%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWX099_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 : n009.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 45.74s 45.96s % Output : Proof 45.74s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWX099_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 % 0.17/0.35 % Computer : n009.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Tue Jun 2 22:55:59 EDT 2026 % 0.17/0.35 % CPUTime : % 0.28/0.51 %----Proving TF0_ARI % 45.74/45.96 --- Run --finite-model-find --decision=internal at 45... % 45.74/45.96 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 60... % 45.74/45.96 % SZS status Theorem % 45.74/45.96 % SZS output start Proof % 45.74/45.96 ( % 45.74/45.96 (declare-sort tptp.symbol 0) % 45.74/45.96 (declare-sort tptp.general 0) % 45.74/45.96 (declare-const tptp.composite_p (-> tptp.general Bool)) % 45.74/45.96 (declare-const tptp.f__integer__ (-> Int tptp.general)) % 45.74/45.96 (declare-const tptp.f__symbolic__ (-> tptp.symbol tptp.general)) % 45.74/45.96 (declare-const tptp.sqrtb (-> tptp.general Bool)) % 45.74/45.96 (declare-const tptp.p__is_symbolic__ (-> tptp.general Bool)) % 45.74/45.96 (declare-const tptp.c__supremum__ tptp.general) % 45.74/45.96 (declare-const tptp.c__infimum__ tptp.general) % 45.74/45.96 (declare-const tptp.p__is_integer__ (-> tptp.general Bool)) % 45.74/45.96 (declare-const tptp.composite (-> tptp.general Bool)) % 45.74/45.96 (declare-const tptp.prime (-> tptp.general Bool)) % 45.74/45.96 (declare-const tptp.p__less_equal__ (-> tptp.general tptp.general Bool)) % 45.74/45.96 (declare-const tptp.sqrt (-> tptp.general tptp.general Bool)) % 45.74/45.96 (declare-const tptp.p__less__ (-> tptp.general tptp.general Bool)) % 45.74/45.96 (declare-const tptp.b_i Int) % 45.74/45.96 (declare-const tptp.p__greater__ (-> tptp.general tptp.general Bool)) % 45.74/45.96 (declare-const tptp.p__greater_equal__ (-> tptp.general tptp.general Bool)) % 45.74/45.96 (declare-const tptp.a_i Int) % 45.74/45.96 (define @t1 () (@var "N" Int)) % 45.74/45.96 (define @t2 () (tptp.f__integer__ @t1)) % 45.74/45.96 (define @t3 () (@var "X" tptp.general)) % 45.74/45.96 (define @t4 () (@list @t1)) % 45.74/45.96 (define @t5 () (tptp.p__is_integer__ @t3)) % 45.74/45.96 (define @t6 () (@list @t3)) % 45.74/45.96 (define @t7 () (@var "X2" tptp.symbol)) % 45.74/45.96 (define @t8 () (@var "X1" tptp.general)) % 45.74/45.96 (define @t9 () (@var "N2" Int)) % 45.74/45.96 (define @t10 () (@var "N1" Int)) % 45.74/45.96 (define @t11 () (tptp.f__integer__ @t9)) % 45.74/45.96 (define @t12 () (tptp.f__integer__ @t10)) % 45.74/45.96 (define @t13 () (@list @t10 @t9)) % 45.74/45.96 (define @t14 () (@var "S2" tptp.symbol)) % 45.74/45.96 (define @t15 () (@var "S1" tptp.symbol)) % 45.74/45.96 (define @t16 () (@var "X2" tptp.general)) % 45.74/45.96 (define @t17 () (= @t8 @t16)) % 45.74/45.96 (define @t18 () (tptp.p__less_equal__ @t16 @t8)) % 45.74/45.96 (define @t19 () (tptp.p__less_equal__ @t8 @t16)) % 45.74/45.96 (define @t20 () (@list @t8 @t16)) % 45.74/45.96 (define @t21 () (@var "X3" tptp.general)) % 45.74/45.96 (define @t22 () (not @t17)) % 45.74/45.96 (define @t23 () (@var "S" tptp.symbol)) % 45.74/45.96 (define @t24 () (tptp.f__symbolic__ @t23)) % 45.74/45.96 (define @t25 () (@var "Z1_g" tptp.general)) % 45.74/45.96 (define @t26 () (@var "Z_g" tptp.general)) % 45.74/45.96 (define @t27 () (= @t26 @t25)) % 45.74/45.96 (define @t28 () (@var "J_i" Int)) % 45.74/45.96 (define @t29 () (@var "K_i" Int)) % 45.74/45.96 (define @t30 () (<= @t29 @t28)) % 45.74/45.96 (define @t31 () (@var "I_i" Int)) % 45.74/45.96 (define @t32 () (<= @t31 @t29)) % 45.74/45.96 (define @t33 () (= @t25 (tptp.f__integer__ @t29))) % 45.74/45.96 (define @t34 () (= @t28 tptp.b_i)) % 45.74/45.96 (define @t35 () (= @t31 2)) % 45.74/45.96 (define @t36 () (@list @t31 @t28 @t29)) % 45.74/45.96 (define @t37 () (exists @t36 (and @t35 @t34 @t33 @t32 @t30))) % 45.74/45.96 (define @t38 () (@var "J_g" tptp.general)) % 45.74/45.96 (define @t39 () (@list @t26 @t25)) % 45.74/45.96 (define @t40 () (exists @t39 (and (= @t26 @t38) @t37 @t27))) % 45.74/45.96 (define @t41 () (@var "I_g" tptp.general)) % 45.74/45.96 (define @t42 () (= @t26 @t41)) % 45.74/45.96 (define @t43 () (@var "J1_i" Int)) % 45.74/45.96 (define @t44 () (@var "I1_i" Int)) % 45.74/45.96 (define @t45 () (tptp.f__integer__ @t44)) % 45.74/45.96 (define @t46 () (@var "V1_g" tptp.general)) % 45.74/45.96 (define @t47 () (exists (@list @t44 @t43) (and (= @t46 (tptp.f__integer__ (* @t44 @t43))) (= @t45 @t41) (= (tptp.f__integer__ @t43) @t38)))) % 45.74/45.96 (define @t48 () (@list @t46)) % 45.74/45.96 (define @t49 () (= @t25 (tptp.f__integer__ tptp.b_i))) % 45.74/45.96 (define @t50 () (@var "M_g" tptp.general)) % 45.74/45.96 (define @t51 () (tptp.f__integer__ @t31)) % 45.74/45.96 (define @t52 () (= @t51 @t50)) % 45.74/45.96 (define @t53 () (= @t26 (tptp.f__integer__ (* @t31 @t28)))) % 45.74/45.96 (define @t54 () (@list @t31 @t28)) % 45.74/45.96 (define @t55 () (= (tptp.f__integer__ @t28) @t50)) % 45.74/45.96 (define @t56 () (= @t26 @t50)) % 45.74/45.96 (define @t57 () (@list @t26)) % 45.74/45.96 (define @t58 () (+ @t31 1)) % 45.74/45.96 (define @t59 () (* @t58 @t58)) % 45.74/45.96 (define @t60 () (@var "N_i" Int)) % 45.74/45.96 (define @t61 () (* @t31 @t31)) % 45.74/45.96 (define @t62 () (<= @t61 @t60)) % 45.74/45.96 (define @t63 () (>= @t31 0)) % 45.74/45.96 (define @t64 () (and @t63 @t62 (< @t60 @t59))) % 45.74/45.96 (define @t65 () (tptp.sqrt @t51 (tptp.f__integer__ @t60))) % 45.74/45.96 (define @t66 () (= @t65 @t64)) % 45.74/45.96 (define @t67 () (@list @t31 @t60)) % 45.74/45.96 (define @t68 () (forall @t67 @t66)) % 45.74/45.96 (define @t69 () (+ @t60 1)) % 45.74/45.96 (define @t70 () (tptp.f__integer__ @t69)) % 45.74/45.96 (define @t71 () (tptp.f__integer__ @t58)) % 45.74/45.96 (define @t72 () (tptp.sqrt @t71 @t70)) % 45.74/45.96 (define @t73 () (<= @t59 @t69)) % 45.74/45.96 (define @t74 () (and @t65 @t73)) % 45.74/45.96 (define @t75 () (=> @t74 @t72)) % 45.74/45.96 (define @t76 () (forall @t67 @t75)) % 45.74/45.96 (define @t77 () (not @t76)) % 45.74/45.96 (define @t78 () (+ 1 @t60)) % 45.74/45.96 (define @t79 () (+ 1 @t31)) % 45.74/45.96 (define @t80 () (tptp.sqrt (tptp.f__integer__ @t79) (tptp.f__integer__ @t78))) % 45.74/45.96 (define @t81 () (* @t31 @t31)) % 45.74/45.96 (define @t82 () (* 2 @t31)) % 45.74/45.96 (define @t83 () (+ @t82 (* -1 @t60) @t81)) % 45.74/45.96 (define @t84 () (>= @t83 1)) % 45.74/45.96 (define @t85 () (not @t65)) % 45.74/45.96 (define @t86 () (or @t85 @t84 @t80)) % 45.74/45.96 (define @t87 () (not @t84)) % 45.74/45.96 (define @t88 () (and @t65 @t87)) % 45.74/45.96 (define @t89 () (+ @t78 1)) % 45.74/45.96 (define @t90 () (+ 1 @t82 @t81)) % 45.74/45.96 (define @t91 () (>= @t90 @t89)) % 45.74/45.96 (define @t92 () (forall @t67 @t86)) % 45.74/45.96 (define @t93 () (@quantifiers_skolemize @t92 1)) % 45.74/45.96 (define @t94 () (+ 1 @t93)) % 45.74/45.96 (define @t95 () (@quantifiers_skolemize @t92 0)) % 45.74/45.96 (define @t96 () (+ 1 @t95)) % 45.74/45.96 (define @t97 () (tptp.sqrt (tptp.f__integer__ @t96) (tptp.f__integer__ @t94))) % 45.74/45.96 (define @t98 () (* @t95 @t95)) % 45.74/45.96 (define @t99 () (* -1 @t93)) % 45.74/45.96 (define @t100 () (* 2 @t95)) % 45.74/45.96 (define @t101 () (+ @t100 @t99 @t98)) % 45.74/45.96 (define @t102 () (>= @t101 1)) % 45.74/45.96 (define @t103 () (tptp.sqrt (tptp.f__integer__ @t95) (tptp.f__integer__ @t93))) % 45.74/45.96 (define @t104 () (not @t103)) % 45.74/45.96 (define @t105 () (or @t104 @t102 @t97)) % 45.74/45.96 (define @t106 () (not @t102)) % 45.74/45.96 (define @t107 () (@list true)) % 45.74/45.96 (define @t108 () (@list @t105)) % 45.74/45.96 (define @t109 () (>= @t83 0)) % 45.74/45.96 (define @t110 () (+ @t83 1)) % 45.74/45.96 (define @t111 () (>= @t60 @t59)) % 45.74/45.96 (define @t112 () (+ @t60 (* -1 @t81))) % 45.74/45.96 (define @t113 () (>= @t112 0)) % 45.74/45.96 (define @t114 () (* 4 @t95)) % 45.74/45.96 (define @t115 () (+ @t114 @t99 @t98)) % 45.74/45.96 (define @t116 () (+ 2 @t114 @t99 @t98)) % 45.74/45.96 (define @t117 () (>= @t115 -2)) % 45.74/45.96 (define @t118 () (+ 1 @t100 @t98)) % 45.74/45.96 (define @t119 () (+ -1 @t99)) % 45.74/45.96 (define @t120 () (+ 2 @t100)) % 45.74/45.96 (define @t121 () (* @t96 @t96)) % 45.74/45.96 (define @t122 () (* -1 @t94)) % 45.74/45.96 (define @t123 () (* 2 @t96)) % 45.74/45.96 (define @t124 () (+ @t123 @t122 @t121)) % 45.74/45.96 (define @t125 () (>= @t124 0)) % 45.74/45.96 (define @t126 () (* -1 @t98)) % 45.74/45.96 (define @t127 () (* -2 @t95)) % 45.74/45.96 (define @t128 () (+ @t127 @t93 @t126)) % 45.74/45.96 (define @t129 () (+ @t101 1)) % 45.74/45.96 (define @t130 () (+ -1 @t127 @t126)) % 45.74/45.96 (define @t131 () (* -1 @t121)) % 45.74/45.96 (define @t132 () (+ @t131 @t93 1)) % 45.74/45.96 (define @t133 () (+ @t94 @t131)) % 45.74/45.96 (define @t134 () (>= @t133 0)) % 45.74/45.96 (define @t135 () (>= @t95 -1)) % 45.74/45.96 (define @t136 () (>= @t96 0)) % 45.74/45.96 (define @t137 () (and @t136 @t134 @t125)) % 45.74/45.96 (define @t138 () (= @t97 @t137)) % 45.74/45.96 (define @t139 () (forall @t67 (= @t65 (and @t63 @t113 @t109)))) % 45.74/45.96 (define @t140 () (and @t135 @t106 @t117)) % 45.74/45.96 (define @t141 () (= @t97 @t140)) % 45.74/45.96 (define @t142 () (@list false)) % 45.74/45.96 (define @t143 () (not @t140)) % 45.74/45.96 (define @t144 () (>= @t101 0)) % 45.74/45.96 (define @t145 () (>= @t95 0)) % 45.74/45.96 (define @t146 () (and @t145 (>= (+ @t93 @t126) 0) @t144)) % 45.74/45.96 (define @t147 () (= @t103 @t146)) % 45.74/45.96 (define @t148 () (@list false false)) % 45.74/45.96 (define @t149 () (not @t146)) % 45.74/45.96 (define @t150 () (@list @t146)) % 45.74/45.96 (define @t151 () (< @t95 -1)) % 45.74/45.96 (define @t152 () (not true)) % 45.74/45.96 (define @t153 () (* -1 0)) % 45.74/45.96 (define @t154 () (+ -1 @t153)) % 45.74/45.96 (define @t155 () (+ @t95 (* -1 @t95))) % 45.74/45.96 (define @t156 () (>= @t155 @t154)) % 45.74/45.96 (define @t157 () (< -1 0)) % 45.74/45.96 (define @t158 () (not @t145)) % 45.74/45.96 (define @t159 () (not @t144)) % 45.74/45.96 (define @t160 () (not @t117)) % 45.74/45.96 (define @t161 () (* -2 0)) % 45.74/45.96 (define @t162 () (+ -2 @t153 @t161)) % 45.74/45.96 (define @t163 () (* 0 @t93)) % 45.74/45.96 (define @t164 () (* 0 @t98)) % 45.74/45.96 (define @t165 () (+ @t114 @t127 @t164 @t163 @t127)) % 45.74/45.96 (define @t166 () (+ @t115 (* -1 @t101) @t127)) % 45.74/45.96 (define @t167 () (>= @t166 @t162)) % 45.74/45.96 (define @t168 () (not @t135)) % 45.74/45.96 (assume @p1 (forall @t6 (= @t5 (exists @t4 (= @t3 @t2))))) % 45.74/45.96 (assume @p2 (forall (@list @t8) (= (tptp.p__is_symbolic__ @t8) (exists (@list @t7) (= @t8 (tptp.f__symbolic__ @t7)))))) % 45.74/45.96 (assume @p3 (forall @t6 (or (= @t3 tptp.c__infimum__) @t5 (tptp.p__is_symbolic__ @t3) (= @t3 tptp.c__supremum__)))) % 45.74/45.96 (assume @p4 (forall @t13 (= (= @t12 @t11) (= @t10 @t9)))) % 45.74/45.96 (assume @p5 (forall (@list @t15 @t14) (= (= (tptp.f__symbolic__ @t15) (tptp.f__symbolic__ @t14)) (= @t15 @t14)))) % 45.74/45.96 (assume @p6 (forall @t13 (= (tptp.p__less_equal__ @t12 @t11) (<= @t10 @t9)))) % 45.74/45.96 (assume @p7 (forall @t20 (=> (and @t19 @t18) @t17))) % 45.74/45.96 (assume @p8 (forall (@list @t8 @t16 @t21) (=> (and @t19 (tptp.p__less_equal__ @t16 @t21)) (tptp.p__less_equal__ @t8 @t21)))) % 45.74/45.96 (assume @p9 (forall @t20 (or @t19 @t18))) % 45.74/45.96 (assume @p10 (forall @t20 (= (tptp.p__less__ @t8 @t16) (and @t19 @t22)))) % 45.74/45.96 (assume @p11 (forall @t20 (= (tptp.p__greater_equal__ @t8 @t16) @t18))) % 45.74/45.96 (assume @p12 (forall @t20 (= (tptp.p__greater__ @t8 @t16) (and @t18 @t22)))) % 45.74/45.96 (assume @p13 (forall @t4 (tptp.p__less__ tptp.c__infimum__ @t2))) % 45.74/45.96 (assume @p14 (forall (@list @t1 @t23) (tptp.p__less__ @t2 @t24))) % 45.74/45.96 (assume @p15 (forall (@list @t23) (tptp.p__less__ @t24 tptp.c__supremum__))) % 45.74/45.96 (assume @p16 (> tptp.a_i 1)) % 45.74/45.96 (assume @p17 (forall @t48 (= (tptp.composite @t46) (exists (@list @t41 @t38) (and @t47 (exists @t39 (and @t42 @t37 @t27)) @t40))))) % 45.74/45.96 (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)))))))) % 45.74/45.96 (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))))) % 45.74/45.96 (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))))))))) % 45.74/45.96 (assume @p21 @t68) % 45.74/45.96 (assume @p22 @t77) % 45.74/45.96 (assume @p23 true) % 45.74/45.96 (step @p24 :rule aci_norm :args ((= (or (or @t85 @t84) @t80) @t86))) % 45.74/45.96 (step @p25 :rule refl :args (@t80)) % 45.74/45.96 (step @p26 :rule bool-double-not-elim :args (@t84)) % 45.74/45.96 (step @p27 :rule refl :args (@t85)) % 45.74/45.96 (step @p28 :rule nary_cong :premises (@p27 @p26) :args ((or @t85 (not @t87)))) % 45.74/45.96 (step @p29 :rule bool-and-de-morgan :args (@t65 @t87 true)) % 45.74/45.96 (step @p30 :rule trans :premises (@p29 @p28)) % 45.74/45.96 (step @p31 :rule nary_cong :premises (@p30 @p25) :args ((or (not @t88) @t80))) % 45.74/45.96 (step @p32 :rule trans :premises (@p31 @p24)) % 45.74/45.96 (step @p33 :rule bool-impl-elim :args (@t88 @t80)) % 45.74/45.96 (step @p34 :rule trans :premises (@p33 @p32)) % 45.74/45.96 (step @p35 :rule cong :premises (@p34) :args ((forall @t67 (=> @t88 @t80)))) % 45.74/45.96 (step @p36 :rule arith_poly_norm :args ((= @t69 @t78))) % 45.74/45.96 (step @p37 :rule cong :premises (@p36) :args (@t70)) % 45.74/45.96 (step @p38 :rule arith_poly_norm :args ((= @t58 @t79))) % 45.74/45.96 (step @p39 :rule cong :premises (@p38) :args (@t71)) % 45.74/45.96 (step @p40 :rule cong :premises (@p39 @p37) :args (@t72)) % 45.74/45.96 (step @p41 :rule arith_poly_norm :args ((= (* -1 (- @t90 @t89)) (* -1 (- @t83 1))))) % 45.74/45.96 (step @p42 :rule arith_poly_norm_rel :premises (@p41) :args ((= @t91 @t84))) % 45.74/45.96 (step @p43 :rule cong :premises (@p42) :args ((not @t91))) % 45.74/45.96 (step @p44 :rule arith-leq-norm :args (@t90 @t78)) % 45.74/45.96 (step @p45 :rule trans :premises (@p44 @p43)) % 45.74/45.96 (step @p46 :rule arith_poly_norm :args ((= (* @t79 @t79) @t90))) % 45.74/45.96 (step @p47 :rule nary_cong :premises (@p38 @p38) :args (@t59)) % 45.74/45.96 (step @p48 :rule trans :premises (@p47 @p46)) % 45.74/45.96 (step @p49 :rule cong :premises (@p48 @p36) :args (@t73)) % 45.74/45.96 (step @p50 :rule trans :premises (@p49 @p45)) % 45.74/45.96 (step @p51 :rule refl :args (@t65)) % 45.74/45.96 (step @p52 :rule nary_cong :premises (@p51 @p50) :args (@t74)) % 45.74/45.96 (step @p53 :rule cong :premises (@p52 @p40) :args (@t75)) % 45.74/45.96 (step @p54 :rule cong :premises (@p53) :args (@t76)) % 45.74/45.96 (step @p55 :rule trans :premises (@p54 @p35)) % 45.74/45.96 (step @p56 :rule cong :premises (@p55) :args (@t77)) % 45.74/45.96 (step @p57 :rule eq_resolve :premises (@p22 @p56)) % 45.74/45.96 (step @p58 :rule skolemize :premises (@p57)) % 45.74/45.96 (step @p59 :rule cnf_or_neg :args (@t105 1)) % 45.74/45.96 (step @p60 :rule chain_m_resolution :premises (@p59 @p58) :args (@t106 @t107 @t108)) % 45.74/45.96 (step @p61 :rule bool-double-not-elim :args (@t109)) % 45.74/45.96 (step @p62 :rule arith_poly_norm :args ((= (* -1 (- 0 @t110)) (* -1 (- @t60 @t90))))) % 45.74/45.96 (step @p63 :rule arith_poly_norm_rel :premises (@p62) :args ((= (>= 0 @t110) (>= @t60 @t90)))) % 45.74/45.96 (step @p64 :rule arith-geq-tighten :args (@t83 0)) % 45.74/45.96 (step @p65 :rule trans :premises (@p64 @p63)) % 45.74/45.96 (step @p66 :rule symm :premises (@p65)) % 45.74/45.96 (step @p67 :rule refl :args (@t60)) % 45.74/45.96 (step @p68 :rule cong :premises (@p67 @p48) :args (@t111)) % 45.74/45.96 (step @p69 :rule trans :premises (@p68 @p66)) % 45.74/45.96 (step @p70 :rule cong :premises (@p69) :args ((not @t111))) % 45.74/45.96 (step @p71 :rule trans :premises (@p70 @p61)) % 45.74/45.96 (step @p72 :rule arith-elim-lt :args (@t60 @t59)) % 45.74/45.96 (step @p73 :rule trans :premises (@p72 @p71)) % 45.74/45.96 (step @p74 :rule arith_poly_norm :args ((= (* 1 (- @t60 @t81)) (* 1 (- @t112 0))))) % 45.74/45.96 (step @p75 :rule arith_poly_norm_rel :premises (@p74) :args ((= (>= @t60 @t81) @t113))) % 45.74/45.96 (step @p76 :rule arith-elim-leq :args (@t81 @t60)) % 45.74/45.96 (step @p77 :rule trans :premises (@p76 @p75)) % 45.74/45.96 (step @p78 :rule arith_poly_norm :args ((= @t61 @t81))) % 45.74/45.96 (step @p79 :rule cong :premises (@p78 @p67) :args (@t62)) % 45.74/45.96 (step @p80 :rule trans :premises (@p79 @p77)) % 45.74/45.96 (step @p81 :rule refl :args (@t63)) % 45.74/45.96 (step @p82 :rule nary_cong :premises (@p81 @p80 @p73) :args (@t64)) % 45.74/45.96 (step @p83 :rule cong :premises (@p51 @p82) :args (@t66)) % 45.74/45.96 (step @p84 :rule cong :premises (@p83) :args (@t68)) % 45.74/45.96 (step @p85 :rule eq_resolve :premises (@p21 @p84)) % 45.74/45.96 (step @p86 :rule arith_poly_norm :args ((= (* 2 (- @t116 0)) (* 2 (- @t115 -2))))) % 45.74/45.96 (step @p87 :rule arith_poly_norm_rel :premises (@p86) :args ((= (>= @t116 0) @t117))) % 45.74/45.96 (step @p88 :rule refl :args (0)) % 45.74/45.96 (step @p89 :rule arith_poly_norm :args ((= (+ @t120 @t119 @t118) @t116))) % 45.74/45.96 (step @p90 :rule arith_poly_norm :args ((= @t121 @t118))) % 45.74/45.96 (step @p91 :rule arith_poly_norm :args ((= @t122 @t119))) % 45.74/45.96 (step @p92 :rule arith_poly_norm :args ((= @t123 @t120))) % 45.74/45.96 (step @p93 :rule nary_cong :premises (@p92 @p91 @p90) :args (@t124)) % 45.74/45.96 (step @p94 :rule trans :premises (@p93 @p89)) % 45.74/45.96 (step @p95 :rule cong :premises (@p94 @p88) :args (@t125)) % 45.74/45.96 (step @p96 :rule trans :premises (@p95 @p87)) % 45.74/45.96 (step @p97 :rule arith_poly_norm :args ((= (* -2 (- 1 @t129)) (* -2 (- @t128 0))))) % 45.74/45.96 (step @p98 :rule arith_poly_norm_rel :premises (@p97) :args ((= (>= 1 @t129) (>= @t128 0)))) % 45.74/45.96 (step @p99 :rule arith-geq-tighten :args (@t101 1)) % 45.74/45.96 (step @p100 :rule trans :premises (@p99 @p98)) % 45.74/45.96 (step @p101 :rule symm :premises (@p100)) % 45.74/45.96 (step @p102 :rule arith_poly_norm :args ((= (+ @t130 @t93 1) @t128))) % 45.74/45.96 (step @p103 :rule refl :args (1)) % 45.74/45.96 (step @p104 :rule refl :args (@t93)) % 45.74/45.96 (step @p105 :rule arith_poly_norm :args ((= (* -1 @t118) @t130))) % 45.74/45.96 (step @p106 :rule refl :args (-1)) % 45.74/45.96 (step @p107 :rule nary_cong :premises (@p106 @p90) :args (@t131)) % 45.74/45.96 (step @p108 :rule trans :premises (@p107 @p105)) % 45.74/45.96 (step @p109 :rule nary_cong :premises (@p108 @p104 @p103) :args (@t132)) % 45.74/45.96 (step @p110 :rule trans :premises (@p109 @p102)) % 45.74/45.96 (step @p111 :rule arith_poly_norm :args ((= @t133 @t132))) % 45.74/45.96 (step @p112 :rule trans :premises (@p111 @p110)) % 45.74/45.96 (step @p113 :rule cong :premises (@p112 @p88) :args (@t134)) % 45.74/45.96 (step @p114 :rule trans :premises (@p113 @p101)) % 45.74/45.96 (step @p115 :rule arith_poly_norm :args ((= (* 1 (- @t96 0)) (* 1 (- @t95 -1))))) % 45.74/45.96 (step @p116 :rule arith_poly_norm_rel :premises (@p115) :args ((= @t136 @t135))) % 45.74/45.96 (step @p117 :rule nary_cong :premises (@p116 @p114 @p96) :args (@t137)) % 45.74/45.96 (step @p118 :rule refl :args (@t97)) % 45.74/45.96 (step @p119 :rule cong :premises (@p118 @p117) :args (@t138)) % 45.74/45.96 (step @p120 :rule refl :args (@t139)) % 45.74/45.96 (step @p121 :rule cong :premises (@p120 @p119) :args ((=> @t139 @t138))) % 45.74/45.96 (assume-push @p247 @t139) % 45.74/45.96 (step @p123 :rule instantiate :premises (@p85) :args ((@list @t96 @t94))) % 45.74/45.96 (step-pop @p248 :rule scope :premises (@p123)) % 45.74/45.96 (step @p124 :rule process_scope :premises (@p248) :args (@t138)) % 45.74/45.96 (step @p126 :rule eq_resolve :premises (@p124 @p121)) % 45.74/45.96 (step @p127 :rule implies_elim :premises (@p126)) % 45.74/45.96 (step @p128 :rule chain_m_resolution :premises (@p127 @p85) :args (@t141 @t142 (@list @t139))) % 45.74/45.96 (step @p129 :rule cnf_or_neg :args (@t105 2)) % 45.74/45.96 (step @p130 :rule chain_m_resolution :premises (@p129 @p58) :args ((not @t97) @t107 @t108)) % 45.74/45.96 (step @p131 :rule cnf_equiv_pos2 :args (@t141)) % 45.74/45.96 (step @p132 :rule reordering :premises (@p131) :args ((or @t97 @t143 (not @t141)))) % 45.74/45.96 (step @p133 :rule chain_m_resolution :premises (@p132 @p130 @p128) :args (@t143 (@list true false) (@list @t97 @t141))) % 45.74/45.96 (step @p134 :rule instantiate :premises (@p85) :args ((@list @t95 @t93))) % 45.74/45.96 (step @p135 :rule bool-double-not-elim :args (@t103)) % 45.74/45.96 (step @p136 :rule refl :args (@t105)) % 45.74/45.96 (step @p137 :rule nary_cong :premises (@p136 @p135) :args ((or @t105 (not @t104)))) % 45.74/45.96 (step @p138 :rule cnf_or_neg :args (@t105 0)) % 45.74/45.96 (step @p139 :rule eq_resolve :premises (@p138 @p137)) % 45.74/45.96 (step @p140 :rule reordering :premises (@p139) :args ((or @t103 @t105))) % 45.74/45.96 (step @p141 :rule chain_m_resolution :premises (@p140 @p58) :args (@t103 @t107 @t108)) % 45.74/45.96 (step @p142 :rule cnf_equiv_pos1 :args (@t147)) % 45.74/45.96 (step @p143 :rule reordering :premises (@p142) :args ((or @t104 @t146 (not @t147)))) % 45.74/45.96 (step @p144 :rule chain_m_resolution :premises (@p143 @p141 @p134) :args (@t146 @t148 (@list @t103 @t147))) % 45.74/45.96 (step @p145 :rule cnf_and_pos :args (@t146 0)) % 45.74/45.96 (step @p146 :rule reordering :premises (@p145) :args ((or @t145 @t149))) % 45.74/45.96 (step @p147 :rule chain_m_resolution :premises (@p146 @p144) :args (@t145 @t142 @t150)) % 45.74/45.96 (assume-push @p249 @t145) % 45.74/45.96 (assume-push @p250 @t145) % 45.74/45.96 (step @p150 :rule bool-double-not-elim :args (@t135)) % 45.74/45.96 (step @p151 :rule arith-elim-lt :args (@t95 -1)) % 45.74/45.96 (step @p152 :rule cong :premises (@p151) :args ((not @t151))) % 45.74/45.96 (step @p153 :rule trans :premises (@p152 @p150)) % 45.74/45.96 (assume-push @p251 @t151) % 45.74/45.96 (step @p155 :rule evaluate :args (@t152)) % 45.74/45.96 (step @p156 :rule evaluate :args ((>= 0 -1))) % 45.74/45.96 (step @p157 :rule evaluate :args ((+ -1 0))) % 45.74/45.96 (step @p158 :rule evaluate :args (@t153)) % 45.74/45.96 (step @p159 :rule nary_cong :premises (@p106 @p158) :args (@t154)) % 45.74/45.96 (step @p160 :rule trans :premises (@p159 @p157)) % 45.74/45.96 (step @p161 :rule arith_poly_norm :args ((= @t155 0))) % 45.74/45.96 (step @p162 :rule cong :premises (@p161 @p160) :args (@t156)) % 45.74/45.96 (step @p163 :rule trans :premises (@p162 @p156)) % 45.74/45.96 (step @p164 :rule cong :premises (@p163) :args ((not @t156))) % 45.74/45.96 (step @p165 :rule trans :premises (@p164 @p155)) % 45.74/45.96 (step @p166 :rule arith-elim-lt :args (@t155 @t154)) % 45.74/45.96 (step @p167 :rule trans :premises (@p166 @p165)) % 45.74/45.96 (step @p168 :rule arith_mult_neg :args (-1 @t145)) % 45.74/45.96 (step @p169 :rule evaluate :args (@t157)) % 45.74/45.96 (step @p170 :rule true_elim :premises (@p169)) % 45.74/45.96 (step @p171 :rule and_intro :premises (@p170 @p147)) % 45.74/45.96 (step @p172 :rule modus_ponens :premises (@p171 @p168)) % 45.74/45.96 (step @p173 :rule arith_sum_ub :premises (@p251 @p172)) % 45.74/45.96 (step @p174 false :rule eq_resolve :premises (@p173 @p167)) % 45.74/45.96 (step-pop @p252 :rule scope :premises (@p174)) % 45.74/45.96 (step @p175 :rule process_scope :premises (@p252) :args (false)) % 45.74/45.96 (step @p177 :rule eq_resolve :premises (@p175 @p153)) % 45.74/45.96 (step-pop @p253 :rule scope :premises (@p177)) % 45.74/45.96 (step @p178 :rule process_scope :premises (@p253) :args (@t135)) % 45.74/45.96 (step @p180 :rule modus_ponens :premises (@p147 @p178)) % 45.74/45.96 (step-pop @p254 :rule scope :premises (@p180)) % 45.74/45.96 (step @p181 :rule process_scope :premises (@p254) :args (@t135)) % 45.74/45.96 (step @p183 :rule implies_elim :premises (@p181)) % 45.74/45.96 (step @p184 :rule reordering :premises (@p183) :args ((or @t135 @t158))) % 45.74/45.96 (step @p185 :rule chain_m_resolution :premises (@p184 @p147) :args (@t135 @t142 (@list @t145))) % 45.74/45.96 (step @p186 :rule cnf_and_pos :args (@t146 2)) % 45.74/45.96 (step @p187 :rule reordering :premises (@p186) :args ((or @t144 @t149))) % 45.74/45.96 (step @p188 :rule chain_m_resolution :premises (@p187 @p144) :args (@t144 @t142 @t150)) % 45.74/45.96 (step @p189 :rule bool-double-not-elim :args (@t117)) % 45.74/45.96 (step @p190 :rule refl :args (@t158)) % 45.74/45.96 (step @p191 :rule refl :args (@t159)) % 45.74/45.96 (step @p192 :rule nary_cong :premises (@p191 @p190 @p189) :args ((or @t159 @t158 (not @t160)))) % 45.74/45.96 (assume-push @p255 @t144) % 45.74/45.96 (assume-push @p256 @t145) % 45.74/45.96 (assume-push @p257 @t160) % 45.74/45.96 (step @p155 :rule evaluate :args (@t152)) % 45.74/45.96 (step @p196 :rule evaluate :args ((>= 0 -2))) % 45.74/45.96 (step @p197 :rule evaluate :args ((+ -2 0 0))) % 45.74/45.96 (step @p198 :rule evaluate :args (@t161)) % 45.74/45.96 (step @p158 :rule evaluate :args (@t153)) % 45.74/45.96 (step @p199 :rule refl :args (-2)) % 45.74/45.96 (step @p200 :rule nary_cong :premises (@p199 @p158 @p198) :args (@t162)) % 45.74/45.96 (step @p201 :rule trans :premises (@p200 @p197)) % 45.74/45.96 (step @p202 :rule arith_poly_norm :args ((= (+ @t114 @t127 0 0 @t127) 0))) % 45.74/45.96 (step @p203 :rule refl :args (@t127)) % 45.74/45.96 (step @p204 :rule arith_poly_norm :args ((= @t163 0))) % 45.74/45.96 (step @p205 :rule arith_poly_norm :args ((= @t164 0))) % 45.74/45.96 (step @p206 :rule refl :args (@t114)) % 45.74/45.96 (step @p207 :rule nary_cong :premises (@p206 @p203 @p205 @p204 @p203) :args (@t165)) % 45.74/45.96 (step @p208 :rule trans :premises (@p207 @p202)) % 45.74/45.96 (step @p209 :rule arith_poly_norm :args ((= @t166 @t165))) % 45.74/45.96 (step @p210 :rule trans :premises (@p209 @p208)) % 45.74/45.96 (step @p211 :rule cong :premises (@p210 @p201) :args (@t167)) % 45.74/45.96 (step @p212 :rule trans :premises (@p211 @p196)) % 45.74/45.96 (step @p213 :rule cong :premises (@p212) :args ((not @t167))) % 45.74/45.96 (step @p214 :rule trans :premises (@p213 @p155)) % 45.74/45.96 (step @p215 :rule arith-elim-lt :args (@t166 @t162)) % 45.74/45.96 (step @p216 :rule trans :premises (@p215 @p214)) % 45.74/45.96 (step @p217 :rule arith_mult_neg :args (-2 @t145)) % 45.74/45.96 (step @p218 :rule evaluate :args ((< -2 0))) % 45.74/45.96 (step @p219 :rule true_elim :premises (@p218)) % 45.74/45.96 (step @p220 :rule and_intro :premises (@p219 @p147)) % 45.74/45.96 (step @p221 :rule modus_ponens :premises (@p220 @p217)) % 45.74/45.96 (step @p222 :rule arith_mult_neg :args (-1 @t144)) % 45.74/45.96 (step @p169 :rule evaluate :args (@t157)) % 45.74/45.96 (step @p170 :rule true_elim :premises (@p169)) % 45.74/45.96 (step @p223 :rule and_intro :premises (@p170 @p188)) % 45.74/45.96 (step @p224 :rule modus_ponens :premises (@p223 @p222)) % 45.74/45.96 (step @p225 :rule arith-elim-lt :args (@t115 -2)) % 45.74/45.96 (step @p226 :rule symm :premises (@p225)) % 45.74/45.96 (step @p227 :rule eq_resolve :premises (@p257 @p226)) % 45.74/45.96 (step @p228 :rule arith_sum_ub :premises (@p227 @p224 @p221)) % 45.74/45.96 (step @p229 false :rule eq_resolve :premises (@p228 @p216)) % 45.74/45.96 (step-pop @p258 :rule scope :premises (@p229)) % 45.74/45.96 (step-pop @p259 :rule scope :premises (@p258)) % 45.74/45.96 (step-pop @p260 :rule scope :premises (@p259)) % 45.74/45.96 (step @p230 :rule process_scope :premises (@p260) :args (false)) % 45.74/45.96 (step @p234 :rule not_and :premises (@p230)) % 45.74/45.96 (step @p235 :rule eq_resolve :premises (@p234 @p192)) % 45.74/45.96 (step @p236 :rule reordering :premises (@p235) :args ((or @t117 @t159 @t158))) % 45.74/45.96 (step @p237 :rule chain_m_resolution :premises (@p236 @p188 @p147) :args (@t117 @t148 (@list @t144 @t145))) % 45.74/45.96 (step @p238 :rule refl :args (@t160)) % 45.74/45.96 (step @p239 :rule bool-double-not-elim :args (@t102)) % 45.74/45.96 (step @p240 :rule refl :args (@t168)) % 45.74/45.96 (step @p241 :rule refl :args (@t140)) % 45.74/45.96 (step @p242 :rule nary_cong :premises (@p241 @p240 @p239 @p238) :args ((or @t140 @t168 (not @t106) @t160))) % 45.74/45.96 (step @p243 :rule cnf_and_neg :args (@t140)) % 45.74/45.96 (step @p244 :rule eq_resolve :premises (@p243 @p242)) % 45.74/45.96 (step @p245 :rule reordering :premises (@p244) :args ((or @t102 @t140 @t168 @t160))) % 45.74/45.96 (step @p246 false :rule chain_m_resolution :premises (@p245 @p237 @p185 @p133 @p60) :args (false (@list false false true true) (@list @t117 @t135 @t140 @t102))) % 45.74/45.96 ) % 45.74/45.96 % SZS output end Proof % 45.74/45.96 % cvc5 exiting %------------------------------------------------------------------------------