%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO556^1 : TPTP v9.2.1. Released v5.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n028.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 09:13:07 AM UTC 2026 % Result : Theorem 0.51s 0.76s % Output : Proof 0.51s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SYO556^1 : TPTP v9.2.1. Released v5.2.0. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n028.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 : Wed Jun 3 00:21:05 EDT 2026 % 0.17/0.35 % CPUTime : % 0.26/0.50 %----Proving TH0 % 0.51/0.76 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.51/0.76 % SZS status Theorem % 0.51/0.76 % SZS output start Proof % 0.51/0.76 ( % 0.51/0.76 (declare-sort $$unsorted 0) % 0.51/0.76 (declare-const tptp.eps (-> (-> $$unsorted Bool) $$unsorted)) % 0.51/0.76 (define tptp.if () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "Z" $$unsorted))) (let ((_let_3 (@var "B" Bool))) (let ((_let_4 (@var "X" $$unsorted))) (lambda (@list _let_3 _let_4 _let_1) (_ tptp.eps (lambda (@list _let_2) (or (and _let_3 (= _let_2 _let_4)) (and (not _let_3) (= _let_2 _let_1))))))))))) % 0.51/0.76 (define @t1 () (@var "P" (-> $$unsorted Bool))) % 0.51/0.76 (define @t2 () (_ tptp.eps @t1)) % 0.51/0.76 (define @t3 () (_ @t1 @t2)) % 0.51/0.76 (define @t4 () (@var "X" $$unsorted)) % 0.51/0.76 (define @t5 () (_ @t1 @t4)) % 0.51/0.76 (define @t6 () (@list @t4)) % 0.51/0.76 (define @t7 () (exists @t6 @t5)) % 0.51/0.76 (define @t8 () (=> @t7 @t3)) % 0.51/0.76 (define @t9 () (@list @t1)) % 0.51/0.76 (define @t10 () (forall @t9 @t8)) % 0.51/0.76 (define @t11 () (lambda @t6 false)) % 0.51/0.76 (define @t12 () (_ tptp.eps @t11)) % 0.51/0.76 (define @t13 () (= @t2 (_ (_ (_ tptp.if @t7) @t2) @t12))) % 0.51/0.76 (define @t14 () (forall @t9 @t13)) % 0.51/0.76 (define @t15 () (not @t14)) % 0.51/0.76 (define @t16 () (@var "Y" $$unsorted)) % 0.51/0.76 (define @t17 () (@var "Z" $$unsorted)) % 0.51/0.76 (define @t18 () (@var "B" Bool)) % 0.51/0.76 (define @t19 () (not @t18)) % 0.51/0.76 (define @t20 () (and @t19 (= @t17 @t16))) % 0.51/0.76 (define @t21 () (and @t18 (= @t17 @t4))) % 0.51/0.76 (define @t22 () (or @t21 @t20)) % 0.51/0.76 (define @t23 () (@list @t17)) % 0.51/0.76 (define @t24 () (lambda @t23 @t22)) % 0.51/0.76 (define @t25 () (@list @t18 @t4 @t16)) % 0.51/0.76 (define @t26 () (lambda @t25 (_ tptp.eps @t24))) % 0.51/0.76 (define @t27 () (@var "BOUND_VARIABLE_7794" $$unsorted)) % 0.51/0.76 (define @t28 () (lambda (@list @t27) false)) % 0.51/0.76 (define @t29 () (tptp.eps @t28)) % 0.51/0.76 (define @t30 () (= @t17 @t29)) % 0.51/0.76 (define @t31 () (@var "BOUND_VARIABLE_7510" $$unsorted)) % 0.51/0.76 (define @t32 () (_ @t1 @t31)) % 0.51/0.76 (define @t33 () (not @t32)) % 0.51/0.76 (define @t34 () (@list @t31)) % 0.51/0.76 (define @t35 () (forall @t34 @t33)) % 0.51/0.76 (define @t36 () (and @t35 @t30)) % 0.51/0.76 (define @t37 () (tptp.eps @t1)) % 0.51/0.76 (define @t38 () (not @t35)) % 0.51/0.76 (define @t39 () (= @t37 @t17)) % 0.51/0.76 (define @t40 () (and @t38 @t39)) % 0.51/0.76 (define @t41 () (or @t40 @t36)) % 0.51/0.76 (define @t42 () (lambda @t23 @t41)) % 0.51/0.76 (define @t43 () (tptp.eps @t42)) % 0.51/0.76 (define @t44 () (= @t37 @t43)) % 0.51/0.76 (define @t45 () (_ tptp.eps @t28)) % 0.51/0.76 (define @t46 () (forall @t34 (not (_ @t1 @t31)))) % 0.51/0.76 (define @t47 () (= @t2 @t17)) % 0.51/0.76 (define @t48 () (lambda @t23 (or (and (not @t46) @t47) (and @t46 (= @t17 @t45))))) % 0.51/0.76 (define @t49 () (_ tptp.eps @t28)) % 0.51/0.76 (define @t50 () (= @t17 @t49)) % 0.51/0.76 (define @t51 () (and @t35 @t50)) % 0.51/0.76 (define @t52 () (and @t38 @t47)) % 0.51/0.76 (define @t53 () (or @t52 @t51)) % 0.51/0.76 (define @t54 () (lambda @t23 @t53)) % 0.51/0.76 (define @t55 () (= @t2 (_ tptp.eps @t54))) % 0.51/0.76 (define @t56 () (and @t35 (= @t49 @t17))) % 0.51/0.76 (define @t57 () (or @t52 @t56)) % 0.51/0.76 (define @t58 () (lambda @t23 @t57)) % 0.51/0.76 (define @t59 () (= @t16 @t17)) % 0.51/0.76 (define @t60 () (and @t35 @t59)) % 0.51/0.76 (define @t61 () (lambda (@list @t16) (_ tptp.eps (lambda @t23 (or @t52 @t60))))) % 0.51/0.76 (define @t62 () (@list @t4)) % 0.51/0.76 (define @t63 () (= @t4 @t17)) % 0.51/0.76 (define @t64 () (@list @t4 @t16)) % 0.51/0.76 (define @t65 () (lambda @t64 (_ tptp.eps (lambda @t23 (or (and @t38 @t63) @t60))))) % 0.51/0.76 (define @t66 () (_ @t1 @t4)) % 0.51/0.76 (define @t67 () (forall @t6 (not @t66))) % 0.51/0.76 (define @t68 () (not @t67)) % 0.51/0.76 (define @t69 () (and @t68 @t63)) % 0.51/0.76 (define @t70 () (not @t68)) % 0.51/0.76 (define @t71 () (and @t70 @t59)) % 0.51/0.76 (define @t72 () (or @t69 @t71)) % 0.51/0.76 (define @t73 () (lambda @t23 @t72)) % 0.51/0.76 (define @t74 () (lambda @t64 (_ tptp.eps @t73))) % 0.51/0.76 (define @t75 () (lambda @t25 (_ tptp.eps (lambda @t23 (or (and @t18 @t63) (and @t19 @t59)))))) % 0.51/0.76 (define @t76 () (not @t5)) % 0.51/0.76 (define @t77 () (forall @t6 @t76)) % 0.51/0.76 (define @t78 () (not @t77)) % 0.51/0.76 (define @t79 () (= @t2 (_ (_ (_ @t75 @t7) @t2) @t12))) % 0.51/0.76 (define @t80 () (forall @t9 @t79)) % 0.51/0.76 (define @t81 () (forall @t9 (= @t37 (tptp.eps (lambda @t23 (or (and @t38 (= @t17 @t37)) @t36)))))) % 0.51/0.76 (define @t82 () (@quantifiers_skolemize @t81 0)) % 0.51/0.76 (define @t83 () (forall @t34 (not (_ @t82 @t31)))) % 0.51/0.76 (define @t84 () (tptp.eps @t82)) % 0.51/0.76 (define @t85 () (not @t83)) % 0.51/0.76 (define @t86 () (or (and @t85 (= @t17 @t84)) (and @t83 @t30))) % 0.51/0.76 (define @t87 () (lambda @t23 @t86)) % 0.51/0.76 (define @t88 () (@purify @t87)) % 0.51/0.76 (define @t89 () (tptp.eps @t88)) % 0.51/0.76 (define @t90 () (= @t84 @t89)) % 0.51/0.76 (define @t91 () (not @t90)) % 0.51/0.76 (define @t92 () (not @t81)) % 0.51/0.76 (define @t93 () (tptp.eps @t87)) % 0.51/0.76 (define @t94 () (= @t84 @t93)) % 0.51/0.76 (define @t95 () (not @t94)) % 0.51/0.76 (define @t96 () (@list true)) % 0.51/0.76 (define @t97 () (_ @t1 @t37)) % 0.51/0.76 (define @t98 () (@var "BOUND_VARIABLE_7477" $$unsorted)) % 0.51/0.76 (define @t99 () (not (_ @t1 @t98))) % 0.51/0.76 (define @t100 () (or @t99 @t97)) % 0.51/0.76 (define @t101 () (@list @t98)) % 0.51/0.76 (define @t102 () (forall @t101 @t100)) % 0.51/0.76 (define @t103 () (forall @t101 @t99)) % 0.51/0.76 (define @t104 () (or @t103 @t97)) % 0.51/0.76 (define @t105 () (or @t67 @t3)) % 0.51/0.76 (define @t106 () (@const 0 $$unsorted)) % 0.51/0.76 (define @t107 () (@purify @t28)) % 0.51/0.76 (define @t108 () (tptp.eps @t107)) % 0.51/0.76 (define @t109 () (= @t84 @t108)) % 0.51/0.76 (define @t110 () (or @t85 (and @t83 @t109))) % 0.51/0.76 (define @t111 () (= @t89 @t108)) % 0.51/0.76 (define @t112 () (and @t83 @t111)) % 0.51/0.76 (define @t113 () (not @t112)) % 0.51/0.76 (define @t114 () (_ @t88 @t17)) % 0.51/0.76 (define @t115 () (_ @t87 @t17)) % 0.51/0.76 (define @t116 () (= @t114 @t115)) % 0.51/0.76 (define @t117 () (forall @t23 @t116)) % 0.51/0.76 (define @t118 () (= @t29 @t84)) % 0.51/0.76 (define @t119 () (and @t83 @t118)) % 0.51/0.76 (define @t120 () (or @t85 @t119)) % 0.51/0.76 (define @t121 () (_ @t88 @t84)) % 0.51/0.76 (define @t122 () (= @t121 @t120)) % 0.51/0.76 (define @t123 () (forall @t23 (= @t86 @t114))) % 0.51/0.76 (define @t124 () (and @t83 (= @t84 @t29))) % 0.51/0.76 (define @t125 () (and @t85 (= @t84 @t84))) % 0.51/0.76 (define @t126 () (or @t125 @t124)) % 0.51/0.76 (define @t127 () (= @t126 @t121)) % 0.51/0.76 (define @t128 () (@list @t84)) % 0.51/0.76 (define @t129 () (= @t121 @t110)) % 0.51/0.76 (define @t130 () (@list false)) % 0.51/0.76 (define @t131 () (@list @t123)) % 0.51/0.76 (define @t132 () (and @t85 @t90)) % 0.51/0.76 (define @t133 () (not @t132)) % 0.51/0.76 (define @t134 () (@list @t90)) % 0.51/0.76 (define @t135 () (or @t132 @t112)) % 0.51/0.76 (define @t136 () (_ @t88 @t89)) % 0.51/0.76 (define @t137 () (not @t121)) % 0.51/0.76 (define @t138 () (or @t137 @t136)) % 0.51/0.76 (define @t139 () (= @t29 @t89)) % 0.51/0.76 (define @t140 () (and @t83 @t139)) % 0.51/0.76 (define @t141 () (or @t132 @t140)) % 0.51/0.76 (define @t142 () (= @t136 @t141)) % 0.51/0.76 (define @t143 () (and @t83 (= @t89 @t29))) % 0.51/0.76 (define @t144 () (and @t85 (= @t89 @t84))) % 0.51/0.76 (define @t145 () (or @t144 @t143)) % 0.51/0.76 (define @t146 () (= @t145 @t136)) % 0.51/0.76 (define @t147 () (= @t136 @t135)) % 0.51/0.76 (define @t148 () (_ @t82 @t84)) % 0.51/0.76 (define @t149 () (_ @t82 @t106)) % 0.51/0.76 (define @t150 () (not @t149)) % 0.51/0.76 (define @t151 () (or @t150 @t148)) % 0.51/0.76 (define @t152 () (@list true false)) % 0.51/0.76 (define @t153 () (_ @t28 @t106)) % 0.51/0.76 (define @t154 () (_ @t107 @t106)) % 0.51/0.76 (define @t155 () (= @t149 @t154)) % 0.51/0.76 (define @t156 () (not @t155)) % 0.51/0.76 (define @t157 () (= @t82 @t107)) % 0.51/0.76 (define @t158 () (or @t157 @t156)) % 0.51/0.76 (define @t159 () (@list @t149)) % 0.51/0.76 (define @t160 () (@const 1 $$unsorted)) % 0.51/0.76 (define @t161 () (= @t29 @t160)) % 0.51/0.76 (define @t162 () (and @t83 @t161)) % 0.51/0.76 (define @t163 () (and @t85 (= @t84 @t160))) % 0.51/0.76 (define @t164 () (or @t163 @t162)) % 0.51/0.76 (define @t165 () (_ @t88 @t160)) % 0.51/0.76 (define @t166 () (= @t165 @t164)) % 0.51/0.76 (define @t167 () (and @t83 (= @t160 @t29))) % 0.51/0.76 (define @t168 () (and @t85 (= @t160 @t84))) % 0.51/0.76 (define @t169 () (or @t168 @t167)) % 0.51/0.76 (define @t170 () (= @t169 @t165)) % 0.51/0.76 (define @t171 () (= @t160 @t108)) % 0.51/0.76 (define @t172 () (and @t83 @t171)) % 0.51/0.76 (define @t173 () (or @t163 @t172)) % 0.51/0.76 (define @t174 () (= @t165 @t173)) % 0.51/0.76 (define @t175 () (= @t82 @t88)) % 0.51/0.76 (define @t176 () (not @t175)) % 0.51/0.76 (define @t177 () (_ @t82 @t160)) % 0.51/0.76 (define @t178 () (= @t177 @t165)) % 0.51/0.76 (define @t179 () (not @t178)) % 0.51/0.76 (define @t180 () (not @t177)) % 0.51/0.76 (define @t181 () (or @t180 @t148)) % 0.51/0.76 (define @t182 () (not @t165)) % 0.51/0.76 (define @t183 () (@list false false)) % 0.51/0.76 (define @t184 () (not @t163)) % 0.51/0.76 (define @t185 () (@list @t83)) % 0.51/0.76 (define @t186 () (@const 2 $$unsorted)) % 0.51/0.76 (define @t187 () (= @t29 @t186)) % 0.51/0.76 (define @t188 () (and @t83 @t187)) % 0.51/0.76 (define @t189 () (and @t85 (= @t84 @t186))) % 0.51/0.76 (define @t190 () (or @t189 @t188)) % 0.51/0.76 (define @t191 () (_ @t88 @t186)) % 0.51/0.76 (define @t192 () (= @t191 @t190)) % 0.51/0.76 (define @t193 () (and @t83 (= @t186 @t29))) % 0.51/0.76 (define @t194 () (and @t85 (= @t186 @t84))) % 0.51/0.76 (define @t195 () (or @t194 @t193)) % 0.51/0.76 (define @t196 () (= @t195 @t191)) % 0.51/0.76 (define @t197 () (= @t108 @t186)) % 0.51/0.76 (define @t198 () (and @t83 @t197)) % 0.51/0.76 (define @t199 () (or @t189 @t198)) % 0.51/0.76 (define @t200 () (= @t191 @t199)) % 0.51/0.76 (define @t201 () (_ @t87 @t160)) % 0.51/0.76 (define @t202 () (_ @t87 @t160)) % 0.51/0.76 (define @t203 () (_ @t88 @t160)) % 0.51/0.76 (define @t204 () (not @t203)) % 0.51/0.76 (define @t205 () (= @t88 @t107)) % 0.51/0.76 (define @t206 () (=> @t205 (= @t203 false))) % 0.51/0.76 (define @t207 () (not @t205)) % 0.51/0.76 (define @t208 () (_ @t28 @t186)) % 0.51/0.76 (define @t209 () (_ @t107 @t186)) % 0.51/0.76 (define @t210 () (= @t191 @t209)) % 0.51/0.76 (define @t211 () (not @t210)) % 0.51/0.76 (define @t212 () (or @t205 @t211)) % 0.51/0.76 (define @t213 () (not @t191)) % 0.51/0.76 (define @t214 () (not @t189)) % 0.51/0.76 (define @t215 () (or @t213 @t136)) % 0.51/0.76 (define @t216 () (not @t111)) % 0.51/0.76 (define @t217 () (not @t197)) % 0.51/0.76 (define @t218 () (not @t157)) % 0.51/0.76 (define @t219 () (not @t171)) % 0.51/0.76 (define @t220 () (and @t171 @t109 @t197 @t111 @t91)) % 0.51/0.76 (assume @p1 @t10) % 0.51/0.76 (assume @p2 @t15) % 0.51/0.76 (assume @p3 true) % 0.51/0.76 (step @p4 (= tptp.if @t26) :rule refl :args (@t26)) % 0.51/0.76 (step @p5 :rule refl :args (@t36)) % 0.51/0.76 (step @p6 :rule eq-symm :args (@t37 @t17)) % 0.51/0.76 (step @p7 :rule refl :args (@t38)) % 0.51/0.76 (step @p8 :rule nary_cong :premises (@p7 @p6) :args (@t40)) % 0.51/0.76 (step @p9 :rule nary_cong :premises (@p8 @p5) :args (@t41)) % 0.51/0.76 (step @p10 :rule cong :premises (@p9) :args (@t42)) % 0.51/0.76 (step @p11 :rule cong :premises (@p10) :args (@t43)) % 0.51/0.76 (step @p12 :rule refl :args (@t37)) % 0.51/0.76 (step @p13 :rule cong :premises (@p12 @p11) :args (@t44)) % 0.51/0.76 (step @p14 :rule cong :premises (@p13) :args ((forall @t9 @t44))) % 0.51/0.76 (step @p15 :rule refl :args ((tptp.eps @t48))) % 0.51/0.76 (step @p16 :rule refl :args (@t29)) % 0.51/0.76 (step @p17 :rule refl :args (@t28)) % 0.51/0.76 (step @p18 :rule cong :premises (@p17) :args (@t29)) % 0.51/0.76 (step @p19 :rule trans :premises (@p18 @p16)) % 0.51/0.76 (step @p20 :rule refl :args (@t17)) % 0.51/0.76 (step @p21 :rule cong :premises (@p20 @p19) :args (@t30)) % 0.51/0.76 (step @p22 :rule refl :args (@t32)) % 0.51/0.76 (step @p23 :rule cong :premises (@p22) :args (@t33)) % 0.51/0.76 (step @p24 :rule cong :premises (@p23) :args (@t35)) % 0.51/0.76 (step @p25 :rule nary_cong :premises (@p24 @p21) :args (@t36)) % 0.51/0.76 (step @p26 :rule refl :args (@t37)) % 0.51/0.76 (step @p27 :rule cong :premises (@p26 @p20) :args (@t39)) % 0.51/0.76 (step @p28 :rule cong :premises (@p24) :args (@t38)) % 0.51/0.76 (step @p29 :rule nary_cong :premises (@p28 @p27) :args (@t40)) % 0.51/0.76 (step @p30 :rule nary_cong :premises (@p29 @p25) :args (@t41)) % 0.51/0.76 (step @p31 :rule cong :premises (@p30) :args (@t42)) % 0.51/0.76 (step @p32 :rule cong :premises (@p31) :args (@t43)) % 0.51/0.76 (step @p33 :rule trans :premises (@p32 @p15)) % 0.51/0.76 (step @p34 :rule refl :args (tptp.eps)) % 0.51/0.76 (step @p35 :rule ho_cong :premises (@p34 @p31)) % 0.51/0.76 (step @p36 :rule cong :premises (@p35 @p33) :args ((= (_ tptp.eps @t42) @t43))) % 0.51/0.76 (step @p37 :rule symm :premises (@p36)) % 0.51/0.76 (step @p38 :rule refl :args ((_ tptp.eps @t48))) % 0.51/0.76 (step @p39 :rule eq_resolve :premises (@p38 @p37)) % 0.51/0.76 (step @p40 :rule ho_cong :premises (@p34 @p17)) % 0.51/0.76 (step @p41 :rule cong :premises (@p40 @p19) :args ((= @t49 @t29))) % 0.51/0.76 (step @p42 :rule symm :premises (@p41)) % 0.51/0.76 (step @p43 :rule refl :args (@t45)) % 0.51/0.76 (step @p44 :rule eq_resolve :premises (@p43 @p42)) % 0.51/0.76 (step @p45 :rule cong :premises (@p20 @p44) :args (@t50)) % 0.51/0.76 (step @p46 :rule refl :args (@t35)) % 0.51/0.76 (step @p47 :rule nary_cong :premises (@p46 @p45) :args (@t51)) % 0.51/0.76 (step @p48 :rule refl :args (@t2)) % 0.51/0.76 (step @p49 :rule cong :premises (@p48 @p26) :args ((= @t2 @t37))) % 0.51/0.76 (step @p50 :rule symm :premises (@p49)) % 0.51/0.76 (step @p51 :rule eq_resolve :premises (@p48 @p50)) % 0.51/0.76 (step @p52 :rule cong :premises (@p51 @p20) :args (@t47)) % 0.51/0.76 (step @p53 :rule refl :args (@t38)) % 0.51/0.76 (step @p54 :rule nary_cong :premises (@p53 @p52) :args (@t52)) % 0.51/0.76 (step @p55 :rule nary_cong :premises (@p54 @p47) :args (@t53)) % 0.51/0.76 (step @p56 :rule cong :premises (@p55) :args (@t54)) % 0.51/0.76 (step @p57 :rule ho_cong :premises (@p34 @p56)) % 0.51/0.76 (step @p58 :rule trans :premises (@p57 @p39)) % 0.51/0.76 (step @p59 :rule cong :premises (@p51 @p58) :args (@t55)) % 0.51/0.76 (step @p60 :rule cong :premises (@p59) :args ((forall @t9 @t55))) % 0.51/0.76 (step @p61 :rule trans :premises (@p60 @p14)) % 0.51/0.76 (step @p62 :rule eq-symm :args (@t49 @t17)) % 0.51/0.76 (step @p63 :rule refl :args (@t35)) % 0.51/0.76 (step @p64 :rule nary_cong :premises (@p63 @p62) :args (@t56)) % 0.51/0.76 (step @p65 :rule refl :args (@t52)) % 0.51/0.76 (step @p66 :rule nary_cong :premises (@p65 @p64) :args (@t57)) % 0.51/0.76 (step @p67 :rule cong :premises (@p66) :args (@t58)) % 0.51/0.76 (step @p68 :rule refl :args 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((= @t153 false))) % 0.51/0.77 (step @p304 :rule cong :premises (@p303) :args ((not @t153))) % 0.51/0.77 (step @p305 :rule trans :premises (@p304 @p302)) % 0.51/0.77 (step @p306 :rule refl :args (@t106)) % 0.51/0.77 (step @p307 :rule ho_cong :premises (@p222 @p306)) % 0.51/0.77 (step @p308 :rule cong :premises (@p307) :args ((not @t154))) % 0.51/0.77 (step @p309 :rule bool-eq-false :args (@t154)) % 0.51/0.77 (step @p310 :rule trans :premises (@p309 @p308 @p305)) % 0.51/0.77 (step @p311 :rule true_elim :premises (@p310)) % 0.51/0.77 (step @p312 :rule refl :args (@t149)) % 0.51/0.77 (step @p313 :rule cong :premises (@p312 @p311) :args (@t155)) % 0.51/0.77 (step @p314 :rule trans :premises (@p313 @p301)) % 0.51/0.77 (step @p315 :rule cong :premises (@p314) :args (@t156)) % 0.51/0.77 (step @p316 :rule trans :premises (@p315 @p300)) % 0.51/0.77 (step @p317 :rule refl :args (@t157)) % 0.51/0.77 (step @p318 :rule nary_cong :premises (@p317 @p316) :args (@t158)) % 0.51/0.77 ; WARNING: add trust step for TRUST % 0.51/0.77 ; trust TRUST THEORY_LEMMA % 0.51/0.77 (step @p319 :rule trust :premises () :args (@t158)) % 0.51/0.77 (step @p320 :rule eq_resolve :premises (@p319 @p318)) % 0.51/0.77 (step @p321 :rule chain_m_resolution :premises (@p320 @p299) :args (@t157 @t96 @t159)) % 0.51/0.77 (step @p322 :rule eq-symm :args (@t108 @t160)) % 0.51/0.77 (step @p323 :rule refl :args (@t160)) % 0.51/0.77 (step @p324 :rule cong :premises (@p226 @p323) :args (@t161)) % 0.51/0.77 (step @p325 :rule trans :premises (@p324 @p322)) % 0.51/0.77 (step @p326 :rule nary_cong :premises (@p229 @p325) :args (@t162)) % 0.51/0.77 (step @p327 :rule refl :args (@t163)) % 0.51/0.77 (step @p328 :rule nary_cong :premises (@p327 @p326) :args (@t164)) % 0.51/0.77 (step @p329 :rule refl :args (@t165)) % 0.51/0.77 (step @p330 :rule cong :premises (@p329 @p328) :args (@t166)) % 0.51/0.77 (step @p331 :rule cong :premises (@p235 @p330) :args ((=> @t123 @t166))) % 0.51/0.77 (step @p332 :rule eq-symm :args (@t160 @t29)) % 0.51/0.77 (step @p333 :rule nary_cong :premises (@p229 @p332) :args (@t167)) % 0.51/0.77 (step @p334 :rule eq-symm :args (@t160 @t84)) % 0.51/0.77 (step @p335 :rule nary_cong :premises (@p231 @p334) :args (@t168)) % 0.51/0.77 (step @p336 :rule nary_cong :premises (@p335 @p333) :args (@t169)) % 0.51/0.77 (step @p337 :rule cong :premises (@p329 @p336) :args ((= @t165 @t169))) % 0.51/0.77 (step @p338 :rule eq-symm :args (@t169 @t165)) % 0.51/0.77 (step @p339 :rule trans :premises (@p338 @p337)) % 0.51/0.77 (step @p340 :rule cong :premises (@p235 @p339) :args ((=> @t123 @t170))) % 0.51/0.77 (assume-push @p525 @t123) % 0.51/0.77 (step @p342 :rule instantiate :premises (@p216) :args ((@list @t160))) % 0.51/0.77 (step-pop @p526 :rule scope :premises (@p342)) % 0.51/0.77 (step @p343 :rule process_scope :premises (@p526) :args (@t170)) % 0.51/0.77 (step @p345 :rule eq_resolve :premises (@p343 @p340)) % 0.51/0.77 (step @p346 :rule eq_resolve :premises (@p345 @p331)) % 0.51/0.77 (step @p347 :rule implies_elim :premises (@p346)) % 0.51/0.77 (step @p348 :rule chain_m_resolution :premises (@p347 @p216) :args (@t174 @t130 @t131)) % 0.51/0.77 (assume-push @p527 @t175) % 0.51/0.77 (assume-push @p528 @t175) % 0.51/0.77 (step @p351 :rule cong :premises (@p527) :args (@t84)) % 0.51/0.77 (step-pop @p529 :rule scope :premises (@p351)) % 0.51/0.77 (step @p352 :rule process_scope :premises (@p529) :args (@t90)) % 0.51/0.77 (step @p354 :rule modus_ponens :premises (@p527 @p352)) % 0.51/0.77 (step-pop @p530 :rule scope :premises (@p354)) % 0.51/0.77 (step @p355 :rule process_scope :premises (@p530) :args (@t90)) % 0.51/0.77 (step @p357 :rule implies_elim :premises (@p355)) % 0.51/0.77 (step @p358 :rule reordering :premises (@p357) :args ((or @t90 @t176))) % 0.51/0.77 (step @p359 :rule chain_m_resolution :premises (@p358 @p154) :args (@t176 @t96 @t134)) % 0.51/0.77 ; trust TRUST THEORY_LEMMA % 0.51/0.77 (step @p360 :rule trust :premises () :args ((or @t175 @t179))) % 0.51/0.77 (step @p361 :rule chain_m_resolution :premises (@p360 @p359) :args (@t179 @t96 (@list @t175))) % 0.51/0.77 (step @p362 :rule instantiate :premises (@p189) :args ((@list @t82 @t160))) % 0.51/0.77 (step @p363 :rule cnf_or_pos :args (@t181)) % 0.51/0.77 (step @p364 :rule reordering :premises (@p363) :args ((or @t180 @t148 (not @t181)))) % 0.51/0.77 (step @p365 :rule chain_m_resolution :premises (@p364 @p296 @p362) :args (@t180 @t152 (@list @t148 @t181))) % 0.51/0.77 (step @p366 :rule cnf_equiv_neg1 :args (@t178)) % 0.51/0.77 (step @p367 :rule reordering :premises (@p366) :args ((or @t177 @t165 @t178))) % 0.51/0.77 (step @p368 :rule chain_m_resolution :premises (@p367 @p365 @p361) :args (@t165 (@list true true) (@list @t177 @t178))) % 0.51/0.77 (step @p369 :rule cnf_equiv_pos1 :args (@t174)) % 0.51/0.77 (step @p370 :rule reordering :premises (@p369) :args ((or @t182 @t173 (not @t174)))) % 0.51/0.77 (step @p371 :rule chain_m_resolution :premises (@p370 @p368 @p348) :args (@t173 @t183 (@list @t165 @t174))) % 0.51/0.77 (step @p372 :rule cnf_and_pos :args (@t163 0)) % 0.51/0.77 (step @p373 :rule reordering :premises (@p372) :args ((or @t85 @t184))) % 0.51/0.77 (step @p374 :rule chain_m_resolution :premises (@p373 @p295) :args (@t184 @t130 @t185)) % 0.51/0.77 (step @p375 :rule cnf_or_pos :args (@t173)) % 0.51/0.77 (step @p376 :rule reordering :premises (@p375) :args ((or @t163 @t172 (not @t173)))) % 0.51/0.77 (step @p377 :rule chain_m_resolution :premises (@p376 @p374 @p371) :args (@t172 @t152 (@list @t163 @t173))) % 0.51/0.77 (step @p378 :rule cnf_and_pos :args (@t172 1)) % 0.51/0.77 (step @p379 :rule reordering :premises (@p378) :args ((or @t171 (not @t172)))) % 0.51/0.77 (step @p380 :rule chain_m_resolution :premises (@p379 @p377) :args (@t171 @t130 (@list @t172))) % 0.51/0.77 (step @p381 :rule refl :args (@t186)) % 0.51/0.77 (step @p382 :rule cong :premises (@p226 @p381) :args (@t187)) % 0.51/0.77 (step @p383 :rule nary_cong :premises (@p229 @p382) :args (@t188)) % 0.51/0.77 (step @p384 :rule refl :args (@t189)) % 0.51/0.77 (step @p385 :rule nary_cong :premises (@p384 @p383) :args (@t190)) % 0.51/0.77 (step @p386 :rule refl :args (@t191)) % 0.51/0.77 (step @p387 :rule cong :premises (@p386 @p385) :args (@t192)) % 0.51/0.77 (step @p388 :rule cong :premises (@p235 @p387) :args ((=> @t123 @t192))) % 0.51/0.77 (step @p389 :rule eq-symm :args (@t186 @t29)) % 0.51/0.77 (step @p390 :rule nary_cong :premises (@p229 @p389) :args (@t193)) % 0.51/0.77 (step @p391 :rule eq-symm :args (@t186 @t84)) % 0.51/0.77 (step @p392 :rule nary_cong :premises (@p231 @p391) :args (@t194)) % 0.51/0.77 (step @p393 :rule nary_cong :premises (@p392 @p390) :args (@t195)) % 0.51/0.77 (step @p394 :rule cong :premises (@p386 @p393) :args ((= @t191 @t195))) % 0.51/0.77 (step @p395 :rule eq-symm :args (@t195 @t191)) % 0.51/0.77 (step @p396 :rule trans :premises (@p395 @p394)) % 0.51/0.77 (step @p397 :rule cong :premises (@p235 @p396) :args ((=> @t123 @t196))) % 0.51/0.77 (assume-push @p531 @t123) % 0.51/0.77 (step @p399 :rule instantiate :premises (@p216) :args ((@list @t186))) % 0.51/0.77 (step-pop @p532 :rule scope :premises (@p399)) % 0.51/0.77 (step @p400 :rule process_scope :premises (@p532) :args (@t196)) % 0.51/0.77 (step @p402 :rule eq_resolve :premises (@p400 @p397)) % 0.51/0.77 (step @p403 :rule eq_resolve :premises (@p402 @p388)) % 0.51/0.77 (step @p404 :rule implies_elim :premises (@p403)) % 0.51/0.77 (step @p405 :rule chain_m_resolution :premises (@p404 @p216) :args (@t200 @t130 @t131)) % 0.51/0.77 (step @p406 :rule eq-refl :args (@t164)) % 0.51/0.77 (step @p407 :rule beta-reduce :args ((= @t201 @t169))) % 0.51/0.77 (step @p408 :rule trans :premises (@p407 @p336)) % 0.51/0.77 (step @p409 :rule beta-reduce :args ((= @t202 @t169))) % 0.51/0.77 (step @p410 :rule trans :premises (@p409 @p336)) % 0.51/0.77 (step @p411 :rule cong :premises (@p410 @p408) :args ((= @t202 @t201))) % 0.51/0.77 (step @p412 :rule trans :premises (@p411 @p406)) % 0.51/0.77 (step @p413 :rule ho_cong :premises (@p136 @p323)) % 0.51/0.77 (step @p414 :rule ho_cong :premises (@p136 @p323)) % 0.51/0.77 (step @p415 :rule cong :premises (@p414 @p413) :args ((= @t165 @t203))) % 0.51/0.77 (step @p416 :rule eq-symm :args (@t203 @t165)) % 0.51/0.77 (step @p417 :rule trans :premises (@p416 @p415 @p412)) % 0.51/0.77 (step @p418 :rule true_elim :premises (@p417)) % 0.51/0.77 (step @p419 :rule cong :premises (@p418) :args (@t204)) % 0.51/0.77 (step @p420 :rule refl :args (@t205)) % 0.51/0.77 (step @p421 :rule cong :premises (@p420 @p419) :args ((=> @t205 @t204))) % 0.51/0.77 (step @p422 :rule bool-eq-false :args (@t203)) % 0.51/0.77 (step @p423 :rule cong :premises (@p420 @p422) :args (@t206)) % 0.51/0.77 (step @p424 :rule trans :premises (@p423 @p421)) % 0.51/0.77 ; trust TRUST THEORY_LEMMA % 0.51/0.77 (step @p425 :rule trust :premises () :args (@t206)) % 0.51/0.77 (step @p426 :rule eq_resolve :premises (@p425 @p424)) % 0.51/0.77 (step @p427 :rule implies_elim :premises (@p426)) % 0.51/0.77 (step @p428 :rule reordering :premises (@p427) :args ((or @t182 @t207))) % 0.51/0.77 (step @p429 :rule chain_m_resolution :premises (@p428 @p368) :args (@t207 @t130 (@list @t165))) % 0.51/0.77 (step @p430 :rule bool-double-not-elim :args (@t191)) % 0.51/0.77 (step @p431 :rule bool-eq-false :args (@t191)) % 0.51/0.77 (step @p432 :rule beta-reduce :args ((= @t208 false))) % 0.51/0.77 (step @p433 :rule cong :premises (@p432) :args ((not @t208))) % 0.51/0.77 (step @p434 :rule trans :premises (@p433 @p302)) % 0.51/0.77 (step @p435 :rule ho_cong :premises (@p222 @p381)) % 0.51/0.77 (step @p436 :rule cong :premises (@p435) :args ((not @t209))) % 0.51/0.77 (step @p437 :rule bool-eq-false :args (@t209)) % 0.51/0.77 (step @p438 :rule trans :premises (@p437 @p436 @p434)) % 0.51/0.77 (step @p439 :rule true_elim :premises (@p438)) % 0.51/0.77 (step @p440 :rule cong :premises (@p386 @p439) :args (@t210)) % 0.51/0.77 (step @p441 :rule trans :premises (@p440 @p431)) % 0.51/0.77 (step @p442 :rule cong :premises (@p441) :args (@t211)) % 0.51/0.77 (step @p443 :rule trans :premises (@p442 @p430)) % 0.51/0.77 (step @p444 :rule nary_cong :premises (@p420 @p443) :args (@t212)) % 0.51/0.77 ; trust TRUST THEORY_LEMMA % 0.51/0.77 (step @p445 :rule trust :premises () :args (@t212)) % 0.51/0.77 (step @p446 :rule eq_resolve :premises (@p445 @p444)) % 0.51/0.77 (step @p447 :rule chain_m_resolution :premises (@p446 @p429) :args (@t191 @t96 (@list @t205))) % 0.51/0.77 (step @p448 :rule cnf_equiv_pos1 :args (@t200)) % 0.51/0.77 (step @p449 :rule reordering :premises (@p448) :args ((or @t213 @t199 (not @t200)))) % 0.51/0.77 (step @p450 :rule chain_m_resolution :premises (@p449 @p447 @p405) :args (@t199 @t183 (@list @t191 @t200))) % 0.51/0.77 (step @p451 :rule cnf_and_pos :args (@t189 0)) % 0.51/0.77 (step @p452 :rule reordering :premises (@p451) :args ((or @t85 @t214))) % 0.51/0.77 (step @p453 :rule chain_m_resolution :premises (@p452 @p295) :args (@t214 @t130 @t185)) % 0.51/0.77 (step @p454 :rule cnf_or_pos :args (@t199)) % 0.51/0.77 (step @p455 :rule reordering :premises (@p454) :args ((or @t189 @t198 (not @t199)))) % 0.51/0.77 (step @p456 :rule chain_m_resolution :premises (@p455 @p453 @p450) :args (@t198 @t152 (@list @t189 @t199))) % 0.51/0.77 (step @p457 :rule cnf_and_pos :args (@t198 1)) % 0.51/0.77 (step @p458 :rule reordering :premises (@p457) :args ((or @t197 (not @t198)))) % 0.51/0.77 (step @p459 :rule chain_m_resolution :premises (@p458 @p456) :args (@t197 @t130 (@list @t198))) % 0.51/0.77 (step @p460 :rule instantiate :premises (@p189) :args ((@list @t88 @t186))) % 0.51/0.77 (step @p461 :rule cnf_or_pos :args (@t215)) % 0.51/0.77 (step @p462 :rule reordering :premises (@p461) :args ((or @t213 @t136 (not @t215)))) % 0.51/0.77 (step @p463 :rule chain_m_resolution :premises (@p462 @p447 @p460) :args (@t136 @t183 (@list @t191 @t215))) % 0.51/0.77 (step @p464 :rule chain_m_resolution :premises (@p294 @p463 @p292) :args (@t135 @t183 (@list @t136 @t147))) % 0.51/0.77 (step @p465 :rule chain_m_resolution :premises (@p262 @p260 @p464) :args (@t112 @t152 (@list @t132 @t135))) % 0.51/0.77 (step @p466 :rule cnf_and_pos :args (@t112 1)) % 0.51/0.77 (step @p467 :rule reordering :premises (@p466) :args ((or @t111 @t113))) % 0.51/0.77 (step @p468 :rule chain_m_resolution :premises (@p467 @p465) :args (@t111 @t130 (@list @t112))) % 0.51/0.77 (step @p469 :rule refl :args (@t216)) % 0.51/0.77 (step @p470 :rule refl :args (@t217)) % 0.51/0.77 (step @p471 :rule refl :args (@t218)) % 0.51/0.77 (step @p472 :rule refl :args (@t219)) % 0.51/0.77 (step @p473 :rule bool-double-not-elim :args (@t90)) % 0.51/0.77 (step @p474 :rule nary_cong :premises (@p473 @p472 @p471 @p470 @p469) :args ((or (not @t91) @t219 @t218 @t217 @t216))) % 0.51/0.77 (assume-push @p533 @t171) % 0.51/0.77 (assume-push @p534 @t109) % 0.51/0.77 (assume-push @p535 @t197) % 0.51/0.77 (assume-push @p536 @t111) % 0.51/0.77 (assume-push @p537 @t91) % 0.51/0.77 (step @p480 :rule evaluate :args ((= false true))) % 0.51/0.77 (step @p481 :rule symm :premises (@p533)) % 0.51/0.77 (step @p482 :rule trans :premises (@p536 @p481)) % 0.51/0.77 (step @p483 :rule symm :premises (@p482)) % 0.51/0.77 (step @p484 :rule trans :premises (@p533 @p535)) % 0.51/0.77 (step @p485 :rule symm :premises (@p484)) % 0.51/0.77 (step @p486 :rule chain_m_resolution :premises (@p320 @p299) :args (@t157 @t96 @t159)) % 0.51/0.77 (step @p487 :rule cong :premises (@p486) :args (@t84)) % 0.51/0.77 (step @p488 :rule trans :premises (@p487 @p481)) % 0.51/0.77 (step @p489 :rule trans :premises (@p488 @p533 @p535 @p485 @p483)) % 0.51/0.77 (step @p490 :rule true_intro :premises (@p489)) % 0.51/0.77 (step @p491 :rule false_intro :premises (@p154)) % 0.51/0.77 (step @p492 :rule symm :premises (@p491)) % 0.51/0.77 (step @p493 :rule trans :premises (@p492 @p490)) % 0.51/0.77 (step @p494 false :rule eq_resolve :premises (@p493 @p480)) % 0.51/0.77 (step-pop @p538 :rule scope :premises (@p494)) % 0.51/0.77 (step-pop @p539 :rule scope :premises (@p538)) % 0.51/0.77 (step-pop @p540 :rule scope :premises (@p539)) % 0.51/0.77 (step-pop @p541 :rule scope :premises (@p540)) % 0.51/0.77 (step-pop @p542 :rule scope :premises (@p541)) % 0.51/0.77 (step @p495 :rule process_scope :premises (@p542) :args (false)) % 0.51/0.77 (assume-push @p543 @t91) % 0.51/0.77 (assume-push @p544 @t171) % 0.51/0.77 (assume-push @p545 @t157) % 0.51/0.77 (assume-push @p546 @t197) % 0.51/0.77 (assume-push @p547 @t111) % 0.51/0.77 (step @p506 :rule cong :premises (@p321) :args (@t84)) % 0.51/0.77 (step @p507 :rule and_intro :premises (@p544 @p506 @p546 @p547 @p154)) % 0.51/0.77 (step-pop @p548 :rule scope :premises (@p507)) % 0.51/0.77 (step-pop @p549 :rule scope :premises (@p548)) % 0.51/0.77 (step-pop @p550 :rule scope :premises (@p549)) % 0.51/0.77 (step-pop @p551 :rule scope :premises (@p550)) % 0.51/0.77 (step-pop @p552 :rule scope :premises (@p551)) % 0.51/0.77 (step @p508 :rule process_scope :premises (@p552) :args (@t220)) % 0.51/0.77 (step @p514 :rule implies_elim :premises (@p508)) % 0.51/0.77 (step @p515 :rule resolution :premises (@p514 @p495) :args (true @t220)) % 0.51/0.77 (step @p516 :rule not_and :premises (@p515)) % 0.51/0.77 (step @p517 :rule eq_resolve :premises (@p516 @p474)) % 0.51/0.77 (step @p518 false :rule chain_m_resolution :premises (@p517 @p468 @p459 @p380 @p321 @p154) :args (false (@list false false false false true) (@list @t111 @t197 @t171 @t157 @t90))) % 0.51/0.77 ) % 0.51/0.77 % SZS output end Proof % 0.51/0.77 % cvc5 exiting %------------------------------------------------------------------------------