@p60)) % 45.66/45.97 (step @p62 :rule bool-double-not-elim :args (@t109)) % 45.66/45.97 (step @p63 :rule refl :args (@t115)) % 45.66/45.97 (step @p64 :rule nary_cong :premises (@p63 @p62) :args ((or @t115 (not @t110)))) % 45.66/45.97 (step @p65 :rule cnf_or_neg :args (@t115 2)) % 45.66/45.97 (step @p66 :rule eq_resolve :premises (@p65 @p64)) % 45.66/45.97 (step @p67 :rule reordering :premises (@p66) :args ((or @t109 @t115))) % 45.66/45.97 (step @p68 :rule chain_m_resolution :premises (@p67 @p61) :args (@t109 @t116 @t117)) % 45.66/45.97 (step @p69 :rule aci_norm :args ((= (or (or @t101 @t123) @t119) @t124))) % 45.66/45.97 (step @p70 :rule refl :args (@t119)) % 45.66/45.97 (step @p71 :rule bool-double-not-elim :args (@t123)) % 45.66/45.97 (step @p72 :rule refl :args (@t101)) % 45.66/45.97 (step @p73 :rule nary_cong :premises (@p72 @p71) :args ((or @t101 (not @t125)))) % 45.66/45.97 (step @p74 :rule bool-and-de-morgan :args (@t66 @t125 true)) % 45.66/45.97 (step @p75 :rule trans :premises (@p74 @p73)) % 45.66/45.97 (step @p76 :rule nary_cong :premises (@p75 @p70) :args ((or (not @t126) @t119))) % 45.66/45.97 (step @p77 :rule trans :premises (@p76 @p69)) % 45.66/45.97 (step @p78 :rule bool-impl-elim :args (@t126 @t119)) % 45.66/45.97 (step @p79 :rule trans :premises (@p78 @p77)) % 45.66/45.97 (step @p80 :rule cong :premises (@p79) :args ((forall @t68 (=> @t126 @t119)))) % 45.66/45.97 (step @p81 :rule arith_poly_norm :args ((= @t58 @t118))) % 45.66/45.97 (step @p82 :rule cong :premises (@p81) :args (@t72)) % 45.66/45.97 (step @p83 :rule cong :premises (@p82 @p48) :args (@t73)) % 45.66/45.97 (step @p84 :rule arith_poly_norm :args ((= (* -1 (- @t128 @t127)) (* -1 (- @t122 1))))) % 45.66/45.97 (step @p85 :rule arith_poly_norm_rel :premises (@p84) :args ((= @t129 @t123))) % 45.66/45.97 (step @p86 :rule cong :premises (@p85) :args ((not @t129))) % 45.66/45.97 (step @p87 :rule arith-leq-norm :args (@t128 @t88)) % 45.66/45.97 (step @p88 :rule trans :premises (@p87 @p86)) % 45.66/45.97 (step @p89 :rule arith_poly_norm :args ((= (* @t118 @t118) @t128))) % 45.66/45.97 (step @p90 :rule nary_cong :premises (@p81 @p81) :args (@t59)) % 45.66/45.97 (step @p91 :rule trans :premises (@p90 @p89)) % 45.66/45.97 (step @p92 :rule cong :premises (@p91 @p47) :args (@t74)) % 45.66/45.97 (step @p93 :rule trans :premises (@p92 @p88)) % 45.66/45.97 (step @p94 :rule refl :args (@t66)) % 45.66/45.97 (step @p95 :rule nary_cong :premises (@p94 @p93) :args (@t75)) % 45.66/45.97 (step @p96 :rule cong :premises (@p95 @p83) :args (@t76)) % 45.66/45.97 (step @p97 :rule cong :premises (@p96) :args (@t77)) % 45.66/45.97 (step @p98 :rule trans :premises (@p97 @p80)) % 45.66/45.97 (step @p99 :rule eq_resolve :premises (@p22 @p98)) % 45.66/45.97 (step @p100 :rule refl :args (@t131)) % 45.66/45.97 (step @p101 :rule arith_poly_norm :args ((= @t139 (* -1 (- @t135 1))))) % 45.66/45.97 (step @p102 :rule arith_poly_norm_rel :premises (@p101) :args ((= @t140 (>= @t135 1)))) % 45.66/45.97 (step @p103 :rule arith-geq-tighten :args (@t137 0)) % 45.66/45.97 (step @p104 :rule trans :premises (@p103 @p102)) % 45.66/45.97 (step @p105 :rule symm :premises (@p104)) % 45.66/45.97 (step @p106 :rule refl :args (1)) % 45.66/45.97 (step @p107 :rule arith_poly_norm :args ((= @t141 @t135))) % 45.66/45.97 (step @p108 :rule cong :premises (@p107 @p106) :args (@t142)) % 45.66/45.97 (step @p109 :rule trans :premises (@p108 @p105)) % 45.66/45.97 (step @p110 :rule refl :args (@t114)) % 45.66/45.97 (step @p111 :rule nary_cong :premises (@p110 @p109 @p100) :args (@t143)) % 45.66/45.97 (step @p112 :rule refl :args (@t144)) % 45.66/45.97 (step @p113 :rule cong :premises (@p112 @p111) :args ((=> @t144 @t143))) % 45.66/45.97 (assume-push @p305 @t144) % 45.66/45.97 (step @p115 :rule instantiate :premises (@p99) :args (@t145)) % 45.66/45.97 (step-pop @p306 :rule scope :premises (@p115)) % 45.66/45.97 (step @p116 :rule process_scope :premises (@p306) :args (@t143)) % 45.66/45.97 (step @p118 :rule eq_resolve :premises (@p116 @p113)) % 45.66/45.97 (step @p119 :rule implies_elim :premises (@p118)) % 45.66/45.97 (step @p120 :rule chain_m_resolution :premises (@p119 @p99) :args (@t148 @t149 (@list @t144))) % 45.66/45.97 (step @p121 :rule bool-double-not-elim :args (@t150)) % 45.66/45.97 (step @p122 :rule arith_poly_norm :args ((= (* -1 (- 0 @t151)) (* -1 (- @t60 @t128))))) % 45.66/45.97 (step @p123 :rule arith_poly_norm_rel :premises (@p122) :args ((= (>= 0 @t151) (>= @t60 @t128)))) % 45.66/45.97 (step @p124 :rule arith-geq-tighten :args (@t122 0)) % 45.66/45.97 (step @p125 :rule trans :premises (@p124 @p123)) % 45.66/45.97 (step @p126 :rule symm :premises (@p125)) % 45.66/45.97 (step @p127 :rule refl :args (@t60)) % 45.66/45.97 (step @p128 :rule cong :premises (@p127 @p91) :args (@t152)) % 45.66/45.97 (step @p129 :rule trans :premises (@p128 @p126)) % 45.66/45.97 (step @p130 :rule cong :premises (@p129) :args ((not @t152))) % 45.66/45.97 (step @p131 :rule trans :premises (@p130 @p121)) % 45.66/45.97 (step @p132 :rule arith-elim-lt :args (@t60 @t59)) % 45.66/45.97 (step @p133 :rule trans :premises (@p132 @p131)) % 45.66/45.97 (step @p134 :rule arith_poly_norm :args ((= (* 1 (- @t60 @t120)) (* 1 (- @t153 0))))) % 45.66/45.97 (step @p135 :rule arith_poly_norm_rel :premises (@p134) :args ((= (>= @t60 @t120) @t154))) % 45.66/45.97 (step @p136 :rule arith-elim-leq :args (@t120 @t60)) % 45.66/45.97 (step @p137 :rule trans :premises (@p136 @p135)) % 45.66/45.97 (step @p138 :rule arith_poly_norm :args ((= @t61 @t120))) % 45.66/45.97 (step @p139 :rule cong :premises (@p138 @p127) :args (@t62)) % 45.66/45.97 (step @p140 :rule trans :premises (@p139 @p137)) % 45.66/45.97 (step @p141 :rule refl :args (@t63)) % 45.66/45.97 (step @p142 :rule nary_cong :premises (@p141 @p140 @p133) :args (@t64)) % 45.66/45.97 (step @p143 :rule cong :premises (@p94 @p142) :args (@t67)) % 45.66/45.97 (step @p144 :rule cong :premises (@p143) :args (@t69)) % 45.66/45.97 (step @p145 :rule eq_resolve :premises (@p21 @p144)) % 45.66/45.97 (step @p146 :rule arith_poly_norm :args ((= (* -1 (- 1 @t138)) (* -1 (- @t135 0))))) % 45.66/45.97 (step @p147 :rule arith_poly_norm_rel :premises (@p146) :args ((= (>= 1 @t138) (>= @t135 0)))) % 45.66/45.97 (step @p148 :rule arith-geq-tighten :args (@t137 1)) % 45.66/45.97 (step @p149 :rule trans :premises (@p148 @p147)) % 45.66/45.97 (step @p150 :rule symm :premises (@p149)) % 45.66/45.97 (step @p151 :rule refl :args (0)) % 45.66/45.97 (step @p152 :rule cong :premises (@p107 @p151) :args (@t155)) % 45.66/45.97 (step @p153 :rule trans :premises (@p152 @p150)) % 45.66/45.97 (step @p154 :rule refl :args (@t157)) % 45.66/45.97 (step @p155 :rule refl :args (@t158)) % 45.66/45.97 (step @p156 :rule nary_cong :premises (@p155 @p154 @p153) :args (@t159)) % 45.66/45.97 (step @p157 :rule refl :args (@t113)) % 45.66/45.97 (step @p158 :rule cong :premises (@p157 @p156) :args (@t160)) % 45.66/45.97 (step @p159 :rule refl :args (@t161)) % 45.66/45.97 (step @p160 :rule cong :premises (@p159 @p158) :args ((=> @t161 @t160))) % 45.66/45.97 (assume-push @p307 @t161) % 45.66/45.97 (step @p162 :rule instantiate :premises (@p145) :args (@t145)) % 45.66/45.97 (step-pop @p308 :rule scope :premises (@p162)) % 45.66/45.97 (step @p163 :rule process_scope :premises (@p308) :args (@t160)) % 45.66/45.97 (step @p165 :rule eq_resolve :premises (@p163 @p160)) % 45.66/45.97 (step @p166 :rule implies_elim :premises (@p165)) % 45.66/45.97 (step @p167 :rule chain_m_resolution :premises (@p166 @p145) :args (@t163 @t149 @t164)) % 45.66/45.97 (step @p168 :rule bool-double-not-elim :args (@t113)) % 45.66/45.97 (step @p169 :rule nary_cong :premises (@p63 @p168) :args ((or @t115 (not @t114)))) % 45.66/45.97 (step @p170 :rule cnf_or_neg :args (@t115 1)) % 45.66/45.97 (step @p171 :rule eq_resolve :premises (@p170 @p169)) % 45.66/45.97 (step @p172 :rule reordering :premises (@p171) :args ((or @t113 @t115))) % 45.66/45.97 (step @p173 :rule chain_m_resolution :premises (@p172 @p61) :args (@t113 @t116 @t117)) % 45.66/45.97 (step @p174 :rule cnf_equiv_pos1 :args (@t163)) % 45.66/45.97 (step @p175 :rule reordering :premises (@p174) :args ((or @t114 @t162 (not @t163)))) % 45.66/45.97 (step @p176 :rule chain_m_resolution :premises (@p175 @p173 @p167) :args (@t162 @t165 (@list @t113 @t163))) % 45.66/45.97 (step @p177 :rule cnf_and_pos :args (@t162 1)) % 45.66/45.97 (step @p178 :rule reordering :premises (@p177) :args ((or @t157 @t166))) % 45.66/45.97 (step @p179 :rule chain_m_resolution :premises (@p178 @p176) :args (@t157 @t149 @t167)) % 45.66/45.97 (step @p180 :rule bool-double-not-elim :args (@t168)) % 45.66/45.97 (step @p181 :rule refl :args (@t169)) % 45.66/45.97 (step @p182 :rule nary_cong :premises (@p181 @p180) :args ((or @t169 (not @t170)))) % 45.66/45.97 (assume-push @p309 @t170) % 45.66/45.97 (assume-push @p310 @t157) % 45.66/45.97 (step @p185 :rule evaluate :args (@t171)) % 45.66/45.97 (step @p186 :rule refl :args (@t156)) % 45.66/45.97 (step @p187 :rule cong :premises (@p186 @p185) :args (@t172)) % 45.66/45.97 (step @p188 :rule cong :premises (@p187) :args ((not @t172))) % 45.66/45.97 (step @p189 :rule arith-leq-norm :args (@t156 -2)) % 45.66/45.97 (step @p190 :rule trans :premises (@p189 @p188)) % 45.66/45.97 (step @p191 :rule cong :premises (@p190) :args ((not @t173))) % 45.66/45.97 (step @p192 :rule trans :premises (@p191 @p180)) % 45.66/45.97 (step @p193 :rule arith-elim-leq :args (@t156 -2)) % 45.66/45.97 (step @p194 :rule symm :premises (@p193)) % 45.66/45.97 (step @p195 :rule cong :premises (@p194) :args ((not (>= -2 @t156)))) % 45.66/45.97 (step @p196 :rule arith-elim-gt :args (@t156 -2)) % 45.66/45.97 (step @p197 :rule trans :premises (@p196 @p195)) % 45.66/45.97 (step @p198 :rule trans :premises (@p197 @p192)) % 45.66/45.97 (step @p199 :rule cong :premises (@p198) :args ((not (> @t156 -2)))) % 45.66/45.97 (step @p200 :rule symm :premises (@p199)) % 45.66/45.97 (step @p201 :rule trans :premises (@p190 @p200)) % 45.66/45.97 (step @p202 :rule arith-elim-lt :args (@t156 -1)) % 45.66/45.97 (step @p203 :rule symm :premises (@p202)) % 45.66/45.97 (step @p204 :rule eq_resolve :premises (@p309 @p203)) % 45.66/45.97 (step @p205 :rule int_tight_ub :premises (@p204)) % 45.66/45.97 (step @p206 :rule eq_resolve :premises (@p205 @p201)) % 45.66/45.97 (step @p207 :rule symm :premises (@p198)) % 45.66/45.97 (step @p208 :rule trans :premises (@p192 @p207)) % 45.66/45.97 (assume-push @p311 @t173) % 45.66/45.97 (step @p210 :rule evaluate :args ((<= 0 -2))) % 45.66/45.97 (step @p211 :rule evaluate :args ((+ -2 0))) % 45.66/45.97 (step @p212 :rule evaluate :args (@t174)) % 45.66/45.97 (step @p213 :rule refl :args (-2)) % 45.66/45.97 (step @p214 :rule nary_cong :premises (@p213 @p212) :args (@t175)) % 45.66/45.97 (step @p215 :rule trans :premises (@p214 @p211)) % 45.66/45.97 (step @p216 :rule evaluate :args ((+ 0 0))) % 45.66/45.97 (step @p217 :rule arith_poly_norm :args ((= @t176 0))) % 45.66/45.97 (step @p218 :rule arith_poly_norm :args ((= @t177 0))) % 45.66/45.97 (step @p219 :rule nary_cong :premises (@p218 @p217) :args (@t178)) % 45.66/45.97 (step @p220 :rule trans :premises (@p219 @p216)) % 45.66/45.97 (step @p221 :rule arith_poly_norm :args ((= @t179 @t178))) % 45.66/45.97 (step @p222 :rule trans :premises (@p221 @p220)) % 45.66/45.97 (step @p223 :rule cong :premises (@p222 @p215) :args ((<= @t179 @t175))) % 45.66/45.97 (step @p224 :rule trans :premises (@p223 @p210)) % 45.66/45.97 (step @p225 :rule arith_mult_neg :args (-1 @t157)) % 45.66/45.97 (step @p226 :rule evaluate :args ((< -1 0))) % 45.66/45.97 (step @p227 :rule true_elim :premises (@p226)) % 45.66/45.97 (step @p228 :rule and_intro :premises (@p227 @p179)) % 45.66/45.97 (step @p229 :rule modus_ponens :premises (@p228 @p225)) % 45.66/45.97 (step @p230 :rule arith_sum_ub :premises (@p311 @p229)) % 45.66/45.97 (step @p231 false :rule eq_resolve :premises (@p230 @p224)) % 45.66/45.97 (step-pop @p312 :rule scope :premises (@p231)) % 45.66/45.97 (step @p232 :rule process_scope :premises (@p312) :args (false)) % 45.66/45.97 (step @p234 :rule eq_resolve :premises (@p232 @p208)) % 45.66/45.97 (step @p235 false :rule contra :premises (@p234 @p206)) % 45.66/45.97 (step-pop @p313 :rule scope :premises (@p235)) % 45.66/45.97 (step-pop @p314 :rule scope :premises (@p313)) % 45.66/45.97 (step @p236 :rule process_scope :premises (@p314) :args (false)) % 45.66/45.97 (assume-push @p315 @t157) % 45.66/45.97 (assume-push @p316 @t170) % 45.66/45.97 (step @p241 :rule and_intro :premises (@p316 @p179)) % 45.66/45.97 (step-pop @p317 :rule scope :premises (@p241)) % 45.66/45.97 (step-pop @p318 :rule scope :premises (@p317)) % 45.66/45.97 (step @p242 :rule process_scope :premises (@p318) :args (@t180)) % 45.66/45.97 (step @p245 :rule implies_elim :premises (@p242)) % 45.66/45.97 (step @p246 :rule resolution :premises (@p245 @p236) :args (true @t180)) % 45.66/45.97 (step @p247 :rule not_and :premises (@p246)) % 45.66/45.97 (step @p248 :rule eq_resolve :premises (@p247 @p182)) % 45.66/45.97 (step @p249 :rule chain_m_resolution :premises (@p248 @p179) :args (@t168 @t149 (@list @t157))) % 45.66/45.97 (step @p250 :rule arith_poly_norm :args ((= @t139 (* -1 (- @t181 0))))) % 45.66/45.97 (step @p251 :rule arith_poly_norm_rel :premises (@p250) :args ((= @t140 (>= @t181 0)))) % 45.66/45.97 (step @p252 :rule trans :premises (@p103 @p251)) % 45.66/45.97 (step @p253 :rule symm :premises (@p252)) % 45.66/45.97 (step @p254 :rule arith_poly_norm :args ((= (+ @t133 @t182 @t132) @t181))) % 45.66/45.97 (step @p255 :rule refl :args (@t132)) % 45.66/45.97 (step @p256 :rule arith_poly_norm :args ((= @t183 @t182))) % 45.66/45.97 (step @p257 :rule refl :args (@t133)) % 45.66/45.97 (step @p258 :rule nary_cong :premises (@p257 @p256 @p255) :args (@t184)) % 45.66/45.97 (step @p259 :rule trans :premises (@p258 @p254)) % 45.66/45.97 (step @p260 :rule cong :premises (@p259 @p151) :args (@t185)) % 45.66/45.97 (step @p261 :rule trans :premises (@p260 @p253)) % 45.66/45.97 (step @p262 :rule arith_poly_norm :args ((= (* 1 (- @t186 0)) (* 1 (- @t156 -1))))) % 45.66/45.97 (step @p263 :rule arith_poly_norm_rel :premises (@p262) :args ((= (>= @t186 0) @t168))) % 45.66/45.97 (step @p264 :rule arith_poly_norm :args ((= @t187 @t186))) % 45.66/45.97 (step @p265 :rule arith_poly_norm :args ((= @t188 @t187))) % 45.66/45.97 (step @p266 :rule trans :premises (@p265 @p264)) % 45.66/45.97 (step @p267 :rule cong :premises (@p266 @p151) :args (@t189)) % 45.66/45.97 (step @p268 :rule trans :premises (@p267 @p263)) % 45.66/45.97 (step @p269 :rule nary_cong :premises (@p155 @p268 @p261) :args (@t190)) % 45.66/45.97 (step @p270 :rule refl :args (@t191)) % 45.66/45.97 (step @p271 :rule cong :premises (@p270 @p269) :args (@t192)) % 45.66/45.97 (step @p272 :rule cong :premises (@p159 @p271) :args ((=> @t161 @t192))) % 45.66/45.97 (assume-push @p319 @t161) % 45.66/45.97 (step @p274 :rule instantiate :premises (@p145) :args ((@list @t111 @t107))) % 45.66/45.97 (step-pop @p320 :rule scope :premises (@p274)) % 45.66/45.97 (step @p275 :rule process_scope :premises (@p320) :args (@t192)) % 45.66/45.97 (step @p277 :rule eq_resolve :premises (@p275 @p272)) % 45.66/45.97 (step @p278 :rule implies_elim :premises (@p277)) % 45.66/45.97 (step @p279 :rule chain_m_resolution :premises (@p278 @p145) :args (@t194 @t149 @t164)) % 45.66/45.97 (step @p280 :rule instantiate :premises (@p68) :args ((@list @t111))) % 45.66/45.97 (step @p281 :rule cnf_equiv_pos2 :args (@t194)) % 45.66/45.97 (step @p282 :rule reordering :premises (@p281) :args ((or @t191 @t195 (not @t194)))) % 45.66/45.97 (step @p283 :rule chain_m_resolution :premises (@p282 @p280 @p279) :args (@t195 (@list true false) (@list @t191 @t194))) % 45.66/45.97 (step @p284 :rule cnf_and_pos :args (@t162 0)) % 45.66/45.97 (step @p285 :rule reordering :premises (@p284) :args ((or @t158 @t166))) % 45.66/45.97 (step @p286 :rule chain_m_resolution :premises (@p285 @p176) :args (@t158 @t149 @t167)) % 45.66/45.97 (step @p287 :rule bool-double-not-elim :args (@t146)) % 45.66/45.97 (step @p288 :rule refl :args (@t170)) % 45.66/45.97 (step @p289 :rule refl :args (@t196)) % 45.66/45.97 (step @p290 :rule refl :args (@t193)) % 45.66/45.97 (step @p291 :rule nary_cong :premises (@p290 @p289 @p288 @p287) :args ((or @t193 @t196 @t170 (not @t147)))) % 45.66/45.97 (step @p292 :rule cnf_and_neg :args (@t193)) % 45.66/45.97 (step @p293 :rule eq_resolve :premises (@p292 @p291)) % 45.66/45.97 (step @p294 :rule reordering :premises (@p293) :args ((or @t146 @t196 @t193 @t170))) % 45.66/45.97 (step @p295 :rule chain_m_resolution :premises (@p294 @p286 @p283 @p249) :args (@t146 (@list false true false) (@list @t158 @t193 @t168))) % 45.66/45.97 (step @p296 :rule cnf_or_pos :args (@t148)) % 45.66/45.97 (step @p297 :rule reordering :premises (@p296) :args ((or @t114 @t131 @t147 (not @t148)))) % 45.66/45.97 (step @p298 :rule chain_m_resolution :premises (@p297 @p173 @p295 @p120) :args (@t131 (@list false false false) (@list @t113 @t146 @t148))) % 45.66/45.97 (assume-push @p321 @t109) % 45.66/45.97 (step @p300 :rule instantiate :premises (@p68) :args ((@list @t130))) % 45.66/45.97 (step-pop @p322 :rule scope :premises (@p300)) % 45.66/45.97 (step @p301 :rule process_scope :premises (@p322) :args ((not @t131))) % 45.66/45.97 (step @p303 :rule implies_elim :premises (@p301)) % 45.66/45.97 (step @p304 false :rule chain_m_resolution :premises (@p303 @p298 @p68) :args (false @t165 (@list @t131 @t109))) % 45.66/45.97 ) % 45.66/45.97 % SZS output end Proof % 45.66/45.97 % cvc5 exiting %------------------------------------------------------------------------------