%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWW101+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 : n024.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 09:04:27 AM UTC 2026 % Result : Theorem 0.16s 0.42s % Output : Proof 0.16s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.07 % Problem : SWW101+1 : TPTP v9.2.1. Released v5.2.0. % 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.09/0.26 % Computer : n024.cluster.edu % 0.09/0.26 % Model : x86_64 x86_64 % 0.09/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.26 % Memory : 8042.1875MB % 0.09/0.26 % OS : Linux 3.10.0-693.el7.x86_64 % 0.09/0.26 % CPULimit : 300 % 0.09/0.26 % WCLimit : 300 % 0.09/0.26 % DateTime : Tue Jun 2 16:37:00 EDT 2026 % 0.09/0.26 % CPUTime : % 0.16/0.35 %----Proving TF0_NAR, FOF, or CNF % 0.16/0.42 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.16/0.42 % SZS status Theorem % 0.16/0.42 % SZS output start Proof % 0.16/0.42 ( % 0.16/0.42 (declare-sort $$unsorted 0) % 0.16/0.42 (declare-const tptp.not1 (-> $$unsorted $$unsorted)) % 0.16/0.42 (declare-const tptp.f1 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.16/0.42 (declare-const tptp.f7 (-> $$unsorted $$unsorted)) % 0.16/0.42 (declare-const tptp.and1 (-> $$unsorted $$unsorted $$unsorted)) % 0.16/0.42 (declare-const tptp.impl (-> $$unsorted $$unsorted $$unsorted)) % 0.16/0.42 (declare-const tptp.lazy_impl (-> $$unsorted $$unsorted $$unsorted)) % 0.16/0.42 (declare-const tptp.bool (-> $$unsorted Bool)) % 0.16/0.42 (declare-const tptp.true $$unsorted) % 0.16/0.42 (declare-const tptp.existsprefers (-> $$unsorted $$unsorted Bool)) % 0.16/0.42 (declare-const tptp.exists1 (-> $$unsorted $$unsorted)) % 0.16/0.42 (declare-const tptp.not2 (-> $$unsorted $$unsorted)) % 0.16/0.42 (declare-const tptp.prop (-> $$unsorted $$unsorted)) % 0.16/0.42 (declare-const tptp.forallprefers (-> $$unsorted $$unsorted Bool)) % 0.16/0.42 (declare-const tptp.or2 (-> $$unsorted $$unsorted $$unsorted)) % 0.16/0.42 (declare-const tptp.d (-> $$unsorted Bool)) % 0.16/0.42 (declare-const tptp.false $$unsorted) % 0.16/0.42 (declare-const tptp.and2 (-> $$unsorted $$unsorted $$unsorted)) % 0.16/0.42 (declare-const tptp.lazy_and1 (-> $$unsorted $$unsorted $$unsorted)) % 0.16/0.42 (declare-const tptp.or1 (-> $$unsorted $$unsorted $$unsorted)) % 0.16/0.42 (declare-const tptp.f2 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.16/0.42 (declare-const tptp.err $$unsorted) % 0.16/0.42 (declare-const tptp.f6 (-> $$unsorted $$unsorted $$unsorted)) % 0.16/0.42 (declare-const tptp.phi (-> $$unsorted $$unsorted)) % 0.16/0.42 (declare-const tptp.lazy_and2 (-> $$unsorted $$unsorted $$unsorted)) % 0.16/0.42 (declare-const tptp.false2 $$unsorted) % 0.16/0.42 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted)) % 0.16/0.42 (declare-const tptp.f4 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.16/0.42 (declare-const tptp.f5 (-> $$unsorted $$unsorted $$unsorted)) % 0.16/0.42 (declare-const tptp.false1 $$unsorted) % 0.16/0.42 (declare-const tptp.f3 (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.16/0.42 (declare-const tptp.exists2 (-> $$unsorted $$unsorted)) % 0.16/0.42 (define @t1 () (@var "X" $$unsorted)) % 0.16/0.42 (define @t2 () (= @t1 tptp.true)) % 0.16/0.42 (define @t3 () (= @t1 tptp.false)) % 0.16/0.42 (define @t4 () (or @t3 @t2)) % 0.16/0.42 (define @t5 () (tptp.bool @t1)) % 0.16/0.42 (define @t6 () (= @t5 @t4)) % 0.16/0.42 (define @t7 () (@list @t1)) % 0.16/0.42 (define @t8 () (forall @t7 @t6)) % 0.16/0.42 (define @t9 () (= tptp.false tptp.err)) % 0.16/0.42 (define @t10 () (= tptp.true tptp.err)) % 0.16/0.42 (define @t11 () (tptp.d tptp.false)) % 0.16/0.42 (define @t12 () (tptp.d tptp.true)) % 0.16/0.42 (define @t13 () (@var "Y" $$unsorted)) % 0.16/0.42 (define @t14 () (and @t3 (= @t13 tptp.true))) % 0.16/0.42 (define @t15 () (not @t5)) % 0.16/0.42 (define @t16 () (tptp.d @t13)) % 0.16/0.42 (define @t17 () (tptp.d @t1)) % 0.16/0.42 (define @t18 () (and @t17 @t16 @t15 (tptp.bool @t13))) % 0.16/0.42 (define @t19 () (not @t17)) % 0.16/0.42 (define @t20 () (and @t19 @t16)) % 0.16/0.42 (define @t21 () (or @t20 @t18 @t14)) % 0.16/0.42 (define @t22 () (tptp.forallprefers @t1 @t13)) % 0.16/0.42 (define @t23 () (= @t22 @t21)) % 0.16/0.42 (define @t24 () (@list @t1 @t13)) % 0.16/0.42 (define @t25 () (forall @t24 @t23)) % 0.16/0.42 (define @t26 () (tptp.phi @t1)) % 0.16/0.42 (define @t27 () (and @t19 (= @t26 tptp.err))) % 0.16/0.42 (define @t28 () (and @t17 (= @t26 @t1))) % 0.16/0.42 (define @t29 () (or @t28 @t27)) % 0.16/0.42 (define @t30 () (forall @t7 @t29)) % 0.16/0.42 (define @t31 () (tptp.prop @t1)) % 0.16/0.42 (define @t32 () (= @t31 tptp.true)) % 0.16/0.42 (define @t33 () (forall @t7 (= @t32 @t5))) % 0.16/0.42 (define @t34 () (= @t31 tptp.false)) % 0.16/0.42 (define @t35 () (forall @t7 (= @t34 @t15))) % 0.16/0.42 (define @t36 () (@var "A" $$unsorted)) % 0.16/0.42 (define @t37 () (tptp.phi @t36)) % 0.16/0.42 (define @t38 () (@var "B" $$unsorted)) % 0.16/0.42 (define @t39 () (tptp.impl @t36 @t38)) % 0.16/0.42 (define @t40 () (tptp.bool @t36)) % 0.16/0.42 (define @t41 () (not @t40)) % 0.16/0.42 (define @t42 () (@list @t36 @t38)) % 0.16/0.42 (define @t43 () (tptp.phi @t38)) % 0.16/0.42 (define @t44 () (tptp.bool @t38)) % 0.16/0.42 (define @t45 () (and @t40 (not @t44))) % 0.16/0.42 (define @t46 () (@list @t38)) % 0.16/0.42 (define @t47 () (tptp.lazy_impl tptp.false @t38)) % 0.16/0.42 (define @t48 () (forall @t46 (= @t47 tptp.true))) % 0.16/0.42 (define @t49 () (tptp.lazy_impl tptp.true @t38)) % 0.16/0.42 (define @t50 () (forall @t46 (= @t49 @t43))) % 0.16/0.42 (define @t51 () (tptp.and1 @t36 @t38)) % 0.16/0.42 (define @t52 () (@var "R" $$unsorted)) % 0.16/0.42 (define @t53 () (@var "Q" $$unsorted)) % 0.16/0.42 (define @t54 () (tptp.impl @t53 @t52)) % 0.16/0.42 (define @t55 () (@var "P" $$unsorted)) % 0.16/0.42 (define @t56 () (tptp.prop @t52)) % 0.16/0.42 (define @t57 () (tptp.f1 @t55 @t53 @t52)) % 0.16/0.42 (define @t58 () (@list @t55 @t53 @t52)) % 0.16/0.42 (define @t59 () (@var "R1" $$unsorted)) % 0.16/0.42 (define @t60 () (@list @t59)) % 0.16/0.42 (define @t61 () (@list @t52)) % 0.16/0.42 (define @t62 () (@list @t55 @t53)) % 0.16/0.42 (define @t63 () (tptp.lazy_and1 tptp.true @t38)) % 0.16/0.42 (define @t64 () (forall @t46 (= @t63 @t43))) % 0.16/0.42 (define @t65 () (tptp.f2 @t55 @t53 @t52)) % 0.16/0.42 (define @t66 () (tptp.or1 @t36 @t38)) % 0.16/0.42 (define @t67 () (tptp.f3 @t55 @t53 @t52)) % 0.16/0.42 (define @t68 () (tptp.apply @t55 @t1)) % 0.16/0.42 (define @t69 () (@var "X1" $$unsorted)) % 0.16/0.42 (define @t70 () (@list @t69)) % 0.16/0.42 (define @t71 () (@list @t55)) % 0.16/0.42 (define @t72 () (tptp.f4 @t55 @t1 @t52)) % 0.16/0.42 (define @t73 () (tptp.f5 @t55 @t52)) % 0.16/0.42 (define @t74 () (@list @t55 @t52)) % 0.16/0.42 (define @t75 () (tptp.f6 @t55 @t52)) % 0.16/0.42 (define @t76 () (tptp.f7 @t55)) % 0.16/0.42 (define @t77 () (@var "P1" $$unsorted)) % 0.16/0.42 (define @t78 () (tptp.f7 @t77)) % 0.16/0.42 (define @t79 () (tptp.forallprefers @t78 @t76)) % 0.16/0.42 (define @t80 () (@list @t77)) % 0.16/0.42 (define @t81 () (exists @t80 @t79)) % 0.16/0.42 (define @t82 () (not @t81)) % 0.16/0.42 (define @t83 () (= tptp.false2 (tptp.phi @t76))) % 0.16/0.42 (define @t84 () (and @t83 @t82)) % 0.16/0.42 (define @t85 () (exists @t71 @t84)) % 0.16/0.42 (define @t86 () (tptp.not1 @t36)) % 0.16/0.42 (define @t87 () (=> @t41 (= @t86 @t37))) % 0.16/0.42 (define @t88 () (@list @t36)) % 0.16/0.42 (define @t89 () (forall @t88 @t87)) % 0.16/0.42 (define @t90 () (tptp.not1 tptp.false)) % 0.16/0.42 (define @t91 () (= tptp.false1 tptp.false2)) % 0.16/0.42 (define @t92 () (not @t91)) % 0.16/0.42 (define @t93 () (forall @t80 (not @t79))) % 0.16/0.42 (define @t94 () (not @t93)) % 0.16/0.42 (define @t95 () (@quantifiers_skolemize (forall @t71 (or (not @t83) @t94)) 0)) % 0.16/0.42 (define @t96 () (@list @t95)) % 0.16/0.42 (define @t97 () (tptp.f7 @t95)) % 0.16/0.42 (define @t98 () (= tptp.true @t97)) % 0.16/0.42 (define @t99 () (and (= tptp.false tptp.false) @t98)) % 0.16/0.42 (define @t100 () (tptp.bool tptp.false)) % 0.16/0.42 (define @t101 () (not @t100)) % 0.16/0.42 (define @t102 () (tptp.d @t97)) % 0.16/0.42 (define @t103 () (and @t11 @t102 @t101 (tptp.bool @t97))) % 0.16/0.42 (define @t104 () (not @t11)) % 0.16/0.42 (define @t105 () (and @t104 @t102)) % 0.16/0.42 (define @t106 () (or @t105 @t103 @t99)) % 0.16/0.42 (define @t107 () (tptp.forallprefers tptp.false @t97)) % 0.16/0.42 (define @t108 () (= @t107 @t106)) % 0.16/0.42 (define @t109 () (forall @t24 (= @t22 (or @t20 @t18 (and (= tptp.false @t1) (= tptp.true @t13)))))) % 0.16/0.42 (define @t110 () (or @t105 @t103 @t98)) % 0.16/0.42 (define @t111 () (= @t107 @t110)) % 0.16/0.42 (define @t112 () (@list false)) % 0.16/0.42 (define @t113 () (and @t83 @t93)) % 0.16/0.42 (define @t114 () (forall @t71 (not @t113))) % 0.16/0.42 (define @t115 () (not @t114)) % 0.16/0.42 (define @t116 () (forall @t80 (not (tptp.forallprefers @t78 @t97)))) % 0.16/0.42 (define @t117 () (not @t116)) % 0.16/0.42 (define @t118 () (tptp.phi @t97)) % 0.16/0.42 (define @t119 () (= tptp.false2 @t118)) % 0.16/0.42 (define @t120 () (not @t119)) % 0.16/0.42 (define @t121 () (or @t120 @t117)) % 0.16/0.42 (define @t122 () (@list true)) % 0.16/0.42 (define @t123 () (@list @t121)) % 0.16/0.42 (define @t124 () (@list tptp.false)) % 0.16/0.42 (define @t125 () (= @t37 @t86)) % 0.16/0.42 (define @t126 () (tptp.phi tptp.false)) % 0.16/0.42 (define @t127 () (or @t100 (= @t126 @t90))) % 0.16/0.42 (define @t128 () (forall @t88 (or @t40 @t125))) % 0.16/0.42 (define @t129 () (= @t90 @t126)) % 0.16/0.42 (define @t130 () (or @t100 @t129)) % 0.16/0.42 (define @t131 () (@list tptp.err)) % 0.16/0.42 (define @t132 () (or @t9 @t10)) % 0.16/0.42 (define @t133 () (not @t132)) % 0.16/0.42 (define @t134 () (tptp.bool tptp.err)) % 0.16/0.42 (define @t135 () (= @t134 @t132)) % 0.16/0.42 (define @t136 () (not @t134)) % 0.16/0.42 (define @t137 () (@list true false)) % 0.16/0.42 (define @t138 () (tptp.prop tptp.err)) % 0.16/0.42 (define @t139 () (= tptp.true @t138)) % 0.16/0.42 (define @t140 () (= @t134 @t139)) % 0.16/0.42 (define @t141 () (not @t139)) % 0.16/0.42 (define @t142 () (= tptp.false @t138)) % 0.16/0.42 (define @t143 () (= @t136 @t142)) % 0.16/0.42 (define @t144 () (not @t143)) % 0.16/0.42 (define @t145 () (and @t104 (= tptp.err @t126))) % 0.16/0.42 (define @t146 () (not @t145)) % 0.16/0.42 (define @t147 () (= tptp.false @t126)) % 0.16/0.42 (define @t148 () (and @t11 @t147)) % 0.16/0.42 (define @t149 () (or @t148 @t145)) % 0.16/0.42 (define @t150 () (tptp.prop tptp.false)) % 0.16/0.42 (define @t151 () (= tptp.true @t150)) % 0.16/0.42 (define @t152 () (= @t100 @t151)) % 0.16/0.42 (define @t153 () (tptp.lazy_impl tptp.true tptp.false)) % 0.16/0.42 (define @t154 () (not @t110)) % 0.16/0.42 (define @t155 () (not @t98)) % 0.16/0.42 (define @t156 () (tptp.prop @t95)) % 0.16/0.42 (define @t157 () (= tptp.true @t156)) % 0.16/0.42 (define @t158 () (tptp.bool @t95)) % 0.16/0.42 (define @t159 () (= @t158 @t157)) % 0.16/0.42 (define @t160 () (not @t158)) % 0.16/0.42 (define @t161 () (= tptp.true @t95)) % 0.16/0.42 (define @t162 () (= tptp.false @t95)) % 0.16/0.42 (define @t163 () (or @t162 @t161)) % 0.16/0.42 (define @t164 () (= @t158 @t163)) % 0.16/0.42 (define @t165 () (not @t162)) % 0.16/0.42 (define @t166 () (tptp.lazy_and1 tptp.true tptp.false)) % 0.16/0.42 (define @t167 () (= @t126 @t166)) % 0.16/0.42 (define @t168 () (not @t167)) % 0.16/0.42 (define @t169 () (= @t126 @t153)) % 0.16/0.42 (define @t170 () (not @t169)) % 0.16/0.42 (define @t171 () (not @t157)) % 0.16/0.42 (define @t172 () (not @t151)) % 0.16/0.42 (define @t173 () (= @t97 (tptp.lazy_impl @t156 @t95))) % 0.16/0.42 (define @t174 () (not @t173)) % 0.16/0.42 (define @t175 () (= @t118 (tptp.lazy_and1 tptp.true @t97))) % 0.16/0.42 (define @t176 () (not @t175)) % 0.16/0.42 (define @t177 () (not @t147)) % 0.16/0.42 (define @t178 () (= tptp.false tptp.false1)) % 0.16/0.42 (define @t179 () (not @t178)) % 0.16/0.42 (define @t180 () (= tptp.false @t97)) % 0.16/0.42 (define @t181 () (= @t97 @t118)) % 0.16/0.42 (define @t182 () (= false true)) % 0.16/0.42 (define @t183 () (tptp.lazy_impl @t150 tptp.false)) % 0.16/0.42 (define @t184 () (and @t178 @t180 @t181 @t119 @t92)) % 0.16/0.42 (define @t185 () (@list tptp.true)) % 0.16/0.42 (define @t186 () (tptp.phi tptp.true)) % 0.16/0.42 (define @t187 () (not @t12)) % 0.16/0.42 (define @t188 () (and @t187 (= tptp.err @t186))) % 0.16/0.42 (define @t189 () (not @t188)) % 0.16/0.42 (define @t190 () (= tptp.true @t186)) % 0.16/0.42 (define @t191 () (and @t12 @t190)) % 0.16/0.42 (define @t192 () (or @t191 @t188)) % 0.16/0.42 (define @t193 () (tptp.lazy_impl tptp.true tptp.true)) % 0.16/0.42 (define @t194 () (= @t186 @t193)) % 0.16/0.42 (define @t195 () (and @t190 @t173 @t157 @t194 @t161)) % 0.16/0.42 (define @t196 () (= tptp.false @t156)) % 0.16/0.42 (define @t197 () (= @t160 @t196)) % 0.16/0.42 (define @t198 () (not @t197)) % 0.16/0.42 (define @t199 () (tptp.lazy_impl tptp.false @t95)) % 0.16/0.42 (define @t200 () (= tptp.true @t199)) % 0.16/0.42 (define @t201 () (not @t200)) % 0.16/0.42 (define @t202 () (not @t196)) % 0.16/0.42 (define @t203 () (and @t201 @t200)) % 0.16/0.42 (assume @p1 @t8) % 0.16/0.42 (assume @p2 (and (not (= tptp.true tptp.false)) (not @t10) (not @t9))) % 0.16/0.42 (assume @p3 (and @t12 @t11 (tptp.d tptp.err))) % 0.16/0.42 (assume @p4 @t25) % 0.16/0.42 (assume @p5 (forall @t24 (= (tptp.existsprefers @t1 @t13) (or @t20 @t18 (and @t2 (= @t13 tptp.false)))))) % 0.16/0.42 (assume @p6 @t30) % 0.16/0.42 (assume @p7 @t33) % 0.16/0.42 (assume @p8 @t35) % 0.16/0.42 (assume @p9 (forall @t42 (=> @t41 (= @t39 @t37)))) % 0.16/0.42 (assume @p10 (forall @t42 (=> @t45 (= @t39 @t43)))) % 0.16/0.42 (assume @p11 (forall @t46 (=> @t44 (= (tptp.impl tptp.false @t38) tptp.true)))) % 0.16/0.42 (assume @p12 (forall @t46 (=> @t44 (= (tptp.impl tptp.true @t38) @t38)))) % 0.16/0.42 (assume @p13 (forall @t42 (=> @t41 (= (tptp.lazy_impl @t36 @t38) @t37)))) % 0.16/0.42 (assume @p14 @t48) % 0.16/0.42 (assume @p15 @t50) % 0.16/0.42 (assume @p16 (forall @t42 (=> @t41 (= @t51 @t37)))) % 0.16/0.42 (assume @p17 (forall @t42 (=> @t45 (= @t51 @t43)))) % 0.16/0.42 (assume @p18 (forall @t46 (=> @t44 (= (tptp.and1 tptp.false @t38) tptp.false)))) % 0.16/0.42 (assume @p19 (forall @t46 (=> @t44 (= (tptp.and1 tptp.true @t38) @t38)))) % 0.16/0.42 (assume @p20 (forall @t58 (= @t57 (tptp.lazy_impl @t56 (tptp.impl (tptp.impl @t55 @t54) @t52))))) % 0.16/0.42 (assume @p21 (forall @t62 (exists @t61 (and (= (tptp.and2 @t55 @t53) (tptp.phi @t57)) (not (exists @t60 (tptp.forallprefers (tptp.f1 @t55 @t53 @t59) @t57))))))) % 0.16/0.42 (assume @p22 (forall @t42 (=> @t41 (= (tptp.lazy_and1 @t36 @t38) @t37)))) % 0.16/0.42 (assume @p23 (forall @t46 (= (tptp.lazy_and1 tptp.false @t38) tptp.false))) % 0.16/0.42 (assume @p24 @t64) % 0.16/0.42 (assume @p25 (forall @t58 (= @t65 (tptp.lazy_impl @t56 (tptp.impl (tptp.lazy_impl @t55 @t54) @t52))))) % 0.16/0.42 (assume @p26 (forall @t62 (exists @t61 (and (= (tptp.lazy_and2 @t55 @t53) (tptp.phi @t65)) (not (exists @t60 (tptp.forallprefers (tptp.f2 @t55 @t53 @t59) @t65))))))) % 0.16/0.42 (assume @p27 (forall @t42 (=> @t41 (= @t66 @t37)))) % 0.16/0.42 (assume @p28 (forall @t42 (=> @t45 (= @t66 @t43)))) % 0.16/0.42 (assume @p29 (forall @t46 (=> @t44 (= (tptp.or1 tptp.true @t38) tptp.true)))) % 0.16/0.42 (assume @p30 (forall @t46 (=> @t44 (= (tptp.or1 tptp.false @t38) @t38)))) % 0.16/0.42 (assume @p31 (forall @t58 (= @t67 (tptp.lazy_impl @t56 (tptp.impl (tptp.impl @t55 @t52) (tptp.impl @t54 @t52)))))) % 0.16/0.42 (assume @p32 (forall @t62 (exists @t61 (and (= (tptp.or2 @t55 @t53) (tptp.phi @t67)) (not (exists @t60 (tptp.forallprefers (tptp.f3 @t55 @t53 @t59) @t67))))))) % 0.16/0.42 (assume @p33 (forall @t71 (exists @t7 (and (= (tptp.exists1 @t55) (tptp.phi @t68)) (not (exists @t70 (tptp.existsprefers (tptp.apply @t55 @t69) @t68))))))) % 0.16/0.42 (assume @p34 (forall (@list @t55 @t1 @t52) (= @t72 (tptp.impl @t68 @t52)))) % 0.16/0.42 (assume @p35 (forall @t74 (exists @t7 (and (= @t73 (tptp.phi @t72)) (not (exists @t70 (tptp.forallprefers (tptp.f4 @t55 @t69 @t52) @t72))))))) % 0.16/0.42 (assume @p36 (forall @t74 (= @t75 (tptp.lazy_impl @t56 (tptp.impl @t73 @t52))))) % 0.16/0.42 (assume @p37 (forall @t71 (exists @t61 (and (= (tptp.exists2 @t55) (tptp.phi @t75)) (not (exists @t60 (tptp.forallprefers (tptp.f6 @t55 @t59) @t75))))))) % 0.16/0.42 (assume @p38 (= tptp.false1 tptp.false)) % 0.16/0.42 (assume @p39 (forall @t71 (= @t76 (tptp.lazy_impl (tptp.prop @t55) @t55)))) % 0.16/0.42 (assume @p40 @t85) % 0.16/0.42 (assume @p41 @t89) % 0.16/0.42 (assume @p42 (= @t90 tptp.true)) % 0.16/0.42 (assume @p43 (= (tptp.not1 tptp.true) tptp.false)) % 0.16/0.42 (assume @p44 (forall @t71 (= (tptp.not2 @t55) (tptp.impl @t55 tptp.false2)))) % 0.16/0.42 (assume @p45 @t92) % 0.16/0.42 (assume @p46 true) % 0.16/0.42 (step @p47 :rule instantiate :premises (@p39) :args (@t96)) % 0.16/0.42 (step @p48 :rule eq-symm :args (@t13 tptp.true)) % 0.16/0.42 (step @p49 :rule eq-symm :args (@t1 tptp.false)) % 0.16/0.42 (step @p50 :rule nary_cong :premises (@p49 @p48) :args (@t14)) % 0.16/0.42 (step @p51 :rule refl :args (@t18)) % 0.16/0.42 (step @p52 :rule refl :args (@t20)) % 0.16/0.42 (step @p53 :rule nary_cong :premises (@p52 @p51 @p50) :args (@t21)) % 0.16/0.42 (step @p54 :rule refl :args (@t22)) % 0.16/0.42 (step @p55 :rule cong :premises (@p54 @p53) :args (@t23)) % 0.16/0.42 (step @p56 :rule cong :premises (@p55) :args (@t25)) % 0.16/0.42 (step @p57 :rule eq_resolve :premises (@p4 @p56)) % 0.16/0.42 (step @p58 :rule aci_norm :args ((= (and true @t98) @t98))) % 0.16/0.42 (step @p59 :rule refl :args (@t98)) % 0.16/0.42 (step @p60 :rule eq-refl :args (tptp.false)) % 0.16/0.42 (step @p61 :rule nary_cong :premises (@p60 @p59) :args (@t99)) % 0.16/0.42 (step @p62 :rule trans :premises (@p61 @p58)) % 0.16/0.42 (step @p63 :rule refl :args (@t103)) % 0.16/0.42 (step @p64 :rule refl :args (@t105)) % 0.16/0.42 (step @p65 :rule nary_cong :premises (@p64 @p63 @p62) :args (@t106)) % 0.16/0.42 (step @p66 :rule refl :args (@t107)) % 0.16/0.42 (step @p67 :rule cong :premises (@p66 @p65) :args (@t108)) % 0.16/0.42 (step @p68 :rule refl :args (@t109)) % 0.16/0.42 (step @p69 :rule cong :premises (@p68 @p67) :args ((=> @t109 @t108))) % 0.16/0.42 (assume-push @p450 @t109) % 0.16/0.42 (step @p71 :rule instantiate :premises (@p57) :args ((@list tptp.false @t97))) % 0.16/0.42 (step-pop @p451 :rule scope :premises (@p71)) % 0.16/0.42 (step @p72 :rule process_scope :premises (@p451) :args (@t108)) % 0.16/0.42 (step @p74 :rule eq_resolve :premises (@p72 @p69)) % 0.16/0.42 (step @p75 :rule implies_elim :premises (@p74)) % 0.16/0.42 (step @p76 :rule chain_m_resolution :premises (@p75 @p57) :args (@t111 @t112 (@list @t109))) % 0.16/0.42 (step @p77 :rule bool-and-de-morgan :args (@t83 @t93 true)) % 0.16/0.42 (step @p78 :rule cong :premises (@p77) :args (@t114)) % 0.16/0.42 (step @p79 :rule cong :premises (@p78) :args (@t115)) % 0.16/0.42 (step @p80 :rule exists-elim :args ((= (exists @t71 @t113) @t115))) % 0.16/0.42 (step @p81 :rule trans :premises (@p80 @p79)) % 0.16/0.42 (step @p82 :rule bool-double-not-elim :args (@t93)) % 0.16/0.42 (step @p83 :rule exists-elim :args ((= @t81 @t94))) % 0.16/0.42 (step @p84 :rule cong :premises (@p83) :args (@t82)) % 0.16/0.42 (step @p85 :rule trans :premises (@p84 @p82)) % 0.16/0.42 (step @p86 :rule refl :args (@t83)) % 0.16/0.42 (step @p87 :rule nary_cong :premises (@p86 @p85) :args (@t84)) % 0.16/0.42 (step @p88 :rule cong :premises (@p87) :args (@t85)) % 0.16/0.42 (step @p89 :rule trans :premises (@p88 @p81)) % 0.16/0.42 (step @p90 :rule eq_resolve :premises (@p40 @p89)) % 0.16/0.42 (step @p91 :rule skolemize :premises (@p90)) % 0.16/0.42 (step @p92 :rule bool-double-not-elim :args (@t116)) % 0.16/0.42 (step @p93 :rule refl :args (@t121)) % 0.16/0.42 (step @p94 :rule nary_cong :premises (@p93 @p92) :args ((or @t121 (not @t117)))) % 0.16/0.42 (step @p95 :rule cnf_or_neg :args (@t121 1)) % 0.16/0.42 (step @p96 :rule eq_resolve :premises (@p95 @p94)) % 0.16/0.42 (step @p97 :rule reordering :premises (@p96) :args ((or @t116 @t121))) % 0.16/0.42 (step @p98 :rule chain_m_resolution :premises (@p97 @p91) :args (@t116 @t122 @t123)) % 0.16/0.42 (step @p99 :rule instantiate :premises (@p98) :args (@t124)) % 0.16/0.42 (step @p100 :rule false_intro :premises (@p99)) % 0.16/0.42 (step @p101 :rule refl :args (@t97)) % 0.16/0.42 (step @p102 :rule instantiate :premises (@p39) :args (@t124)) % 0.16/0.42 (step @p103 :rule symm :premises (@p102)) % 0.16/0.42 (step @p104 :rule refl :args (tptp.false)) % 0.16/0.42 (step @p105 :rule eq-symm :args (@t31 tptp.true)) % 0.16/0.42 (step @p106 :rule refl :args (@t5)) % 0.16/0.42 (step @p107 :rule cong :premises (@p106 @p105) :args ((= @t5 @t32))) % 0.16/0.42 (step @p108 :rule eq-symm :args (@t32 @t5)) % 0.16/0.42 (step @p109 :rule trans :premises (@p108 @p107)) % 0.16/0.42 (step @p110 :rule cong :premises (@p109) :args (@t33)) % 0.16/0.42 (step @p111 :rule eq_resolve :premises (@p7 @p110)) % 0.16/0.42 (step @p112 :rule instantiate :premises (@p111) :args (@t124)) % 0.16/0.42 (step @p113 :rule refl :args (@t125)) % 0.16/0.42 (step @p114 :rule bool-double-not-elim :args (@t40)) % 0.16/0.42 (step @p115 :rule nary_cong :premises (@p114 @p113) :args ((or (not @t41) @t125))) % 0.16/0.42 (step @p116 :rule bool-impl-elim :args (@t41 @t125)) % 0.16/0.42 (step @p117 :rule trans :premises (@p116 @p115)) % 0.16/0.42 (step @p118 :rule cong :premises (@p117) :args ((forall @t88 (=> @t41 @t125)))) % 0.16/0.42 (step @p119 :rule eq-symm :args (@t86 @t37)) % 0.16/0.42 (step @p120 :rule refl :args (@t41)) % 0.16/0.42 (step @p121 :rule cong :premises (@p120 @p119) :args (@t87)) % 0.16/0.42 (step @p122 :rule cong :premises (@p121) :args (@t89)) % 0.16/0.42 (step @p123 :rule trans :premises (@p122 @p118)) % 0.16/0.42 (step @p124 :rule eq_resolve :premises (@p41 @p123)) % 0.16/0.42 (step @p125 :rule eq-symm :args (@t126 @t90)) % 0.16/0.42 (step @p126 :rule refl :args (@t100)) % 0.16/0.42 (step @p127 :rule nary_cong :premises (@p126 @p125) :args (@t127)) % 0.16/0.42 (step @p128 :rule refl :args (@t128)) % 0.16/0.42 (step @p129 :rule cong :premises (@p128 @p127) :args ((=> @t128 @t127))) % 0.16/0.42 (assume-push @p452 @t128) % 0.16/0.42 (step @p131 :rule instantiate :premises (@p124) :args (@t124)) % 0.16/0.42 (step-pop @p453 :rule scope :premises (@p131)) % 0.16/0.42 (step @p132 :rule process_scope :premises (@p453) :args (@t127)) % 0.16/0.42 (step @p134 :rule eq_resolve :premises (@p132 @p129)) % 0.16/0.42 (step @p135 :rule implies_elim :premises (@p134)) % 0.16/0.42 (step @p136 :rule chain_m_resolution :premises (@p135 @p124) :args (@t130 @t112 (@list @t128))) % 0.16/0.42 (step @p137 :rule instantiate :premises (@p111) :args (@t131)) % 0.16/0.42 (step @p138 :rule eq-symm :args (@t1 tptp.true)) % 0.16/0.42 (step @p139 :rule nary_cong :premises (@p49 @p138) :args (@t4)) % 0.16/0.42 (step @p140 :rule cong :premises (@p106 @p139) :args (@t6)) % 0.16/0.42 (step @p141 :rule cong :premises (@p140) :args (@t8)) % 0.16/0.42 (step @p142 :rule eq_resolve :premises (@p1 @p141)) % 0.16/0.42 (step @p143 :rule instantiate :premises (@p142) :args (@t131)) % 0.16/0.42 (step @p144 :rule and_elim :premises (@p2) :args (2)) % 0.16/0.42 (step @p145 :rule and_elim :premises (@p2) :args (1)) % 0.16/0.42 (step @p146 :rule cnf_or_pos :args (@t132)) % 0.16/0.42 (step @p147 :rule reordering :premises (@p146) :args ((or @t10 @t9 @t133))) % 0.16/0.42 (step @p148 :rule chain_m_resolution :premises (@p147 @p145 @p144) :args (@t133 (@list true true) (@list @t10 @t9))) % 0.16/0.42 (step @p149 :rule cnf_equiv_pos1 :args (@t135)) % 0.16/0.42 (step @p150 :rule reordering :premises (@p149) :args ((or @t136 @t132 (not @t135)))) % 0.16/0.42 (step @p151 :rule chain_m_resolution :premises (@p150 @p148 @p143) :args (@t136 @t137 (@list @t132 @t135))) % 0.16/0.42 (step @p152 :rule cnf_equiv_pos2 :args (@t140)) % 0.16/0.42 (step @p153 :rule reordering :premises (@p152) :args ((or @t134 @t141 (not @t140)))) % 0.16/0.42 (step @p154 :rule chain_m_resolution :premises (@p153 @p151 @p137) :args (@t141 @t137 (@list @t134 @t140))) % 0.16/0.42 (step @p155 :rule false_intro :premises (@p154)) % 0.16/0.42 (step @p156 :rule eq-symm :args (@t31 tptp.false)) % 0.16/0.42 (step @p157 :rule refl :args (@t15)) % 0.16/0.42 (step @p158 :rule cong :premises (@p157 @p156) :args ((= @t15 @t34))) % 0.16/0.42 (step @p159 :rule eq-symm :args (@t34 @t15)) % 0.16/0.42 (step @p160 :rule trans :premises (@p159 @p158)) % 0.16/0.42 (step @p161 :rule cong :premises (@p160) :args (@t35)) % 0.16/0.42 (step @p162 :rule eq_resolve :premises (@p8 @p161)) % 0.16/0.42 (step @p163 :rule instantiate :premises (@p162) :args (@t131)) % 0.16/0.42 (step @p164 :rule refl :args (@t142)) % 0.16/0.42 (step @p165 :rule bool-double-not-elim :args (@t134)) % 0.16/0.42 (step @p166 :rule refl :args (@t144)) % 0.16/0.42 (step @p167 :rule nary_cong :premises (@p166 @p165 @p164) :args ((or @t144 (not @t136) @t142))) % 0.16/0.42 (step @p168 :rule cnf_equiv_pos1 :args (@t143)) % 0.16/0.42 (step @p169 :rule eq_resolve :premises (@p168 @p167)) % 0.16/0.42 (step @p170 :rule reordering :premises (@p169) :args ((or @t134 @t142 @t144))) % 0.16/0.42 (step @p171 :rule chain_m_resolution :premises (@p170 @p151 @p163) :args (@t142 @t137 (@list @t134 @t143))) % 0.16/0.42 (step @p172 :rule eq-symm :args (@t26 tptp.err)) % 0.16/0.42 (step @p173 :rule refl :args (@t19)) % 0.16/0.42 (step @p174 :rule nary_cong :premises (@p173 @p172) :args (@t27)) % 0.16/0.42 (step @p175 :rule eq-symm :args (@t26 @t1)) % 0.16/0.42 (step @p176 :rule refl :args (@t17)) % 0.16/0.42 (step @p177 :rule nary_cong :premises (@p176 @p175) :args (@t28)) % 0.16/0.42 (step @p178 :rule nary_cong :premises (@p177 @p174) :args (@t29)) % 0.16/0.42 (step @p179 :rule cong :premises (@p178) :args (@t30)) % 0.16/0.42 (step @p180 :rule eq_resolve :premises (@p6 @p179)) % 0.16/0.42 (step @p181 :rule instantiate :premises (@p180) :args (@t124)) % 0.16/0.42 (step @p182 :rule and_elim :premises (@p3) :args (1)) % 0.16/0.42 (step @p183 :rule cnf_and_pos :args (@t145 0)) % 0.16/0.42 (step @p184 :rule reordering :premises (@p183) :args ((or @t104 @t146))) % 0.16/0.42 (step @p185 :rule chain_m_resolution :premises (@p184 @p182) :args (@t146 @t112 (@list @t11))) % 0.16/0.42 (step @p186 :rule cnf_or_pos :args (@t149)) % 0.16/0.42 (step @p187 :rule reordering :premises (@p186) :args ((or @t148 @t145 (not @t149)))) % 0.16/0.42 (step @p188 :rule chain_m_resolution :premises (@p187 @p185 @p181) :args (@t148 @t137 (@list @t145 @t149))) % 0.16/0.42 (step @p189 :rule cnf_and_pos :args (@t148 1)) % 0.16/0.42 (step @p190 :rule reordering :premises (@p189) :args ((or @t147 (not @t148)))) % 0.16/0.42 (step @p191 :rule chain_m_resolution :premises (@p190 @p188) :args (@t147 @t112 (@list @t148))) % 0.16/0.42 (step @p192 :rule symm :premises (@p191)) % 0.16/0.42 (step @p193 :rule trans :premises (@p192 @p171)) % 0.16/0.42 (step @p194 :rule cong :premises (@p42 @p193) :args (@t129)) % 0.16/0.42 (step @p195 :rule trans :premises (@p194 @p155)) % 0.16/0.42 (step @p196 :rule false_elim :premises (@p195)) % 0.16/0.42 (step @p197 :rule cnf_or_pos :args (@t130)) % 0.16/0.42 (step @p198 :rule reordering :premises (@p197) :args ((or @t100 @t129 (not @t130)))) % 0.16/0.42 (step @p199 :rule chain_m_resolution :premises (@p198 @p196 @p136) :args (@t100 @t137 (@list @t129 @t130))) % 0.16/0.42 (step @p200 :rule cnf_equiv_pos1 :args (@t152)) % 0.16/0.42 (step @p201 :rule reordering :premises (@p200) :args ((or @t101 @t151 (not @t152)))) % 0.16/0.42 (step @p202 :rule chain_m_resolution :premises (@p201 @p199 @p112) :args (@t151 (@list false false) (@list @t100 @t152))) % 0.16/0.42 (step @p203 :rule cong :premises (@p202 @p104) :args (@t153)) % 0.16/0.42 (step @p204 :rule eq-symm :args (@t49 @t43)) % 0.16/0.42 (step @p205 :rule cong :premises (@p204) :args (@t50)) % 0.16/0.42 (step @p206 :rule eq_resolve :premises (@p15 @p205)) % 0.16/0.42 (step @p207 :rule instantiate :premises (@p206) :args (@t124)) % 0.16/0.42 (step @p208 :rule trans :premises (@p191 @p207 @p203 @p103)) % 0.16/0.42 (step @p209 :rule cong :premises (@p208 @p101) :args (@t107)) % 0.16/0.42 (step @p210 :rule trans :premises (@p209 @p100)) % 0.16/0.42 (step @p211 :rule false_elim :premises (@p210)) % 0.16/0.42 (step @p212 :rule cnf_equiv_pos2 :args (@t111)) % 0.16/0.42 (step @p213 :rule reordering :premises (@p212) :args ((or @t107 @t154 (not @t111)))) % 0.16/0.42 (step @p214 :rule chain_m_resolution :premises (@p213 @p211 @p76) :args (@t154 @t137 (@list @t107 @t111))) % 0.16/0.42 (step @p215 :rule cnf_or_neg :args (@t110 2)) % 0.16/0.42 (step @p216 :rule reordering :premises (@p215) :args ((or @t155 @t110))) % 0.16/0.42 (step @p217 :rule chain_m_resolution :premises (@p216 @p214) :args (@t155 @t122 (@list @t110))) % 0.16/0.42 (step @p218 :rule instantiate :premises (@p162) :args (@t96)) % 0.16/0.42 (step @p219 :rule instantiate :premises (@p111) :args (@t96)) % 0.16/0.42 (step @p220 :rule cnf_equiv_pos1 :args (@t159)) % 0.16/0.42 (step @p221 :rule reordering :premises (@p220) :args ((or @t157 @t160 (not @t159)))) % 0.16/0.42 (step @p222 :rule instantiate :premises (@p142) :args (@t96)) % 0.16/0.42 (step @p223 :rule cnf_equiv_pos1 :args (@t164)) % 0.16/0.42 (step @p224 :rule reordering :premises (@p223) :args ((or @t160 @t163 (not @t164)))) % 0.16/0.42 (step @p225 :rule symm :premises (@p38)) % 0.16/0.42 (step @p226 :rule bool-double-not-elim :args (@t119)) % 0.16/0.42 (step @p227 :rule nary_cong :premises (@p93 @p226) :args ((or @t121 (not @t120)))) % 0.16/0.42 (step @p228 :rule cnf_or_neg :args (@t121 0)) % 0.16/0.42 (step @p229 :rule eq_resolve :premises (@p228 @p227)) % 0.16/0.42 (step @p230 :rule reordering :premises (@p229) :args ((or @t119 @t121))) % 0.16/0.42 (step @p231 :rule chain_m_resolution :premises (@p230 @p91) :args (@t119 @t122 @t123)) % 0.16/0.42 (step @p232 :rule eq-symm :args (@t63 @t43)) % 0.16/0.42 (step @p233 :rule cong :premises (@p232) :args (@t64)) % 0.16/0.42 (step @p234 :rule eq_resolve :premises (@p24 @p233)) % 0.16/0.42 (step @p235 :rule instantiate :premises (@p234) :args ((@list @t97))) % 0.16/0.42 (step @p236 :rule instantiate :premises (@p234) :args (@t124)) % 0.16/0.42 (step @p237 :rule refl :args (@t165)) % 0.16/0.42 (step @p238 :rule refl :args (@t168)) % 0.16/0.42 (step @p239 :rule refl :args (@t170)) % 0.16/0.42 (step @p240 :rule refl :args (@t171)) % 0.16/0.42 (step @p241 :rule refl :args (@t172)) % 0.16/0.42 (step @p242 :rule refl :args (@t174)) % 0.16/0.42 (step @p243 :rule refl :args (@t176)) % 0.16/0.42 (step @p244 :rule refl :args (@t177)) % 0.16/0.42 (step @p245 :rule refl :args (@t120)) % 0.16/0.42 (step @p246 :rule refl :args (@t179)) % 0.16/0.42 (step @p247 :rule bool-double-not-elim :args (@t91)) % 0.16/0.42 (step @p248 :rule nary_cong :premises (@p247 @p246 @p245 @p244 @p243 @p242 @p241 @p240 @p239 @p238 @p237) :args ((or (not @t92) @t179 @t120 @t177 @t176 @t174 @t172 @t171 @t170 @t168 @t165))) % 0.16/0.42 (assume-push @p454 @t178) % 0.16/0.42 (assume-push @p455 @t180) % 0.16/0.42 (assume-push @p456 @t181) % 0.16/0.42 (assume-push @p457 @t119) % 0.16/0.42 (assume-push @p458 @t92) % 0.16/0.42 (step @p254 :rule evaluate :args (@t182)) % 0.16/0.42 (step @p255 :rule symm :premises (@p455)) % 0.16/0.42 (step @p256 :rule symm :premises (@p456)) % 0.16/0.42 (step @p257 :rule trans :premises (@p231 @p256 @p255 @p225)) % 0.16/0.42 (step @p258 :rule symm :premises (@p257)) % 0.16/0.42 (step @p259 :rule true_intro :premises (@p258)) % 0.16/0.42 (step @p260 :rule false_intro :premises (@p45)) % 0.16/0.42 (step @p261 :rule symm :premises (@p260)) % 0.16/0.42 (step @p262 :rule trans :premises (@p261 @p259)) % 0.16/0.42 (step @p263 false :rule eq_resolve :premises (@p262 @p254)) % 0.16/0.42 (step-pop @p459 :rule scope :premises (@p263)) % 0.16/0.42 (step-pop @p460 :rule scope :premises (@p459)) % 0.16/0.42 (step-pop @p461 :rule scope :premises (@p460)) % 0.16/0.42 (step-pop @p462 :rule scope :premises (@p461)) % 0.16/0.42 (step-pop @p463 :rule scope :premises (@p462)) % 0.16/0.42 (step @p264 :rule process_scope :premises (@p463) :args (false)) % 0.16/0.42 (assume-push @p464 @t92) % 0.16/0.42 (assume-push @p465 @t178) % 0.16/0.42 (assume-push @p466 @t119) % 0.16/0.42 (assume-push @p467 @t147) % 0.16/0.42 (assume-push @p468 @t175) % 0.16/0.42 (assume-push @p469 @t173) % 0.16/0.42 (assume-push @p470 @t151) % 0.16/0.42 (assume-push @p471 @t157) % 0.16/0.42 (assume-push @p472 @t169) % 0.16/0.42 (assume-push @p473 @t167) % 0.16/0.42 (assume-push @p474 @t162) % 0.16/0.42 (assume-push @p475 @t175) % 0.16/0.42 (assume-push @p476 @t173) % 0.16/0.42 (assume-push @p477 @t157) % 0.16/0.42 (assume-push @p478 @t151) % 0.16/0.42 (assume-push @p479 @t162) % 0.16/0.42 (assume-push @p480 @t169) % 0.16/0.42 (assume-push @p481 @t147) % 0.16/0.42 (assume-push @p482 @t167) % 0.16/0.42 (step @p289 :rule symm :premises (@p235)) % 0.16/0.42 (step @p290 :rule symm :premises (@p47)) % 0.16/0.42 (step @p291 :rule symm :premises (@p202)) % 0.16/0.42 (step @p292 :rule trans :premises (@p291 @p471)) % 0.16/0.42 (step @p293 :rule cong :premises (@p292 @p474) :args (@t183)) % 0.16/0.42 (step @p294 :rule trans :premises (@p191 @p207 @p203 @p293 @p290)) % 0.16/0.42 (step @p295 :rule refl :args (tptp.true)) % 0.16/0.42 (step @p296 :rule cong :premises (@p295 @p294) :args (@t166)) % 0.16/0.42 (step @p297 :rule symm :premises (@p207)) % 0.16/0.42 (step @p298 :rule symm :premises (@p203)) % 0.16/0.42 (step @p299 :rule symm :premises (@p293)) % 0.16/0.42 (step @p300 :rule trans :premises (@p47 @p299 @p298 @p297 @p236 @p296 @p289)) % 0.16/0.42 (step-pop @p483 :rule scope :premises (@p300)) % 0.16/0.42 (step-pop @p484 :rule scope :premises (@p483)) % 0.16/0.42 (step-pop @p485 :rule scope :premises (@p484)) % 0.16/0.42 (step-pop @p486 :rule scope :premises (@p485)) % 0.16/0.42 (step-pop @p487 :rule scope :premises (@p486)) % 0.16/0.42 (step-pop @p488 :rule scope :premises (@p487)) % 0.16/0.42 (step-pop @p489 :rule scope :premises (@p488)) % 0.16/0.42 (step-pop @p490 :rule scope :premises (@p489)) % 0.16/0.42 (step @p301 :rule process_scope :premises (@p490) :args (@t181)) % 0.16/0.42 (step @p310 :rule and_intro :premises (@p235 @p47 @p471 @p202 @p474 @p207 @p191 @p236)) % 0.16/0.42 (step @p311 :rule modus_ponens :premises (@p310 @p301)) % 0.16/0.42 (assume-push @p491 @t173) % 0.16/0.42 (assume-push @p492 @t157) % 0.16/0.42 (assume-push @p493 @t151) % 0.16/0.42 (assume-push @p494 @t162) % 0.16/0.42 (assume-push @p495 @t169) % 0.16/0.42 (assume-push @p496 @t147) % 0.16/0.42 (step @p290 :rule symm :premises (@p47)) % 0.16/0.42 (step @p291 :rule symm :premises (@p202)) % 0.16/0.42 (step @p318 :rule trans :premises (@p291 @p471)) % 0.16/0.42 (step @p319 :rule cong :premises (@p318 @p474) :args (@t183)) % 0.16/0.42 (step @p320 :rule trans :premises (@p191 @p207 @p203 @p319 @p290)) % 0.16/0.42 (step-pop @p497 :rule scope :premises (@p320)) % 0.16/0.42 (step-pop @p498 :rule scope :premises (@p497)) % 0.16/0.42 (step-pop @p499 :rule scope :premises (@p498)) % 0.16/0.42 (step-pop @p500 :rule scope :premises (@p499)) % 0.16/0.42 (step-pop @p501 :rule scope :premises (@p500)) % 0.16/0.42 (step-pop @p502 :rule scope :premises (@p501)) % 0.16/0.42 (step @p321 :rule process_scope :premises (@p502) :args (@t180)) % 0.16/0.42 (step @p328 :rule and_intro :premises (@p47 @p471 @p202 @p474 @p207 @p191)) % 0.16/0.42 (step @p329 :rule modus_ponens :premises (@p328 @p321)) % 0.16/0.42 (step @p330 :rule and_intro :premises (@p225 @p329 @p311 @p231 @p45)) % 0.16/0.42 (step-pop @p503 :rule scope :premises (@p330)) % 0.16/0.42 (step-pop @p504 :rule scope :premises (@p503)) % 0.16/0.42 (step-pop @p505 :rule scope :premises (@p504)) % 0.16/0.42 (step-pop @p506 :rule scope :premises (@p505)) % 0.16/0.42 (step-pop @p507 :rule scope :premises (@p506)) % 0.16/0.42 (step-pop @p508 :rule scope :premises (@p507)) % 0.16/0.42 (step-pop @p509 :rule scope :premises (@p508)) % 0.16/0.42 (step-pop @p510 :rule scope :premises (@p509)) % 0.16/0.42 (step-pop @p511 :rule scope :premises (@p510)) % 0.16/0.42 (step-pop @p512 :rule scope :premises (@p511)) % 0.16/0.42 (step-pop @p513 :rule scope :premises (@p512)) % 0.16/0.42 (step @p331 :rule process_scope :premises (@p513) :args (@t184)) % 0.16/0.42 (step @p343 :rule implies_elim :premises (@p331)) % 0.16/0.42 (step @p344 :rule resolution :premises (@p343 @p264) :args (true @t184)) % 0.16/0.42 (step @p345 :rule not_and :premises (@p344)) % 0.16/0.42 (step @p346 :rule eq_resolve :premises (@p345 @p248)) % 0.16/0.42 (step @p347 :rule cnf_or_pos :args (@t163)) % 0.16/0.42 (step @p348 :rule reordering :premises (@p347) :args ((or @t162 @t161 (not @t163)))) % 0.16/0.42 (step @p349 :rule instantiate :premises (@p180) :args (@t185)) % 0.16/0.42 (step @p350 :rule and_elim :premises (@p3) :args (0)) % 0.16/0.42 (step @p351 :rule cnf_and_pos :args (@t188 0)) % 0.16/0.42 (step @p352 :rule reordering :premises (@p351) :args ((or @t187 @t189))) % 0.16/0.42 (step @p353 :rule chain_m_resolution :premises (@p352 @p350) :args (@t189 @t112 (@list @t12))) % 0.16/0.42 (step @p354 :rule cnf_or_pos :args (@t192)) % 0.16/0.42 (step @p355 :rule reordering :premises (@p354) :args ((or @t191 @t188 (not @t192)))) % 0.16/0.42 (step @p356 :rule chain_m_resolution :premises (@p355 @p353 @p349) :args (@t191 @t137 (@list @t188 @t192))) % 0.16/0.42 (step @p357 :rule cnf_and_pos :args (@t191 1)) % 0.16/0.42 (step @p358 :rule reordering :premises (@p357) :args ((or @t190 (not @t191)))) % 0.16/0.42 (step @p359 :rule chain_m_resolution :premises (@p358 @p356) :args (@t190 @t112 (@list @t191))) % 0.16/0.42 (step @p360 :rule instantiate :premises (@p206) :args (@t185)) % 0.16/0.42 (assume-push @p514 @t190) % 0.16/0.42 (assume-push @p515 @t173) % 0.16/0.42 (assume-push @p516 @t157) % 0.16/0.42 (assume-push @p517 @t194) % 0.16/0.42 (assume-push @p518 @t161) % 0.16/0.42 (assume-push @p519 @t173) % 0.16/0.42 (assume-push @p520 @t157) % 0.16/0.42 (assume-push @p521 @t161) % 0.16/0.42 (assume-push @p522 @t194) % 0.16/0.42 (assume-push @p523 @t190) % 0.16/0.42 (step @p290 :rule symm :premises (@p47)) % 0.16/0.42 (step @p371 :rule cong :premises (@p516 @p518) :args (@t193)) % 0.16/0.42 (step @p372 :rule trans :premises (@p359 @p360 @p371 @p290)) % 0.16/0.42 (step-pop @p524 :rule scope :premises (@p372)) % 0.16/0.42 (step-pop @p525 :rule scope :premises (@p524)) % 0.16/0.42 (step-pop @p526 :rule scope :premises (@p525)) % 0.16/0.42 (step-pop @p527 :rule scope :premises (@p526)) % 0.16/0.42 (step-pop @p528 :rule scope :premises (@p527)) % 0.16/0.42 (step @p373 :rule process_scope :premises (@p528) :args (@t98)) % 0.16/0.42 (step @p379 :rule and_intro :premises (@p47 @p516 @p518 @p360 @p359)) % 0.16/0.42 (step @p380 :rule modus_ponens :premises (@p379 @p373)) % 0.16/0.42 (step-pop @p529 :rule scope :premises (@p380)) % 0.16/0.42 (step-pop @p530 :rule scope :premises (@p529)) % 0.16/0.42 (step-pop @p531 :rule scope :premises (@p530)) % 0.16/0.42 (step-pop @p532 :rule scope :premises (@p531)) % 0.16/0.42 (step-pop @p533 :rule scope :premises (@p532)) % 0.16/0.42 (step @p381 :rule process_scope :premises (@p533) :args (@t98)) % 0.16/0.42 (step @p387 :rule implies_elim :premises (@p381)) % 0.16/0.42 (step @p388 :rule cnf_and_neg :args (@t195)) % 0.16/0.42 (step @p389 :rule resolution :premises (@p388 @p387) :args (true @t195)) % 0.16/0.42 (step @p390 :rule reordering :premises (@p389) :args ((or (not @t190) @t174 @t98 @t171 (not @t194) (not @t161)))) % 0.16/0.42 (step @p391 :rule chain_m_resolution :premises (@p390 @p217 @p360 @p359 @p47 @p348 @p346 @p202 @p236 @p207 @p191 @p47 @p235 @p231 @p45 @p225 @p224 @p222 @p221 @p219) :args (@t160 (@list true false false false false true false false false false false false false true false false false false false) (@list @t98 @t194 @t190 @t173 @t161 @t162 @t151 @t167 @t169 @t147 @t173 @t175 @t119 @t91 @t178 @t163 @t164 @t157 @t159))) % 0.16/0.42 (step @p392 :rule refl :args (@t196)) % 0.16/0.42 (step @p393 :rule bool-double-not-elim :args (@t158)) % 0.16/0.42 (step @p394 :rule refl :args (@t198)) % 0.16/0.42 (step @p395 :rule nary_cong :premises (@p394 @p393 @p392) :args ((or @t198 (not @t160) @t196))) % 0.16/0.42 (step @p396 :rule cnf_equiv_pos1 :args (@t197)) % 0.16/0.42 (step @p397 :rule eq_resolve :premises (@p396 @p395)) % 0.16/0.42 (step @p398 :rule reordering :premises (@p397) :args ((or @t158 @t196 @t198))) % 0.16/0.42 (step @p399 :rule chain_m_resolution :premises (@p398 @p391 @p218) :args (@t196 @t137 (@list @t158 @t197))) % 0.16/0.42 (step @p400 :rule eq-symm :args (@t47 tptp.true)) % 0.16/0.42 (step @p401 :rule cong :premises (@p400) :args (@t48)) % 0.16/0.42 (step @p402 :rule eq_resolve :premises (@p14 @p401)) % 0.16/0.42 (step @p403 :rule instantiate :premises (@p402) :args (@t96)) % 0.16/0.42 (step @p404 :rule refl :args (@t201)) % 0.16/0.42 (step @p405 :rule bool-double-not-elim :args (@t98)) % 0.16/0.42 (step @p406 :rule refl :args (@t202)) % 0.16/0.42 (step @p407 :rule nary_cong :premises (@p242 @p406 @p405 @p404) :args ((or @t174 @t202 (not @t155) @t201))) % 0.16/0.42 (assume-push @p534 @t201) % 0.16/0.42 (assume-push @p535 @t200) % 0.16/0.42 (step @p254 :rule evaluate :args (@t182)) % 0.16/0.42 (step @p410 :rule true_intro :premises (@p403)) % 0.16/0.42 (step @p411 :rule false_intro :premises (@p534)) % 0.16/0.42 (step @p412 :rule symm :premises (@p411)) % 0.16/0.42 (step @p413 :rule trans :premises (@p412 @p410)) % 0.16/0.42 (step @p414 false :rule eq_resolve :premises (@p413 @p254)) % 0.16/0.42 (step-pop @p536 :rule scope :premises (@p414)) % 0.16/0.42 (step-pop @p537 :rule scope :premises (@p536)) % 0.16/0.42 (step @p415 :rule process_scope :premises (@p537) :args (false)) % 0.16/0.42 (assume-push @p538 @t173) % 0.16/0.42 (assume-push @p539 @t196) % 0.16/0.42 (assume-push @p540 @t155) % 0.16/0.42 (assume-push @p541 @t200) % 0.16/0.42 (assume-push @p542 @t196) % 0.16/0.42 (assume-push @p543 @t155) % 0.16/0.42 (assume-push @p544 @t173) % 0.16/0.42 (step @p425 :rule false_intro :premises (@p217)) % 0.16/0.42 (step @p290 :rule symm :premises (@p47)) % 0.16/0.42 (step @p426 :rule refl :args (@t95)) % 0.16/0.42 (step @p427 :rule cong :premises (@p539 @p426) :args (@t199)) % 0.16/0.42 (step @p428 :rule trans :premises (@p427 @p290)) % 0.16/0.42 (step @p295 :rule refl :args (tptp.true)) % 0.16/0.42 (step @p429 :rule cong :premises (@p295 @p428) :args (@t200)) % 0.16/0.42 (step @p430 :rule trans :premises (@p429 @p425)) % 0.16/0.42 (step @p431 :rule false_elim :premises (@p430)) % 0.16/0.42 (step-pop @p545 :rule scope :premises (@p431)) % 0.16/0.42 (step-pop @p546 :rule scope :premises (@p545)) % 0.16/0.42 (step-pop @p547 :rule scope :premises (@p546)) % 0.16/0.42 (step @p432 :rule process_scope :premises (@p547) :args (@t201)) % 0.16/0.42 (step @p436 :rule and_intro :premises (@p539 @p217 @p47)) % 0.16/0.42 (step @p437 :rule modus_ponens :premises (@p436 @p432)) % 0.16/0.42 (step @p438 :rule and_intro :premises (@p437 @p403)) % 0.16/0.42 (step-pop @p548 :rule scope :premises (@p438)) % 0.16/0.42 (step-pop @p549 :rule scope :premises (@p548)) % 0.16/0.42 (step-pop @p550 :rule scope :premises (@p549)) % 0.16/0.42 (step-pop @p551 :rule scope :premises (@p550)) % 0.16/0.42 (step @p439 :rule process_scope :premises (@p551) :args (@t203)) % 0.16/0.42 (step @p444 :rule implies_elim :premises (@p439)) % 0.16/0.42 (step @p445 :rule resolution :premises (@p444 @p415) :args (true @t203)) % 0.16/0.42 (step @p446 :rule not_and :premises (@p445)) % 0.16/0.42 (step @p447 :rule eq_resolve :premises (@p446 @p407)) % 0.16/0.42 (step @p448 :rule reordering :premises (@p447) :args ((or @t174 @t98 @t202 @t201))) % 0.16/0.42 (step @p449 false :rule chain_m_resolution :premises (@p448 @p403 @p399 @p217 @p47) :args (false (@list false false true false) (@list @t200 @t196 @t98 @t173))) % 0.16/0.42 ) % 0.16/0.42 % SZS output end Proof % 0.16/0.42 % cvc5 exiting %------------------------------------------------------------------------------