%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO535^1 : TPTP v9.2.1. Released v5.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n016.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 09:13:05 AM UTC 2026 % Result : Theorem 2.20s 2.50s % Output : Proof 0.34s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.13 % Problem : SYO535^1 : TPTP v9.2.1. Released v5.2.0. % 0.11/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.35 % Computer : n016.cluster.edu % 0.16/0.35 % Model : x86_64 x86_64 % 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.35 % Memory : 8042.1875MB % 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.35 % CPULimit : 300 % 0.16/0.35 % WCLimit : 300 % 0.16/0.35 % DateTime : Wed Jun 3 00:20:09 EDT 2026 % 0.16/0.36 % CPUTime : % 0.26/0.51 %----Proving TH0 % 2.20/2.50 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 2.20/2.50 % SZS status Theorem % 2.20/2.50 % SZS output start Proof % 2.20/2.50 ( % 2.20/2.50 (declare-sort $$unsorted 0) % 2.20/2.50 (declare-const tptp.eps (-> (-> $$unsorted Bool) $$unsorted)) % 2.20/2.50 (declare-const tptp.epsii (-> (-> (-> $$unsorted $$unsorted) Bool) $$unsorted $$unsorted)) % 2.20/2.50 (define tptp.epsa () (let ((_let_1 (@var "Y" (-> $$unsorted $$unsorted)))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted (-> $$unsorted $$unsorted) Bool)))) (lambda (@list _let_3) (_ tptp.eps (lambda (@list _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1))))))))) % 2.20/2.50 (define tptp.epsb () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted $$unsorted)))) (let ((_let_3 (@var "R" (-> $$unsorted (-> $$unsorted $$unsorted) Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.epsii (lambda (@list _let_2) (_ (_ _let_3 (_ tptp.epsa _let_3)) _let_2))) _let_1)))))) % 2.20/2.50 (define @t1 () (@var "P" (-> $$unsorted Bool))) % 2.20/2.50 (define @t2 () (_ tptp.eps @t1)) % 2.20/2.50 (define @t3 () (_ @t1 @t2)) % 2.20/2.50 (define @t4 () (@var "X" $$unsorted)) % 2.20/2.50 (define @t5 () (_ @t1 @t4)) % 2.20/2.50 (define @t6 () (@list @t4)) % 2.20/2.50 (define @t7 () (exists @t6 @t5)) % 2.20/2.50 (define @t8 () (=> @t7 @t3)) % 2.20/2.50 (define @t9 () (@list @t1)) % 2.20/2.50 (define @t10 () (forall @t9 @t8)) % 2.20/2.50 (define @t11 () (@var "P" (-> (-> $$unsorted $$unsorted) Bool))) % 2.20/2.50 (define @t12 () (_ tptp.epsii @t11)) % 2.20/2.50 (define @t13 () (_ @t11 @t12)) % 2.20/2.50 (define @t14 () (@var "X" (-> $$unsorted $$unsorted))) % 2.20/2.50 (define @t15 () (_ @t11 @t14)) % 2.20/2.50 (define @t16 () (@list @t14)) % 2.20/2.50 (define @t17 () (exists @t16 @t15)) % 2.20/2.50 (define @t18 () (=> @t17 @t13)) % 2.20/2.50 (define @t19 () (@list @t11)) % 2.20/2.50 (define @t20 () (forall @t19 @t18)) % 2.20/2.50 (define @t21 () (@var "R" (-> $$unsorted (-> $$unsorted $$unsorted) Bool))) % 2.20/2.50 (define @t22 () (_ @t21 (_ tptp.epsa @t21))) % 2.20/2.50 (define @t23 () (@var "Y" (-> $$unsorted $$unsorted))) % 2.20/2.50 (define @t24 () (_ @t21 @t4)) % 2.20/2.50 (define @t25 () (_ @t24 @t23)) % 2.20/2.50 (define @t26 () (@list @t4 @t23)) % 2.20/2.50 (define @t27 () (exists @t26 @t25)) % 2.20/2.50 (define @t28 () (=> @t27 (_ @t22 (_ tptp.epsb @t21)))) % 2.20/2.50 (define @t29 () (@list @t21)) % 2.20/2.50 (define @t30 () (forall @t29 @t28)) % 2.20/2.50 (define @t31 () (not @t30)) % 2.20/2.50 (define @t32 () (@list @t23)) % 2.20/2.50 (define @t33 () (exists @t32 @t25)) % 2.20/2.50 (define @t34 () (lambda @t6 @t33)) % 2.20/2.50 (define @t35 () (lambda @t29 (_ tptp.eps @t34))) % 2.20/2.50 (define @t36 () (@var "__flatten_var_0" $$unsorted)) % 2.20/2.50 (define @t37 () (lambda @t32 (_ @t22 @t23))) % 2.20/2.50 (define @t38 () (@list @t21 @t36)) % 2.20/2.50 (define @t39 () (lambda @t38 (_ (_ tptp.epsii @t37) @t36))) % 2.20/2.50 (define @t40 () (_ @t11 @t12)) % 2.20/2.50 (define @t41 () (@var "BOUND_VARIABLE_7552" (-> $$unsorted $$unsorted))) % 2.20/2.50 (define @t42 () (not (_ @t11 @t41))) % 2.20/2.50 (define @t43 () (or @t42 @t40)) % 2.20/2.50 (define @t44 () (forall (@list @t11 @t41) @t43)) % 2.20/2.50 (define @t45 () (@list @t41)) % 2.20/2.50 (define @t46 () (forall @t45 @t43)) % 2.20/2.50 (define @t47 () (forall @t45 @t42)) % 2.20/2.50 (define @t48 () (or @t47 @t40)) % 2.20/2.50 (define @t49 () (_ @t11 @t14)) % 2.20/2.50 (define @t50 () (forall @t16 (not @t49))) % 2.20/2.50 (define @t51 () (or @t50 @t13)) % 2.20/2.50 (define @t52 () (not @t50)) % 2.20/2.50 (define @t53 () (not @t15)) % 2.20/2.50 (define @t54 () (forall @t16 @t53)) % 2.20/2.50 (define @t55 () (not @t54)) % 2.20/2.50 (define @t56 () (@var "BOUND_VARIABLE_7484" (-> $$unsorted $$unsorted))) % 2.20/2.50 (define @t57 () (_ @t21 @t4 @t56)) % 2.20/2.50 (define @t58 () (not @t57)) % 2.20/2.50 (define @t59 () (@list @t56)) % 2.20/2.50 (define @t60 () (forall @t59 @t58)) % 2.20/2.50 (define @t61 () (not @t60)) % 2.20/2.50 (define @t62 () (lambda @t6 @t61)) % 2.20/2.50 (define @t63 () (tptp.eps @t62)) % 2.20/2.50 (define @t64 () (_ @t21 @t63 @t23)) % 2.20/2.50 (define @t65 () (lambda @t32 @t64)) % 2.20/2.50 (define @t66 () (tptp.epsii @t65 @t36)) % 2.20/2.50 (define @t67 () (@list @t36)) % 2.20/2.50 (define @t68 () (lambda @t67 @t66)) % 2.20/2.50 (define @t69 () (_ @t21 @t4 @t23)) % 2.20/2.50 (define @t70 () (not @t69)) % 2.20/2.50 (define @t71 () (forall @t32 @t70)) % 2.20/2.50 (define @t72 () (not @t71)) % 2.20/2.50 (define @t73 () (lambda @t6 @t72)) % 2.20/2.50 (define @t74 () (tptp.eps @t73)) % 2.20/2.50 (define @t75 () (_ @t21 @t74 @t68)) % 2.20/2.50 (define @t76 () (@var "BOUND_VARIABLE_7599" (-> $$unsorted $$unsorted))) % 2.20/2.50 (define @t77 () (@var "BOUND_VARIABLE_7597" $$unsorted)) % 2.20/2.50 (define @t78 () (not (_ @t21 @t77 @t76))) % 2.20/2.50 (define @t79 () (or @t78 @t75)) % 2.20/2.50 (define @t80 () (forall (@list @t21 @t77 @t76) @t79)) % 2.20/2.50 (define @t81 () (@quantifiers_skolemize @t80 0)) % 2.20/2.50 (define @t82 () (not (forall @t59 (not (_ @t81 @t4 @t56))))) % 2.20/2.50 (define @t83 () (lambda @t6 @t82)) % 2.20/2.50 (define @t84 () (@purify @t83)) % 2.20/2.50 (define @t85 () (_ @t84 @t4)) % 2.20/2.50 (define @t86 () (_ @t83 @t4)) % 2.20/2.50 (define @t87 () (= @t85 @t86)) % 2.20/2.50 (define @t88 () (forall @t6 @t87)) % 2.20/2.50 (define @t89 () (tptp.eps @t84)) % 2.20/2.50 (define @t90 () (forall @t59 (not (_ @t81 @t89 @t56)))) % 2.20/2.50 (define @t91 () (not @t90)) % 2.20/2.50 (define @t92 () (_ @t84 @t89)) % 2.20/2.50 (define @t93 () (forall @t6 (= @t82 @t85))) % 2.20/2.50 (define @t94 () (= @t91 @t92)) % 2.20/2.50 (define @t95 () (= @t92 @t91)) % 2.20/2.50 (define @t96 () (@list false)) % 2.20/2.50 (define @t97 () (@list @t93)) % 2.20/2.50 (define @t98 () (tptp.eps @t1)) % 2.20/2.50 (define @t99 () (_ @t1 @t98)) % 2.20/2.50 (define @t100 () (@var "BOUND_VARIABLE_7530" $$unsorted)) % 2.20/2.50 (define @t101 () (not (_ @t1 @t100))) % 2.20/2.50 (define @t102 () (or @t101 @t99)) % 2.20/2.50 (define @t103 () (@list @t100)) % 2.20/2.50 (define @t104 () (forall @t103 @t102)) % 2.20/2.50 (define @t105 () (forall @t103 @t101)) % 2.20/2.50 (define @t106 () (or @t105 @t99)) % 2.20/2.50 (define @t107 () (_ @t1 @t4)) % 2.20/2.50 (define @t108 () (forall @t6 (not @t107))) % 2.20/2.50 (define @t109 () (or @t108 @t3)) % 2.20/2.50 (define @t110 () (not @t108)) % 2.20/2.50 (define @t111 () (not @t5)) % 2.20/2.50 (define @t112 () (forall @t6 @t111)) % 2.20/2.50 (define @t113 () (not @t112)) % 2.20/2.50 (define @t114 () (@quantifiers_skolemize @t80 1)) % 2.20/2.50 (define @t115 () (@list @t77 @t76)) % 2.20/2.50 (define @t116 () (forall @t115 @t79)) % 2.20/2.50 (define @t117 () (forall @t115 @t78)) % 2.20/2.50 (define @t118 () (or @t117 @t75)) % 2.20/2.50 (define @t119 () (forall @t26 @t70)) % 2.20/2.50 (define @t120 () (lambda @t6 (not (forall @t59 (not (_ @t24 @t56)))))) % 2.20/2.50 (define @t121 () (_ tptp.eps @t120)) % 2.20/2.50 (define @t122 () (_ (_ @t21 @t121) @t23)) % 2.20/2.50 (define @t123 () (lambda @t32 @t122)) % 2.20/2.50 (define @t124 () (_ (_ tptp.epsii @t123) @t36)) % 2.20/2.50 (define @t125 () (lambda @t67 @t124)) % 2.20/2.50 (define @t126 () (not @t25)) % 2.20/2.50 (define @t127 () (forall @t32 @t126)) % 2.20/2.50 (define @t128 () (not @t127)) % 2.20/2.50 (define @t129 () (lambda @t6 @t128)) % 2.20/2.50 (define @t130 () (_ tptp.eps @t129)) % 2.20/2.50 (define @t131 () (_ tptp.eps @t62)) % 2.20/2.50 (define @t132 () (lambda @t32 (_ (_ @t21 @t131) @t23))) % 2.20/2.50 (define @t133 () (_ (_ tptp.epsii @t132) @t36)) % 2.20/2.50 (define @t134 () (lambda @t67 @t133)) % 2.20/2.50 (define @t135 () (_ tptp.eps @t73)) % 2.20/2.50 (define @t136 () (_ @t21 @t135)) % 2.20/2.50 (define @t137 () (_ @t136 @t134)) % 2.20/2.50 (define @t138 () (or @t119 @t137)) % 2.20/2.50 (define @t139 () (not @t119)) % 2.20/2.50 (define @t140 () (_ (lambda @t38 @t133) @t21)) % 2.20/2.50 (define @t141 () (_ (lambda @t29 @t135) @t21)) % 2.20/2.50 (define @t142 () (forall @t26 @t126)) % 2.20/2.50 (define @t143 () (not @t142)) % 2.20/2.50 (define @t144 () (_ @t21 @t141)) % 2.20/2.50 (define @t145 () (=> @t27 (_ @t144 @t140))) % 2.20/2.50 (define @t146 () (forall @t29 @t145)) % 2.20/2.50 (define @t147 () (_ @t81 @t89)) % 2.20/2.50 (define @t148 () (_ tptp.epsii @t147)) % 2.20/2.50 (define @t149 () (not (forall @t32 (not (_ @t81 @t4 @t23))))) % 2.20/2.50 (define @t150 () (lambda @t6 @t149)) % 2.20/2.50 (define @t151 () (@purify @t150)) % 2.20/2.50 (define @t152 () (_ @t81 (tptp.eps @t151) @t148)) % 2.20/2.50 (define @t153 () (@quantifiers_skolemize @t80 2)) % 2.20/2.50 (define @t154 () (_ @t81 @t114 @t153)) % 2.20/2.50 (define @t155 () (not @t154)) % 2.20/2.50 (define @t156 () (or @t155 @t152)) % 2.20/2.50 (define @t157 () (not @t156)) % 2.20/2.50 (define @t158 () (not @t80)) % 2.20/2.50 (define @t159 () (tptp.eps @t83)) % 2.20/2.50 (define @t160 () (lambda @t32 (_ @t81 @t159 @t23))) % 2.20/2.50 (define @t161 () (lambda @t67 (tptp.epsii @t160 @t36))) % 2.20/2.50 (define @t162 () (tptp.eps @t150)) % 2.20/2.50 (define @t163 () (_ @t81 @t162 @t161)) % 2.20/2.50 (define @t164 () (or @t155 @t163)) % 2.20/2.50 (define @t165 () (not @t164)) % 2.20/2.50 (define @t166 () (@list true)) % 2.20/2.50 (define @t167 () (@list @t156)) % 2.20/2.50 (define @t168 () (forall @t59 (not (_ @t81 @t114 @t56)))) % 2.20/2.50 (define @t169 () (not @t168)) % 2.20/2.50 (define @t170 () (_ @t84 @t114)) % 2.20/2.50 (define @t171 () (= @t169 @t170)) % 2.20/2.50 (define @t172 () (not @t171)) % 2.20/2.50 (define @t173 () (@list true false)) % 2.20/2.50 (define @t174 () (not @t170)) % 2.20/2.50 (define @t175 () (or @t174 @t92)) % 2.20/2.50 (define @t176 () (@list false false)) % 2.20/2.50 (define @t177 () (@quantifiers_skolemize @t90 0)) % 2.20/2.50 (define @t178 () (_ @t81 @t89 @t177)) % 2.20/2.50 (define @t179 () (not @t178)) % 2.20/2.50 (define @t180 () (not @t179)) % 2.20/2.50 (define @t181 () (@const 0 $$unsorted)) % 2.20/2.50 (define @t182 () (_ @t151 @t181)) % 2.20/2.50 (define @t183 () (_ @t84 @t181)) % 2.20/2.50 (define @t184 () (= @t183 @t182)) % 2.20/2.50 (define @t185 () (forall @t59 (not (_ @t81 @t181 @t56)))) % 2.20/2.50 (define @t186 () (not @t185)) % 2.20/2.50 (define @t187 () (= @t186 @t183)) % 2.20/2.50 (define @t188 () (@list @t181)) % 2.20/2.50 (define @t189 () (= @t183 @t186)) % 2.20/2.50 (define @t190 () (not @t189)) % 2.20/2.50 (define @t191 () (not @t183)) % 2.20/2.50 (define @t192 () (_ @t151 @t4)) % 2.20/2.50 (define @t193 () (_ @t150 @t4)) % 2.20/2.50 (define @t194 () (= @t192 @t193)) % 2.20/2.50 (define @t195 () (forall @t6 @t194)) % 2.20/2.50 (define @t196 () (forall @t32 (not (_ @t81 @t181 @t23)))) % 2.20/2.50 (define @t197 () (not @t196)) % 2.20/2.50 (define @t198 () (forall @t6 (= @t149 @t192))) % 2.20/2.50 (define @t199 () (= @t197 @t182)) % 2.20/2.50 (define @t200 () (= @t182 @t197)) % 2.20/2.50 (define @t201 () (not @t200)) % 2.20/2.50 (define @t202 () (= @t84 @t151)) % 2.20/2.50 (define @t203 () (_ @t81 @t89 @t148)) % 2.20/2.50 (define @t204 () (or @t179 @t203)) % 2.20/2.50 (define @t205 () (not @t204)) % 2.20/2.50 (define @t206 () (_ tptp.eps @t84)) % 2.20/2.50 (define @t207 () (_ @t81 @t206)) % 2.20/2.50 (define @t208 () (_ tptp.epsii @t207)) % 2.20/2.50 (define @t209 () (_ @t147 @t148)) % 2.20/2.50 (define @t210 () (_ @t147 @t177)) % 2.20/2.50 (define @t211 () (not @t210)) % 2.20/2.50 (define @t212 () (or @t211 @t209)) % 2.20/2.50 (define @t213 () (_ @t147 @t148)) % 2.20/2.50 (define @t214 () (_ @t147 @t177)) % 2.20/2.50 (define @t215 () (not @t214)) % 2.20/2.50 (define @t216 () (or @t215 @t213)) % 2.20/2.50 (assume @p1 @t10) % 2.20/2.50 (assume @p2 @t20) % 2.20/2.50 (assume @p3 @t31) % 2.20/2.50 (assume @p4 true) % 2.20/2.50 (step @p5 (= tptp.epsa @t35) :rule refl :args (@t35)) % 2.20/2.50 (step @p6 (= tptp.epsb @t39) :rule refl :args (@t39)) % 2.20/2.50 (step @p7 :rule quant-merge-prenex :args ((= (forall @t19 @t46) @t44))) % 2.20/2.50 (step @p8 :rule refl :args (@t40)) % 2.20/2.50 (step @p9 :rule alpha_equiv :args (@t47 (@list @t41) (@list @t14))) % 2.20/2.50 (step @p10 :rule nary_cong :premises (@p9 @p8) :args (@t48)) % 2.20/2.50 (step @p11 :rule quant-miniscope-or :args ((= @t46 @t48))) % 2.20/2.50 (step @p12 :rule trans :premises (@p11 @p10)) % 2.20/2.50 (step @p13 :rule symm :premises (@p12)) % 2.20/2.50 (step @p14 :rule cong :premises (@p13) :args ((forall @t19 (or @t50 @t40)))) % 2.20/2.50 (step @p15 :rule trans :premises (@p14 @p7)) % 2.20/2.50 (step @p16 :rule refl :args (@t40)) % 2.20/2.50 (step @p17 :rule refl :args (@t13)) % 2.20/2.50 (step @p18 :rule cong :premises (@p17 @p16) :args ((= @t13 @t40))) % 2.20/2.50 (step @p19 :rule symm :premises (@p18)) % 2.20/2.50 (step @p20 :rule eq_resolve :premises (@p17 @p19)) % 2.20/2.50 (step @p21 :rule refl :args (@t50)) % 2.20/2.50 (step @p22 :rule nary_cong :premises (@p21 @p20) :args (@t51)) % 2.20/2.50 (step @p23 :rule cong :premises (@p22) :args ((forall @t19 @t51))) % 2.20/2.50 (step @p24 :rule trans :premises (@p23 @p15)) % 2.20/2.50 (step @p25 :rule bool-double-not-elim :args (@t50)) % 2.20/2.50 (step @p26 :rule nary_cong :premises (@p25 @p17) :args ((or (not @t52) @t13))) % 2.20/2.50 (step @p27 :rule bool-impl-elim :args (@t52 @t13)) % 2.20/2.50 (step @p28 :rule trans :premises (@p27 @p26)) % 2.20/2.50 (step @p29 :rule cong :premises (@p28) :args ((forall @t19 (=> @t52 @t13)))) % 2.20/2.50 (step @p30 :rule trans :premises (@p29 @p24)) % 2.20/2.50 (step @p31 :rule refl :args (@t13)) % 2.20/2.50 (step @p32 :rule refl :args (@t49)) % 2.20/2.50 (step @p33 :rule refl :args (@t15)) % 2.20/2.50 (step @p34 :rule cong :premises (@p33 @p32) :args ((= @t15 @t49))) % 2.20/2.50 (step @p35 :rule symm :premises (@p34)) % 2.20/2.50 (step @p36 :rule eq_resolve :premises (@p33 @p35)) % 2.20/2.50 (step @p37 :rule cong :premises (@p36) :args (@t53)) % 2.20/2.50 (step @p38 :rule cong :premises (@p37) :args (@t54)) % 2.20/2.50 (step @p39 :rule cong :premises (@p38) :args (@t55)) % 2.20/2.50 (step @p40 :rule exists-elim :args ((= @t17 @t55))) % 2.20/2.50 (step @p41 :rule trans :premises (@p40 @p39)) % 2.20/2.50 (step @p42 :rule cong :premises (@p41 @p31) :args (@t18)) % 2.20/2.50 (step @p43 :rule cong :premises (@p42) :args (@t20)) % 2.20/2.50 (step @p44 :rule trans :premises (@p43 @p30)) % 2.20/2.50 (step @p45 :rule eq_resolve :premises (@p2 @p44)) % 2.20/2.50 (step @p46 :rule eq-symm :args (@t85 @t82)) % 2.20/2.50 (step @p47 :rule beta-reduce :args ((= @t86 @t82))) % 2.20/2.50 (step @p48 :rule refl :args (@t85)) % 2.20/2.50 (step @p49 :rule cong :premises (@p48 @p47) :args (@t87)) % 2.20/2.50 (step @p50 :rule trans :premises (@p49 @p46)) % 2.20/2.50 (step @p51 :rule cong :premises (@p50) :args (@t88)) % 2.20/2.50 (step @p52 :rule quant-unused-vars :args ((= (forall @t6 true) true))) % 2.20/2.50 (step @p53 :rule eq-refl :args (@t86)) % 2.20/2.50 (step @p54 :rule cong :premises (@p53) :args ((forall @t6 (= @t86 @t86)))) % 2.20/2.50 (step @p55 :rule trans :premises (@p54 @p52)) % 2.20/2.50 (step @p56 :rule refl :args (@t86)) % 2.20/2.50 (step @p57 :rule refl :args (@t4)) % 2.20/2.50 (step @p58 :rule skolem_intro :args (@t84)) % 2.20/2.50 (step @p59 :rule ho_cong :premises (@p58 @p57)) % 2.20/2.50 (step @p60 :rule 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@p299)) % 0.34/2.50 (step @p305 :rule implies_elim :premises (@p304)) % 0.34/2.50 (step @p306 :rule eq_resolve :premises (@p305 @p273)) % 0.34/2.50 (step @p307 :rule chain_m_resolution :premises (@p306 @p270) :args (@t157 @t166 (@list @t80))) % 0.34/2.50 (step @p308 :rule bool-double-not-elim :args (@t154)) % 0.34/2.50 (step @p309 :rule refl :args (@t156)) % 0.34/2.50 (step @p310 :rule nary_cong :premises (@p309 @p308) :args ((or @t156 (not @t155)))) % 0.34/2.50 (step @p311 :rule cnf_or_neg :args (@t156 0)) % 0.34/2.50 (step @p312 :rule eq_resolve :premises (@p311 @p310)) % 0.34/2.50 (step @p313 :rule reordering :premises (@p312) :args ((or @t154 @t156))) % 0.34/2.50 (step @p314 :rule chain_m_resolution :premises (@p313 @p307) :args (@t154 @t166 @t167)) % 0.34/2.50 (assume-push @p476 @t168) % 0.34/2.50 (step @p316 :rule instantiate :premises (@p476) :args ((@list @t153))) % 0.34/2.50 (step-pop @p477 :rule scope :premises (@p316)) % 0.34/2.50 (step @p317 :rule process_scope :premises (@p477) :args (@t155)) % 0.34/2.50 (step @p319 :rule implies_elim :premises (@p317)) % 0.34/2.50 (step @p320 :rule reordering :premises (@p319) :args ((or @t155 @t169))) % 0.34/2.50 (step @p321 :rule chain_m_resolution :premises (@p320 @p314) :args (@t169 @t96 (@list @t154))) % 0.34/2.50 (step @p322 :rule refl :args (@t170)) % 0.34/2.50 (step @p323 :rule bool-double-not-elim :args (@t168)) % 0.34/2.50 (step @p324 :rule refl :args (@t172)) % 0.34/2.50 (step @p325 :rule nary_cong :premises (@p324 @p323 @p322) :args ((or @t172 (not @t169) @t170))) % 0.34/2.50 (step @p326 :rule cnf_equiv_pos1 :args (@t171)) % 0.34/2.50 (step @p327 :rule eq_resolve :premises (@p326 @p325)) % 0.34/2.50 (step @p328 :rule reordering :premises (@p327) :args ((or @t168 @t170 @t172))) % 0.34/2.50 (step @p329 :rule chain_m_resolution :premises (@p328 @p321 @p126) :args (@t170 @t173 (@list @t168 @t171))) % 0.34/2.50 (step @p330 :rule cnf_or_pos :args (@t175)) % 0.34/2.50 (step @p331 :rule reordering :premises (@p330) :args ((or @t92 @t174 (not @t175)))) % 0.34/2.50 (step @p332 :rule chain_m_resolution :premises (@p331 @p329 @p125) :args (@t92 @t176 (@list @t170 @t175))) % 0.34/2.50 (step @p333 :rule cnf_equiv_pos1 :args (@t95)) % 0.34/2.50 (step @p334 :rule reordering :premises (@p333) :args ((or (not @t92) @t91 (not @t95)))) % 0.34/2.50 (step @p335 :rule chain_m_resolution :premises (@p334 @p332 @p74) :args (@t91 @t176 (@list @t92 @t95))) % 0.34/2.50 (step @p336 :rule refl :args (@t178)) % 0.34/2.50 (step @p337 :rule bool-double-not-elim :args (@t90)) % 0.34/2.50 (step @p338 :rule nary_cong :premises (@p337 @p336) :args ((or (not @t91) @t178))) % 0.34/2.50 (step @p339 :rule bool-double-not-elim :args (@t178)) % 0.34/2.50 (step @p340 :rule refl :args (@t91)) % 0.34/2.50 (step @p341 :rule cong :premises (@p340 @p339) :args ((=> @t91 @t180))) % 0.34/2.50 (assume-push @p478 @t91) % 0.34/2.50 (step @p343 :rule skolemize :premises (@p478)) % 0.34/2.50 (step-pop @p479 :rule scope :premises (@p343)) % 0.34/2.50 (step @p344 :rule process_scope :premises (@p479) :args (@t180)) % 0.34/2.50 (step @p346 :rule eq_resolve :premises (@p344 @p341)) % 0.34/2.50 (step @p347 :rule implies_elim :premises (@p346)) % 0.34/2.50 (step @p348 :rule eq_resolve :premises (@p347 @p338)) % 0.34/2.50 (step @p349 :rule chain_m_resolution :premises (@p348 @p335) :args (@t178 @t166 (@list @t90))) % 0.34/2.50 (step @p350 :rule cnf_or_neg :args (@t156 1)) % 0.34/2.50 (step @p351 :rule chain_m_resolution :premises (@p350 @p307) :args ((not @t152) @t166 @t167)) % 0.34/2.50 (step @p352 :rule false_intro :premises (@p351)) % 0.34/2.50 (step @p353 :rule refl :args (@t148)) % 0.34/2.50 (step @p354 :rule cnf_equiv_neg2 :args (@t184)) % 0.34/2.50 (step @p355 :rule eq-symm :args (@t186 @t183)) % 0.34/2.50 (step @p356 :rule cong :premises (@p66 @p355) :args ((=> @t93 @t187))) % 0.34/2.50 (assume-push @p480 @t93) % 0.34/2.50 (step @p358 :rule instantiate :premises (@p64) :args (@t188)) % 0.34/2.50 (step-pop @p481 :rule scope :premises (@p358)) % 0.34/2.50 (step @p359 :rule process_scope :premises (@p481) :args (@t187)) % 0.34/2.50 (step @p361 :rule eq_resolve :premises (@p359 @p356)) % 0.34/2.50 (step @p362 :rule implies_elim :premises (@p361)) % 0.34/2.50 (step @p363 :rule chain_m_resolution :premises (@p362 @p64) :args (@t189 @t96 @t97)) % 0.34/2.50 (step @p364 :rule cnf_equiv_pos1 :args (@t189)) % 0.34/2.50 (step @p365 :rule reordering :premises (@p364) :args ((or @t191 @t186 @t190))) % 0.34/2.50 (step @p366 :rule eq-symm :args (@t192 @t149)) % 0.34/2.50 (step @p367 :rule beta-reduce :args ((= @t193 @t149))) % 0.34/2.50 (step @p368 :rule refl :args (@t192)) % 0.34/2.50 (step @p369 :rule cong :premises (@p368 @p367) :args (@t194)) % 0.34/2.50 (step @p370 :rule trans :premises (@p369 @p366)) % 0.34/2.50 (step @p371 :rule cong :premises (@p370) :args (@t195)) % 0.34/2.50 (step @p372 :rule eq-refl :args (@t193)) % 0.34/2.50 (step @p373 :rule cong :premises (@p372) :args ((forall @t6 (= @t193 @t193)))) % 0.34/2.50 (step @p374 :rule trans :premises (@p373 @p52)) % 0.34/2.50 (step @p375 :rule refl :args (@t193)) % 0.34/2.50 (step @p376 :rule ho_cong :premises (@p288 @p57)) % 0.34/2.50 (step @p377 :rule cong :premises (@p376 @p375) :args (@t194)) % 0.34/2.50 (step @p378 :rule cong :premises (@p377) :args (@t195)) % 0.34/2.50 (step @p379 :rule trans :premises (@p378 @p374)) % 0.34/2.50 (step @p380 :rule true_elim :premises (@p379)) % 0.34/2.50 (step @p381 :rule eq_resolve :premises (@p380 @p371)) % 0.34/2.50 (step @p382 :rule eq-symm :args (@t197 @t182)) % 0.34/2.50 (step @p383 :rule refl :args (@t198)) % 0.34/2.50 (step @p384 :rule cong :premises (@p383 @p382) :args ((=> @t198 @t199))) % 0.34/2.50 (assume-push @p482 @t198) % 0.34/2.50 (step @p386 :rule instantiate :premises (@p381) :args (@t188)) % 0.34/2.50 (step-pop @p483 :rule scope :premises (@p386)) % 0.34/2.50 (step @p387 :rule process_scope :premises (@p483) :args (@t199)) % 0.34/2.50 (step @p389 :rule eq_resolve :premises (@p387 @p384)) % 0.34/2.50 (step @p390 :rule implies_elim :premises (@p389)) % 0.34/2.50 (step @p391 :rule chain_m_resolution :premises (@p390 @p381) :args (@t200 @t96 (@list @t198))) % 0.34/2.50 (step @p392 :rule bool-double-not-elim :args (@t196)) % 0.34/2.50 (step @p393 :rule refl :args (@t182)) % 0.34/2.50 (step @p394 :rule refl :args (@t201)) % 0.34/2.50 (step @p395 :rule nary_cong :premises (@p394 @p393 @p392) :args ((or @t201 @t182 (not @t197)))) % 0.34/2.50 (step @p396 :rule cnf_equiv_pos2 :args (@t200)) % 0.34/2.50 (step @p397 :rule eq_resolve :premises (@p396 @p395)) % 0.34/2.50 (step @p398 :rule reordering :premises (@p397) :args ((or @t182 @t196 @t201))) % 0.34/2.50 (step @p399 :rule alpha_equiv :args (@t185 (@list @t56) (@list @t23))) % 0.34/2.50 (step @p400 :rule equiv_elim2 :premises (@p399)) % 0.34/2.50 (step @p401 :rule chain_m_resolution :premises (@p400 @p398 @p391 @p365 @p363 @p354) :args ((or @t184 @t191) (@list false false true false true) (@list @t196 @t200 @t185 @t189 @t182))) % 0.34/2.50 (step @p402 :rule cnf_equiv_neg1 :args (@t184)) % 0.34/2.50 (step @p403 :rule reordering :premises (@p402) :args ((or @t183 @t182 @t184))) % 0.34/2.50 (step @p404 :rule bool-double-not-elim :args (@t185)) % 0.34/2.50 (step @p405 :rule refl :args (@t183)) % 0.34/2.50 (step @p406 :rule refl :args (@t190)) % 0.34/2.50 (step @p407 :rule nary_cong :premises (@p406 @p405 @p404) :args ((or @t190 @t183 (not @t186)))) % 0.34/2.50 (step @p408 :rule cnf_equiv_pos2 :args (@t189)) % 0.34/2.50 (step @p409 :rule eq_resolve :premises (@p408 @p407)) % 0.34/2.50 (step @p410 :rule reordering :premises (@p409) :args ((or @t183 @t185 @t190))) % 0.34/2.50 (step @p411 :rule cnf_equiv_pos1 :args (@t200)) % 0.34/2.50 (step @p412 :rule reordering :premises (@p411) :args ((or (not @t182) @t197 @t201))) % 0.34/2.50 (step @p413 :rule equiv_elim1 :premises (@p399)) % 0.34/2.50 (step @p414 :rule chain_m_resolution :premises (@p413 @p412 @p391 @p410 @p363 @p403 @p401) :args (@t184 (@list true false false false false true) (@list @t196 @t200 @t185 @t189 @t182 @t183))) % 0.34/2.50 ; WARNING: add trust step for TRUST % 0.34/2.50 ; trust TRUST THEORY_LEMMA % 0.34/2.50 (step @p415 :rule trust :premises () :args ((or @t202 (not @t184)))) % 0.34/2.50 (step @p416 :rule chain_m_resolution :premises (@p415 @p414) :args (@t202 @t96 (@list @t184))) % 0.34/2.50 (step @p417 :rule cong :premises (@p416) :args (@t89)) % 0.34/2.50 (step @p418 :rule cong :premises (@p417 @p353) :args (@t203)) % 0.34/2.50 (step @p419 :rule trans :premises (@p418 @p352)) % 0.34/2.50 (step @p420 :rule false_elim :premises (@p419)) % 0.34/2.50 (step @p421 :rule cnf_or_pos :args (@t204)) % 0.34/2.50 (step @p422 :rule reordering :premises (@p421) :args ((or @t203 @t179 @t205))) % 0.34/2.50 (step @p423 :rule chain_m_resolution :premises (@p422 @p420 @p349) :args (@t205 @t173 (@list @t203 @t178))) % 0.34/2.50 (step @p424 :rule refl :args ((_ @t81 @t206 @t208))) % 0.34/2.50 (step @p425 :rule refl :args (@t89)) % 0.34/2.50 (step @p426 :rule refl :args (@t81)) % 0.34/2.50 (step @p427 :rule ho_cong :premises (@p426 @p425)) % 0.34/2.50 (step @p428 :rule ho_cong :premises (@p172 @p427)) % 0.34/2.50 (step @p429 :rule cong :premises (@p425 @p428) :args (@t203)) % 0.34/2.50 (step @p430 :rule trans :premises (@p429 @p424)) % 0.34/2.50 (step @p431 :rule ho_cong :premises (@p427 @p428)) % 0.34/2.50 (step @p432 :rule cong :premises (@p431 @p430) :args ((= @t209 @t203))) % 0.34/2.50 (step @p433 :rule symm :premises (@p432)) % 0.34/2.50 (step @p434 :rule refl :args ((_ @t207 @t208))) % 0.34/2.50 (step @p435 :rule eq_resolve :premises (@p434 @p433)) % 0.34/2.50 (step @p436 :rule refl :args ((_ @t81 @t206 @t177))) % 0.34/2.50 (step @p437 :rule refl :args (@t177)) % 0.34/2.50 (step @p438 :rule cong :premises (@p425 @p437) :args (@t178)) % 0.34/2.50 (step @p439 :rule trans :premises (@p438 @p436)) % 0.34/2.50 (step @p440 :rule ho_cong :premises (@p427 @p437)) % 0.34/2.50 (step @p441 :rule cong :premises (@p440 @p439) :args ((= @t210 @t178))) % 0.34/2.50 (step @p442 :rule symm :premises (@p441)) % 0.34/2.50 (step @p443 :rule refl :args ((_ @t207 @t177))) % 0.34/2.50 (step @p444 :rule eq_resolve :premises (@p443 @p442)) % 0.34/2.50 (step @p445 :rule cong :premises (@p444) :args (@t211)) % 0.34/2.50 (step @p446 :rule nary_cong :premises (@p445 @p435) :args (@t212)) % 0.34/2.50 (step @p447 :rule refl :args (@t44)) % 0.34/2.50 (step @p448 :rule cong :premises (@p447 @p446) :args ((=> @t44 @t212))) % 0.34/2.50 (step @p449 :rule refl :args ((_ @t207 @t208))) % 0.34/2.50 (step @p450 :rule ho_cong :premises (@p427 @p428)) % 0.34/2.50 (step @p451 :rule trans :premises (@p450 @p449)) % 0.34/2.50 (step @p452 :rule cong :premises (@p451 @p431) :args ((= @t213 @t209))) % 0.34/2.50 (step @p453 :rule symm :premises (@p452)) % 0.34/2.50 (step @p454 :rule eq_resolve :premises (@p434 @p453)) % 0.34/2.50 (step @p455 :rule refl :args ((_ @t207 @t177))) % 0.34/2.50 (step @p456 :rule ho_cong :premises (@p427 @p437)) % 0.34/2.50 (step @p457 :rule trans :premises (@p456 @p455)) % 0.34/2.50 (step @p458 :rule cong :premises (@p457 @p440) :args ((= @t214 @t210))) % 0.34/2.50 (step @p459 :rule symm :premises (@p458)) % 0.34/2.50 (step @p460 :rule eq_resolve :premises (@p443 @p459)) % 0.34/2.50 (step @p461 :rule cong :premises (@p460) :args (@t215)) % 0.34/2.50 (step @p462 :rule nary_cong :premises (@p461 @p454) :args (@t216)) % 0.34/2.50 (step @p463 :rule cong :premises (@p447 @p462) :args ((=> @t44 @t216))) % 0.34/2.50 (assume-push @p484 @t44) % 0.34/2.50 (step @p465 :rule instantiate :premises (@p45) :args ((@list @t147 @t177))) % 0.34/2.50 (step-pop @p485 :rule scope :premises (@p465)) % 0.34/2.50 (step @p466 :rule process_scope :premises (@p485) :args (@t216)) % 0.34/2.50 (step @p468 :rule eq_resolve :premises (@p466 @p463)) % 0.34/2.50 (step @p469 :rule eq_resolve :premises (@p468 @p448)) % 0.34/2.50 (step @p470 :rule implies_elim :premises (@p469)) % 0.34/2.50 (step @p471 false :rule chain_m_resolution :premises (@p470 @p423 @p45) :args (false @t173 (@list @t204 @t44))) % 0.34/2.50 ) % 0.34/2.50 % SZS output end Proof % 0.34/2.50 % cvc5 exiting %------------------------------------------------------------------------------