%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM552+1 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n003.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 08:39:49 AM UTC 2026 % Result : Theorem 42.63s 42.89s % Output : Proof 42.63s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : NUM552+1 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.18/0.35 % Computer : n003.cluster.edu % 0.18/0.35 % Model : x86_64 x86_64 % 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.35 % Memory : 8042.1875MB % 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.35 % CPULimit : 300 % 0.18/0.35 % WCLimit : 300 % 0.18/0.35 % DateTime : Tue Jun 2 11:28:59 EDT 2026 % 0.18/0.35 % CPUTime : % 0.33/0.52 %----Proving TF0_NAR, FOF, or CNF % 42.63/42.89 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 42.63/42.89 --- Run --no-e-matching --full-saturate-quant at 6... % 42.63/42.89 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 6... % 42.63/42.89 --- Run --finite-model-find --uf-ss=no-minimal at 6... % 42.63/42.89 --- Run --multi-trigger-when-single --full-saturate-quant at 30... % 42.63/42.89 % SZS status Theorem % 42.63/42.89 % SZS output start Proof % 42.63/42.89 ( % 42.63/42.89 (declare-sort $$unsorted 0) % 42.63/42.89 (declare-const tptp.xT $$unsorted) % 42.63/42.89 (declare-const tptp.xy $$unsorted) % 42.63/42.89 (declare-const tptp.slbdtsldtrb0 (-> $$unsorted $$unsorted $$unsorted)) % 42.63/42.89 (declare-const tptp.slbdtrb0 (-> $$unsorted $$unsorted)) % 42.63/42.89 (declare-const tptp.szmzazxdt0 (-> $$unsorted $$unsorted)) % 42.63/42.89 (declare-const tptp.szmzizndt0 (-> $$unsorted $$unsorted)) % 42.63/42.89 (declare-const tptp.sbrdtbr0 (-> $$unsorted $$unsorted)) % 42.63/42.89 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 42.63/42.89 (declare-const tptp.xQ $$unsorted) % 42.63/42.89 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 42.63/42.89 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 42.63/42.89 (declare-const tptp.xS $$unsorted) % 42.63/42.89 (declare-const tptp.isFinite0 (-> $$unsorted Bool)) % 42.63/42.89 (declare-const tptp.xx $$unsorted) % 42.63/42.89 (declare-const tptp.isCountable0 (-> $$unsorted Bool)) % 42.63/42.89 (declare-const tptp.slcrc0 $$unsorted) % 42.63/42.89 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 42.63/42.89 (declare-const tptp.aSubsetOf0 (-> $$unsorted $$unsorted Bool)) % 42.63/42.89 (declare-const tptp.sdtlseqdt0 (-> $$unsorted $$unsorted Bool)) % 42.63/42.89 (declare-const tptp.xk $$unsorted) % 42.63/42.89 (declare-const tptp.szszuzczcdt0 (-> $$unsorted $$unsorted)) % 42.63/42.89 (declare-const tptp.sdtmndt0 (-> $$unsorted $$unsorted $$unsorted)) % 42.63/42.89 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 42.63/42.89 (declare-const tptp.szNzAzT0 $$unsorted) % 42.63/42.89 (declare-const tptp.sz00 $$unsorted) % 42.63/42.89 (define @t1 () (@var "W0" $$unsorted)) % 42.63/42.89 (define @t2 () (tptp.aSet0 @t1)) % 42.63/42.89 (define @t3 () (@list @t1)) % 42.63/42.89 (define @t4 () (tptp.aElement0 @t1)) % 42.63/42.89 (define @t5 () (@var "W1" $$unsorted)) % 42.63/42.89 (define @t6 () (tptp.aElement0 @t5)) % 42.63/42.89 (define @t7 () (tptp.aElementOf0 @t5 @t1)) % 42.63/42.89 (define @t8 () (@list @t5)) % 42.63/42.89 (define @t9 () (tptp.isFinite0 @t1)) % 42.63/42.89 (define @t10 () (= @t1 tptp.slcrc0)) % 42.63/42.89 (define @t11 () (tptp.isCountable0 @t1)) % 42.63/42.89 (define @t12 () (not @t9)) % 42.63/42.89 (define @t13 () (and @t2 @t11)) % 42.63/42.89 (define @t14 () (not @t10)) % 42.63/42.89 (define @t15 () (@var "W2" $$unsorted)) % 42.63/42.89 (define @t16 () (tptp.aElementOf0 @t15 @t1)) % 42.63/42.89 (define @t17 () (tptp.aElementOf0 @t15 @t5)) % 42.63/42.89 (define @t18 () (@list @t15)) % 42.63/42.89 (define @t19 () (forall @t18 (=> @t17 @t16))) % 42.63/42.89 (define @t20 () (tptp.aSet0 @t5)) % 42.63/42.89 (define @t21 () (and @t20 @t19)) % 42.63/42.89 (define @t22 () (tptp.aSubsetOf0 @t5 @t1)) % 42.63/42.89 (define @t23 () (= @t22 @t21)) % 42.63/42.89 (define @t24 () (forall @t8 @t23)) % 42.63/42.89 (define @t25 () (=> @t2 @t24)) % 42.63/42.89 (define @t26 () (forall @t3 @t25)) % 42.63/42.89 (define @t27 () (tptp.isFinite0 @t5)) % 42.63/42.89 (define @t28 () (and @t2 @t9)) % 42.63/42.89 (define @t29 () (= @t1 @t5)) % 42.63/42.89 (define @t30 () (tptp.aSubsetOf0 @t1 @t5)) % 42.63/42.89 (define @t31 () (@list @t1 @t5)) % 42.63/42.89 (define @t32 () (tptp.aSet0 @t15)) % 42.63/42.89 (define @t33 () (@list @t1 @t5 @t15)) % 42.63/42.89 (define @t34 () (@var "W3" $$unsorted)) % 42.63/42.89 (define @t35 () (= @t34 @t5)) % 42.63/42.89 (define @t36 () (tptp.aElementOf0 @t34 @t1)) % 42.63/42.89 (define @t37 () (tptp.aElement0 @t34)) % 42.63/42.89 (define @t38 () (tptp.aElementOf0 @t34 @t15)) % 42.63/42.89 (define @t39 () (@list @t34)) % 42.63/42.89 (define @t40 () (tptp.sdtpldt0 @t1 @t5)) % 42.63/42.89 (define @t41 () (and @t2 @t6)) % 42.63/42.89 (define @t42 () (tptp.sdtmndt0 @t1 @t5)) % 42.63/42.89 (define @t43 () (tptp.sdtpldt0 @t5 @t1)) % 42.63/42.89 (define @t44 () (and @t20 (tptp.isCountable0 @t5))) % 42.63/42.89 (define @t45 () (tptp.sdtmndt0 @t5 @t1)) % 42.63/42.89 (define @t46 () (and @t20 @t27)) % 42.63/42.89 (define @t47 () (tptp.szszuzczcdt0 @t1)) % 42.63/42.89 (define @t48 () (tptp.aElementOf0 @t1 tptp.szNzAzT0)) % 42.63/42.89 (define @t49 () (tptp.szszuzczcdt0 @t5)) % 42.63/42.89 (define @t50 () (tptp.aElementOf0 @t5 tptp.szNzAzT0)) % 42.63/42.89 (define @t51 () (and @t48 @t50)) % 42.63/42.89 (define @t52 () (tptp.sdtlseqdt0 @t1 @t5)) % 42.63/42.89 (define @t53 () (tptp.sdtlseqdt0 @t5 @t15)) % 42.63/42.89 (define @t54 () (tptp.aElementOf0 @t15 tptp.szNzAzT0)) % 42.63/42.89 (define @t55 () (tptp.sbrdtbr0 @t1)) % 42.63/42.89 (define @t56 () (and @t2 @t50)) % 42.63/42.89 (define @t57 () (tptp.szmzizndt0 @t1)) % 42.63/42.89 (define @t58 () (tptp.aSubsetOf0 @t1 tptp.szNzAzT0)) % 42.63/42.89 (define @t59 () (tptp.szmzizndt0 @t5)) % 42.63/42.89 (define @t60 () (tptp.slbdtrb0 @t1)) % 42.63/42.89 (define @t61 () (tptp.slbdtrb0 @t5)) % 42.63/42.89 (define @t62 () (tptp.sbrdtbr0 @t34)) % 42.63/42.89 (define @t63 () (tptp.aSubsetOf0 @t34 @t1)) % 42.63/42.89 (define @t64 () (and @t63 (= @t62 @t5))) % 42.63/42.89 (define @t65 () (= @t38 @t64)) % 42.63/42.89 (define @t66 () (forall @t39 @t65)) % 42.63/42.89 (define @t67 () (and @t32 @t66)) % 42.63/42.89 (define @t68 () (tptp.slbdtsldtrb0 @t1 @t5)) % 42.63/42.89 (define @t69 () (= @t15 @t68)) % 42.63/42.89 (define @t70 () (= @t69 @t67)) % 42.63/42.89 (define @t71 () (forall @t18 @t70)) % 42.63/42.89 (define @t72 () (=> @t56 @t71)) % 42.63/42.89 (define @t73 () (forall @t31 @t72)) % 42.63/42.89 (define @t74 () (tptp.aElementOf0 tptp.xk tptp.szNzAzT0)) % 42.63/42.89 (define @t75 () (tptp.aSet0 tptp.xT)) % 42.63/42.89 (define @t76 () (tptp.slbdtsldtrb0 tptp.xS tptp.xk)) % 42.63/42.89 (define @t77 () (tptp.slbdtsldtrb0 tptp.xT tptp.xk)) % 42.63/42.89 (define @t78 () (tptp.aSubsetOf0 @t76 @t77)) % 42.63/42.89 (define @t79 () (tptp.aElementOf0 tptp.xQ @t76)) % 42.63/42.89 (define @t80 () (tptp.sbrdtbr0 tptp.xQ)) % 42.63/42.89 (define @t81 () (tptp.aSet0 tptp.xQ)) % 42.63/42.89 (define @t82 () (tptp.aElementOf0 tptp.xx tptp.xT)) % 42.63/42.89 (define @t83 () (tptp.aElementOf0 tptp.xx tptp.xQ)) % 42.63/42.89 (define @t84 () (@var "BOUND_VARIABLE_7899" $$unsorted)) % 42.63/42.89 (define @t85 () (= (tptp.aSubsetOf0 @t84 @t1) (and (tptp.aSet0 @t84) (forall @t18 (or (not (tptp.aElementOf0 @t15 @t84)) @t16))))) % 42.63/42.89 (define @t86 () (not @t2)) % 42.63/42.89 (define @t87 () (or @t86 @t85)) % 42.63/42.89 (define @t88 () (@list @t84)) % 42.63/42.89 (define @t89 () (forall @t88 @t87)) % 42.63/42.89 (define @t90 () (forall @t88 @t85)) % 42.63/42.89 (define @t91 () (or @t86 @t90)) % 42.63/42.89 (define @t92 () (forall @t8 (= @t22 (and @t20 (forall @t18 (or (not @t17) @t16)))))) % 42.63/42.89 (define @t93 () (forall @t18 (or (not (tptp.aElementOf0 @t15 tptp.xQ)) (tptp.aElementOf0 @t15 tptp.xT)))) % 42.63/42.89 (define @t94 () (and @t81 @t93)) % 42.63/42.89 (define @t95 () (tptp.aSubsetOf0 tptp.xQ tptp.xT)) % 42.63/42.89 (define @t96 () (= @t95 @t94)) % 42.63/42.89 (define @t97 () (not @t75)) % 42.63/42.89 (define @t98 () (or @t97 @t96)) % 42.63/42.89 (define @t99 () (@list false false)) % 42.63/42.89 (define @t100 () (@var "BOUND_VARIABLE_8475" $$unsorted)) % 42.63/42.89 (define @t101 () (tptp.aElementOf0 @t34 @t100)) % 42.63/42.89 (define @t102 () (and @t63 (= @t5 @t62))) % 42.63/42.89 (define @t103 () (forall @t39 (= @t101 @t102))) % 42.63/42.89 (define @t104 () (tptp.aSet0 @t100)) % 42.63/42.89 (define @t105 () (and @t104 @t103)) % 42.63/42.89 (define @t106 () (= (= @t100 @t68) @t105)) % 42.63/42.89 (define @t107 () (not @t50)) % 42.63/42.89 (define @t108 () (or @t86 @t107 @t106)) % 42.63/42.89 (define @t109 () (@list @t1 @t5 @t100)) % 42.63/42.89 (define @t110 () (forall @t109 @t108)) % 42.63/42.89 (define @t111 () (@list @t100)) % 42.63/42.89 (define @t112 () (forall @t111 @t108)) % 42.63/42.89 (define @t113 () (forall @t111 @t106)) % 42.63/42.89 (define @t114 () (or @t86 @t107 @t113)) % 42.63/42.89 (define @t115 () (forall @t18 (= @t69 (and @t32 (forall @t39 (= @t38 @t102)))))) % 42.63/42.89 (define @t116 () (or @t86 @t107 @t115)) % 42.63/42.89 (define @t117 () (tptp.aSubsetOf0 @t34 tptp.xT)) % 42.63/42.89 (define @t118 () (and @t117 (= @t62 @t80))) % 42.63/42.89 (define @t119 () (tptp.slbdtsldtrb0 tptp.xT @t80)) % 42.63/42.89 (define @t120 () (tptp.aElementOf0 @t34 @t119)) % 42.63/42.89 (define @t121 () (forall @t39 (= @t120 @t118))) % 42.63/42.89 (define @t122 () (tptp.aSet0 @t119)) % 42.63/42.89 (define @t123 () (and @t122 @t121)) % 42.63/42.89 (define @t124 () (and @t117 (= @t80 @t62))) % 42.63/42.89 (define @t125 () (= @t124 @t120)) % 42.63/42.89 (define @t126 () (forall @t39 @t125)) % 42.63/42.89 (define @t127 () (and @t122 @t126)) % 42.63/42.89 (define @t128 () (= (= @t119 @t119) @t127)) % 42.63/42.89 (define @t129 () (tptp.aElementOf0 @t80 tptp.szNzAzT0)) % 42.63/42.89 (define @t130 () (not @t129)) % 42.63/42.89 (define @t131 () (or @t97 @t130 @t128)) % 42.63/42.89 (define @t132 () (forall @t109 (or @t86 @t107 (= (= @t68 @t100) (and @t104 (forall @t39 (= @t102 @t101))))))) % 42.63/42.89 (define @t133 () (or @t97 @t130 @t123)) % 42.63/42.89 (define @t134 () (@list false)) % 42.63/42.89 (define @t135 () (not @t123)) % 42.63/42.89 (define @t136 () (@list @t123)) % 42.63/42.89 (define @t137 () (and @t95 (= @t80 @t80))) % 42.63/42.89 (define @t138 () (tptp.aElementOf0 tptp.xQ @t119)) % 42.63/42.89 (define @t139 () (= @t138 @t137)) % 42.63/42.89 (define @t140 () (@list tptp.xQ)) % 42.63/42.89 (define @t141 () (= @t138 @t95)) % 42.63/42.89 (define @t142 () (tptp.slbdtsldtrb0 tptp.xS @t80)) % 42.63/42.89 (define @t143 () (forall @t18 (or (not (tptp.aElementOf0 @t15 @t142)) (tptp.aElementOf0 @t15 @t119)))) % 42.63/42.89 (define @t144 () (and (tptp.aSet0 @t142) @t143)) % 42.63/42.89 (define @t145 () (tptp.aSubsetOf0 @t142 @t119)) % 42.63/42.89 (define @t146 () (= @t145 @t144)) % 42.63/42.89 (define @t147 () (not @t122)) % 42.63/42.89 (define @t148 () (or @t147 @t146)) % 42.63/42.89 (define @t149 () (tptp.aElementOf0 tptp.xQ @t142)) % 42.63/42.89 (define @t150 () (not @t149)) % 42.63/42.89 (define @t151 () (or @t150 @t138)) % 42.63/42.89 (define @t152 () (not @t83)) % 42.63/42.89 (define @t153 () (or @t152 @t82)) % 42.63/42.89 (define @t154 () (not @t153)) % 42.63/42.89 (define @t155 () (@list true false)) % 42.63/42.89 (assume @p1 (forall @t3 (=> @t2 true))) % 42.63/42.89 (assume @p2 (forall @t3 (=> @t4 true))) % 42.63/42.89 (assume @p3 (forall @t3 (=> @t2 (forall @t8 (=> @t7 @t6))))) % 42.63/42.89 (assume @p4 (forall @t3 (=> @t2 (=> @t9 true)))) % 42.63/42.89 (assume @p5 (forall @t3 (= @t10 (and @t2 (not (exists @t8 @t7)))))) % 42.63/42.89 (assume @p6 (tptp.isFinite0 tptp.slcrc0)) % 42.63/42.89 (assume @p7 (forall @t3 (=> @t2 (=> @t11 true)))) % 42.63/42.89 (assume @p8 (forall @t3 (=> @t13 @t12))) % 42.63/42.89 (assume @p9 (forall @t3 (=> @t13 @t14))) % 42.63/42.89 (assume @p10 @t26) % 42.63/42.89 (assume @p11 (forall @t3 (=> @t28 (forall @t8 (=> @t22 @t27))))) % 42.63/42.89 (assume @p12 (forall @t3 (=> @t2 (tptp.aSubsetOf0 @t1 @t1)))) % 42.63/42.89 (assume @p13 (forall @t31 (=> (and @t2 @t20) (=> (and @t30 @t22) @t29)))) % 42.63/42.89 (assume @p14 (forall @t33 (=> (and @t2 @t20 @t32) (=> (and @t30 (tptp.aSubsetOf0 @t5 @t15)) (tptp.aSubsetOf0 @t1 @t15))))) % 42.63/42.89 (assume @p15 (forall @t31 (=> @t41 (forall @t18 (= (= @t15 @t40) (and @t32 (forall @t39 (= @t38 (and @t37 (or @t36 @t35)))))))))) % 42.63/42.89 (assume @p16 (forall @t31 (=> @t41 (forall @t18 (= (= @t15 @t42) (and @t32 (forall @t39 (= @t38 (and @t37 @t36 (not @t35)))))))))) % 42.63/42.89 (assume @p17 (forall @t3 (=> @t2 (forall @t8 (=> @t7 (= (tptp.sdtpldt0 @t42 @t5) @t1)))))) % 42.63/42.89 (assume @p18 (forall @t31 (=> (and @t4 @t20) (=> (not (tptp.aElementOf0 @t1 @t5)) (= (tptp.sdtmndt0 @t43 @t1) @t5))))) % 42.63/42.89 (assume @p19 (forall @t3 (=> @t4 (forall @t8 (=> @t44 (tptp.isCountable0 @t43)))))) % 42.63/42.89 (assume @p20 (forall @t3 (=> @t4 (forall @t8 (=> @t44 (tptp.isCountable0 @t45)))))) % 42.63/42.89 (assume @p21 (forall @t3 (=> @t4 (forall @t8 (=> @t46 (tptp.isFinite0 @t43)))))) % 42.63/42.89 (assume @p22 (forall @t3 (=> @t4 (forall @t8 (=> @t46 (tptp.isFinite0 @t45)))))) % 42.63/42.89 (assume @p23 (and (tptp.aSet0 tptp.szNzAzT0) (tptp.isCountable0 tptp.szNzAzT0))) % 42.63/42.89 (assume @p24 (tptp.aElementOf0 tptp.sz00 tptp.szNzAzT0)) % 42.63/42.89 (assume @p25 (forall @t3 (=> @t48 (and (tptp.aElementOf0 @t47 tptp.szNzAzT0) (not (= @t47 tptp.sz00)))))) % 42.63/42.89 (assume @p26 (forall @t31 (=> @t51 (=> (= @t47 @t49) @t29)))) % 42.63/42.89 (assume @p27 (forall @t3 (=> @t48 (or (= @t1 tptp.sz00) (exists @t8 (and @t50 (= @t1 @t49))))))) % 42.63/42.89 (assume @p28 (forall @t3 (=> @t48 (not (= @t1 @t47))))) % 42.63/42.89 (assume @p29 (forall @t31 (=> @t51 (=> @t52 true)))) % 42.63/42.89 (assume @p30 (forall @t3 (=> @t48 (tptp.sdtlseqdt0 tptp.sz00 @t1)))) % 42.63/42.89 (assume @p31 (forall @t3 (=> @t48 (not (tptp.sdtlseqdt0 @t47 tptp.sz00))))) % 42.63/42.89 (assume @p32 (forall @t31 (=> @t51 (= @t52 (tptp.sdtlseqdt0 @t47 @t49))))) % 42.63/42.89 (assume @p33 (forall @t3 (=> @t48 (tptp.sdtlseqdt0 @t1 @t47)))) % 42.63/42.89 (assume @p34 (forall @t3 (=> @t48 (tptp.sdtlseqdt0 @t1 @t1)))) % 42.63/42.89 (assume @p35 (forall @t31 (=> @t51 (=> (and @t52 (tptp.sdtlseqdt0 @t5 @t1)) @t29)))) % 42.63/42.89 (assume @p36 (forall @t33 (=> (and @t48 @t50 @t54) (=> (and @t52 @t53) (tptp.sdtlseqdt0 @t1 @t15))))) % 42.63/42.89 (assume @p37 (forall @t31 (=> @t51 (or @t52 (tptp.sdtlseqdt0 @t49 @t1))))) % 42.63/42.89 (assume @p38 (forall @t31 (=> @t51 (=> (tptp.iLess0 @t1 @t5) true)))) % 42.63/42.89 (assume @p39 (forall @t3 (=> @t48 (tptp.iLess0 @t1 @t47)))) % 42.63/42.89 (assume @p40 (forall @t3 (=> @t2 (tptp.aElement0 @t55)))) % 42.63/42.89 (assume @p41 (forall @t3 (=> @t2 (= (tptp.aElementOf0 @t55 tptp.szNzAzT0) @t9)))) % 42.63/42.89 (assume @p42 (forall @t3 (=> @t2 (= (= @t55 tptp.sz00) @t10)))) % 42.63/42.89 (assume @p43 (forall @t3 (=> @t28 (forall @t8 (=> @t6 (=> (not @t7) (= (tptp.sbrdtbr0 @t40) (tptp.szszuzczcdt0 @t55)))))))) % 42.63/42.89 (assume @p44 (forall @t3 (=> @t2 (forall @t8 (=> (and @t9 @t7) (= (tptp.szszuzczcdt0 (tptp.sbrdtbr0 @t42)) @t55)))))) % 42.63/42.89 (assume @p45 (forall @t3 (=> @t2 (forall @t8 (=> (and @t9 @t22) (tptp.sdtlseqdt0 (tptp.sbrdtbr0 @t5) @t55)))))) % 42.63/42.89 (assume @p46 (forall @t31 (=> @t56 (=> (and @t9 (tptp.sdtlseqdt0 @t5 @t55)) (exists @t18 (and (tptp.aSubsetOf0 @t15 @t1) (= (tptp.sbrdtbr0 @t15) @t5))))))) % 42.63/42.89 (assume @p47 (forall @t3 (=> (and @t58 @t14) (forall @t8 (= (= @t5 @t57) (and @t7 (forall @t18 (=> @t16 @t53)))))))) % 42.63/42.89 (assume @p48 (forall @t3 (=> (and @t58 @t9 @t14) (forall @t8 (= (= @t5 (tptp.szmzazxdt0 @t1)) (and @t7 (forall @t18 (=> @t16 (tptp.sdtlseqdt0 @t15 @t5))))))))) % 42.63/42.89 (assume @p49 (forall @t31 (=> (and @t58 (tptp.aSubsetOf0 @t5 tptp.szNzAzT0) @t14 (not (= @t5 tptp.slcrc0))) (=> (and (tptp.aElementOf0 @t57 @t5) (tptp.aElementOf0 @t59 @t1)) (= @t57 @t59))))) % 42.63/42.89 (assume @p50 (forall @t3 (=> @t48 (forall @t8 (= (= @t5 @t60) (and @t20 (forall @t18 (= @t17 (and @t54 (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 @t15) @t1)))))))))) % 42.63/42.89 (assume @p51 (forall @t3 (=> @t48 (tptp.isFinite0 @t60)))) % 42.63/42.89 (assume @p52 (= (tptp.slbdtrb0 tptp.sz00) tptp.slcrc0)) % 42.63/42.89 (assume @p53 (forall @t31 (=> @t51 (= (tptp.aElementOf0 @t1 (tptp.slbdtrb0 @t49)) (or (tptp.aElementOf0 @t1 @t61) @t29))))) % 42.63/42.89 (assume @p54 (forall @t31 (=> @t51 (= @t52 (tptp.aSubsetOf0 @t60 @t61))))) % 42.63/42.89 (assume @p55 (forall @t3 (=> (and @t58 @t9) (exists @t8 (and @t50 (tptp.aSubsetOf0 @t1 @t61)))))) % 42.63/42.89 (assume @p56 (forall @t3 (=> @t48 (= (tptp.sbrdtbr0 @t60) @t1)))) % 42.63/42.89 (assume @p57 @t73) % 42.63/42.89 (assume @p58 (forall @t3 (=> @t28 (forall @t8 (=> @t50 (tptp.isFinite0 @t68)))))) % 42.63/42.89 (assume @p59 (forall @t3 (=> (and @t2 @t12) (forall @t8 (=> @t50 (not (= @t68 tptp.slcrc0))))))) % 42.63/42.89 (assume @p60 (forall @t3 (=> @t13 (forall @t8 (=> (and @t50 (not (= @t5 tptp.sz00))) (tptp.isCountable0 @t68)))))) % 42.63/42.89 (assume @p61 @t74) % 42.63/42.89 (assume @p62 (and (tptp.aSet0 tptp.xS) @t75 (not (= tptp.xk tptp.sz00)))) % 42.63/42.89 (assume @p63 (and @t78 (not (= @t76 tptp.slcrc0)))) % 42.63/42.89 (assume @p64 (tptp.aElementOf0 tptp.xx tptp.xS)) % 42.63/42.89 (assume @p65 @t79) % 42.63/42.89 (assume @p66 (and @t81 (tptp.isFinite0 tptp.xQ) (= @t80 tptp.xk))) % 42.63/42.89 (assume @p67 (and (tptp.aElement0 tptp.xy) (tptp.aElementOf0 tptp.xy tptp.xQ))) % 42.63/42.89 (assume @p68 (not (=> @t83 @t82))) % 42.63/42.89 (assume @p69 true) % 42.63/42.89 (step @p70 :rule quant-merge-prenex :args ((= (forall @t3 @t89) (forall (@list @t1 @t84) @t87)))) % 42.63/42.89 (step @p71 :rule alpha_equiv :args (@t90 (@list @t84) (@list @t5))) % 42.63/42.89 (step @p72 :rule refl :args (@t86)) % 42.63/42.89 (step @p73 :rule nary_cong :premises (@p72 @p71) :args (@t91)) % 42.63/42.89 (step @p74 :rule quant-miniscope-or :args ((= @t89 @t91))) % 42.63/42.89 (step @p75 :rule trans :premises (@p74 @p73)) % 42.63/42.89 (step @p76 :rule symm :premises (@p75)) % 42.63/42.89 (step @p77 :rule cong :premises (@p76) :args ((forall @t3 (or @t86 @t92)))) % 42.63/42.89 (step @p78 :rule trans :premises (@p77 @p70)) % 42.63/42.89 (step @p79 :rule bool-impl-elim :args (@t2 @t92)) % 42.63/42.89 (step @p80 :rule cong :premises (@p79) :args ((forall @t3 (=> @t2 @t92)))) % 42.63/42.89 (step @p81 :rule trans :premises (@p80 @p78)) % 42.63/42.89 (step @p82 :rule bool-impl-elim :args (@t17 @t16)) % 42.63/42.89 (step @p83 :rule cong :premises (@p82) :args (@t19)) % 42.63/42.89 (step @p84 :rule refl :args (@t20)) % 42.63/42.89 (step @p85 :rule nary_cong :premises (@p84 @p83) :args (@t21)) % 42.63/42.89 (step @p86 :rule refl :args (@t22)) % 42.63/42.89 (step @p87 :rule cong :premises (@p86 @p85) :args (@t23)) % 42.63/42.89 (step @p88 :rule cong :premises (@p87) :args (@t24)) % 42.63/42.89 (step @p89 :rule refl :args (@t2)) % 42.63/42.89 (step @p90 :rule cong :premises (@p89 @p88) :args (@t25)) % 42.63/42.89 (step @p91 :rule cong :premises (@p90) :args (@t26)) % 42.63/42.89 (step @p92 :rule trans :premises (@p91 @p81)) % 42.63/42.89 (step @p93 :rule eq_resolve :premises (@p10 @p92)) % 42.63/42.89 (step @p94 :rule instantiate :premises (@p93) :args ((@list tptp.xT tptp.xQ))) % 42.63/42.89 (step @p95 :rule and_elim :premises (@p62) :args (1)) % 42.63/42.89 (step @p96 :rule cnf_or_pos :args (@t98)) % 42.63/42.89 (step @p97 :rule reordering :premises (@p96) :args ((or @t97 @t96 (not @t98)))) % 42.63/42.89 (step @p98 :rule chain_m_resolution :premises (@p97 @p95 @p94) :args (@t96 @t99 (@list @t75 @t98))) % 42.63/42.89 (step @p99 :rule eq-symm :args (@t101 @t102)) % 42.63/42.89 (step @p100 :rule cong :premises (@p99) :args (@t103)) % 42.63/42.89 (step @p101 :rule refl :args (@t104)) % 42.63/42.89 (step @p102 :rule nary_cong :premises (@p101 @p100) :args (@t105)) % 42.63/42.89 (step @p103 :rule eq-symm :args (@t100 @t68)) % 42.63/42.89 (step @p104 :rule cong :premises (@p103 @p102) :args (@t106)) % 42.63/42.89 (step @p105 :rule refl :args (@t107)) % 42.63/42.89 (step @p106 :rule refl :args (@t86)) % 42.63/42.89 (step @p107 :rule nary_cong :premises (@p106 @p105 @p104) :args (@t108)) % 42.63/42.89 (step @p108 :rule cong :premises (@p107) :args (@t110)) % 42.63/42.89 (step @p109 :rule quant-merge-prenex :args ((= (forall @t31 @t112) @t110))) % 42.63/42.89 (step @p110 :rule alpha_equiv :args (@t113 (@list @t100) (@list @t15))) % 42.63/42.89 (step @p111 :rule refl :args (@t107)) % 42.63/42.89 (step @p112 :rule nary_cong :premises (@p72 @p111 @p110) :args (@t114)) % 42.63/42.89 (step @p113 :rule quant-miniscope-or :args ((= @t112 @t114))) % 42.63/42.89 (step @p114 :rule trans :premises (@p113 @p112)) % 42.63/42.89 (step @p115 :rule symm :premises (@p114)) % 42.63/42.89 (step @p116 :rule cong :premises (@p115) :args ((forall @t31 @t116))) % 42.63/42.89 (step @p117 :rule trans :premises (@p116 @p109)) % 42.63/42.89 (step @p118 :rule trans :premises (@p117 @p108)) % 42.63/42.89 (step @p119 :rule aci_norm :args ((= (or (or @t86 @t107) @t115) @t116))) % 42.63/42.89 (step @p120 :rule refl :args (@t115)) % 42.63/42.89 (step @p121 :rule bool-and-de-morgan :args (@t2 @t50 true)) % 42.63/42.89 (step @p122 :rule nary_cong :premises (@p121 @p120) :args ((or (not @t56) @t115))) % 42.63/42.89 (step @p123 :rule trans :premises (@p122 @p119)) % 42.63/42.89 (step @p124 :rule bool-impl-elim :args (@t56 @t115)) % 42.63/42.89 (step @p125 :rule trans :premises (@p124 @p123)) % 42.63/42.89 (step @p126 :rule cong :premises (@p125) :args ((forall @t31 (=> @t56 @t115)))) % 42.63/42.89 (step @p127 :rule trans :premises (@p126 @p118)) % 42.63/42.89 (step @p128 :rule eq-symm :args (@t62 @t5)) % 42.63/42.89 (step @p129 :rule refl :args (@t63)) % 42.63/42.89 (step @p130 :rule nary_cong :premises (@p129 @p128) :args (@t64)) % 42.63/42.89 (step @p131 :rule refl :args (@t38)) % 42.63/42.89 (step @p132 :rule cong :premises (@p131 @p130) :args (@t65)) % 42.63/42.89 (step @p133 :rule cong :premises (@p132) :args (@t66)) % 42.63/42.89 (step @p134 :rule refl :args (@t32)) % 42.63/42.89 (step @p135 :rule nary_cong :premises (@p134 @p133) :args (@t67)) % 42.63/42.89 (step @p136 :rule refl :args (@t69)) % 42.63/42.89 (step @p137 :rule cong :premises (@p136 @p135) :args (@t70)) % 42.63/42.89 (step @p138 :rule cong :premises (@p137) :args (@t71)) % 42.63/42.89 (step @p139 :rule refl :args (@t56)) % 42.63/42.89 (step @p140 :rule cong :premises (@p139 @p138) :args (@t72)) % 42.63/42.89 (step @p141 :rule cong :premises (@p140) :args (@t73)) % 42.63/42.89 (step @p142 :rule trans :premises (@p141 @p127)) % 42.63/42.89 (step @p143 :rule eq_resolve :premises (@p57 @p142)) % 42.63/42.89 (step @p144 :rule bool-eq-true :args (@t123)) % 42.63/42.89 (step @p145 :rule eq-symm :args (true @t123)) % 42.63/42.89 (step @p146 :rule trans :premises (@p145 @p144)) % 42.63/42.89 (step @p147 :rule eq-symm :args (@t118 @t120)) % 42.63/42.89 (step @p148 :rule refl :args (@t120)) % 42.63/42.89 (step @p149 :rule eq-symm :args (@t80 @t62)) % 42.63/42.89 (step @p150 :rule refl :args (@t117)) % 42.63/42.89 (step @p151 :rule nary_cong :premises (@p150 @p149) :args (@t124)) % 42.63/42.89 (step @p152 :rule cong :premises (@p151 @p148) :args (@t125)) % 42.63/42.89 (step @p153 :rule trans :premises (@p152 @p147)) % 42.63/42.89 (step @p154 :rule cong :premises (@p153) :args (@t126)) % 42.63/42.89 (step @p155 :rule refl :args (@t122)) % 42.63/42.89 (step @p156 :rule nary_cong :premises (@p155 @p154) :args (@t127)) % 42.63/42.89 (step @p157 :rule eq-refl :args (@t119)) % 42.63/42.89 (step @p158 :rule cong :premises (@p157 @p156) :args (@t128)) % 42.63/42.89 (step @p159 :rule trans :premises (@p158 @p146)) % 42.63/42.89 (step @p160 :rule refl :args (@t130)) % 42.63/42.89 (step @p161 :rule refl :args (@t97)) % 42.63/42.89 (step @p162 :rule nary_cong :premises (@p161 @p160 @p159) :args (@t131)) % 42.63/42.89 (step @p163 :rule refl :args (@t132)) % 42.63/42.89 (step @p164 :rule cong :premises (@p163 @p162) :args ((=> @t132 @t131))) % 42.63/42.89 (assume-push @p246 @t132) % 42.63/42.89 (step @p166 :rule instantiate :premises (@p143) :args ((@list tptp.xT @t80 @t119))) % 42.63/42.89 (step-pop @p247 :rule scope :premises (@p166)) % 42.63/42.89 (step @p167 :rule process_scope :premises (@p247) :args (@t131)) % 42.63/42.89 (step @p169 :rule eq_resolve :premises (@p167 @p164)) % 42.63/42.89 (step @p170 :rule implies_elim :premises (@p169)) % 42.63/42.89 (step @p171 :rule chain_m_resolution :premises (@p170 @p143) :args (@t133 @t134 (@list @t132))) % 42.63/42.89 (step @p172 :rule refl :args (tptp.szNzAzT0)) % 42.63/42.89 (step @p173 :rule and_elim :premises (@p66) :args (2)) % 42.63/42.89 (step @p174 :rule symm :premises (@p173)) % 42.63/42.89 (step @p175 :rule cong :premises (@p174 @p172) :args (@t74)) % 42.63/42.89 (step @p176 :rule eq_resolve :premises (@p61 @p175)) % 42.63/42.89 (step @p177 :rule cnf_or_pos :args (@t133)) % 42.63/42.89 (step @p178 :rule reordering :premises (@p177) :args ((or @t130 @t97 @t123 (not @t133)))) % 42.63/42.89 (step @p179 :rule chain_m_resolution :premises (@p178 @p176 @p95 @p171) :args (@t123 (@list false false false) (@list @t129 @t75 @t133))) % 42.63/42.89 (step @p180 :rule cnf_and_pos :args (@t123 1)) % 42.63/42.89 (step @p181 :rule reordering :premises (@p180) :args ((or @t121 @t135))) % 42.63/42.89 (step @p182 :rule chain_m_resolution :premises (@p181 @p179) :args (@t121 @t134 @t136)) % 42.63/42.89 (step @p183 :rule aci_norm :args ((= (and @t95 true) @t95))) % 42.63/42.89 (step @p184 :rule eq-refl :args (@t80)) % 42.63/42.89 (step @p185 :rule refl :args (@t95)) % 42.63/42.89 (step @p186 :rule nary_cong :premises (@p185 @p184) :args (@t137)) % 42.63/42.89 (step @p187 :rule trans :premises (@p186 @p183)) % 42.63/42.89 (step @p188 :rule refl :args (@t138)) % 42.63/42.89 (step @p189 :rule cong :premises (@p188 @p187) :args (@t139)) % 42.63/42.89 (step @p190 :rule refl :args (@t121)) % 42.63/42.89 (step @p191 :rule cong :premises (@p190 @p189) :args ((=> @t121 @t139))) % 42.63/42.89 (assume-push @p248 @t121) % 42.63/42.89 (step @p193 :rule instantiate :premises (@p182) :args (@t140)) % 42.63/42.89 (step-pop @p249 :rule scope :premises (@p193)) % 42.63/42.89 (step @p194 :rule process_scope :premises (@p249) :args (@t139)) % 42.63/42.89 (step @p196 :rule eq_resolve :premises (@p194 @p191)) % 42.63/42.89 (step @p197 :rule implies_elim :premises (@p196)) % 42.63/42.89 (step @p198 :rule chain_m_resolution :premises (@p197 @p182) :args (@t141 @t134 (@list @t121))) % 42.63/42.89 (step @p199 :rule instantiate :premises (@p93) :args ((@list @t119 @t142))) % 42.63/42.89 (step @p200 :rule cnf_and_pos :args (@t123 0)) % 42.63/42.89 (step @p201 :rule reordering :premises (@p200) :args ((or @t122 @t135))) % 42.63/42.89 (step @p202 :rule chain_m_resolution :premises (@p201 @p179) :args (@t122 @t134 @t136)) % 42.63/42.89 (step @p203 :rule cnf_or_pos :args (@t148)) % 42.63/42.89 (step @p204 :rule reordering :premises (@p203) :args ((or @t147 @t146 (not @t148)))) % 42.63/42.89 (step @p205 :rule chain_m_resolution :premises (@p204 @p202 @p199) :args (@t146 @t99 (@list @t122 @t148))) % 42.63/42.89 (step @p206 :rule refl :args (tptp.xT)) % 42.63/42.89 (step @p207 :rule cong :premises (@p206 @p174) :args (@t77)) % 42.63/42.89 (step @p208 :rule refl :args (tptp.xS)) % 42.63/42.89 (step @p209 :rule cong :premises (@p208 @p174) :args (@t76)) % 42.63/42.89 (step @p210 :rule cong :premises (@p209 @p207) :args (@t78)) % 42.63/42.89 (step @p211 :rule and_elim :premises (@p63) :args (0)) % 42.63/42.89 (step @p212 :rule eq_resolve :premises (@p211 @p210)) % 42.63/42.89 (step @p213 :rule cnf_equiv_pos1 :args (@t146)) % 42.63/42.89 (step @p214 :rule reordering :premises (@p213) :args ((or (not @t145) @t144 (not @t146)))) % 42.63/42.89 (step @p215 :rule chain_m_resolution :premises (@p214 @p212 @p205) :args (@t144 @t99 (@list @t145 @t146))) % 42.63/42.89 (step @p216 :rule cnf_and_pos :args (@t144 1)) % 42.63/42.89 (step @p217 :rule reordering :premises (@p216) :args ((or @t143 (not @t144)))) % 42.63/42.89 (step @p218 :rule chain_m_resolution :premises (@p217 @p215) :args (@t143 @t134 (@list @t144))) % 42.63/42.89 (step @p219 :rule instantiate :premises (@p218) :args (@t140)) % 42.63/42.89 (step @p220 :rule refl :args (tptp.xQ)) % 42.63/42.89 (step @p221 :rule cong :premises (@p220 @p209) :args (@t79)) % 42.63/42.89 (step @p222 :rule eq_resolve :premises (@p65 @p221)) % 42.63/42.89 (step @p223 :rule cnf_or_pos :args (@t151)) % 42.63/42.89 (step @p224 :rule reordering :premises (@p223) :args ((or @t150 @t138 (not @t151)))) % 42.63/42.89 (step @p225 :rule chain_m_resolution :premises (@p224 @p222 @p219) :args (@t138 @t99 (@list @t149 @t151))) % 42.63/42.89 (step @p226 :rule cnf_equiv_pos1 :args (@t141)) % 42.63/42.89 (step @p227 :rule reordering :premises (@p226) :args ((or @t95 (not @t138) (not @t141)))) % 42.63/42.89 (step @p228 :rule chain_m_resolution :premises (@p227 @p225 @p198) :args (@t95 @t99 (@list @t138 @t141))) % 42.63/42.89 (step @p229 :rule cnf_equiv_pos1 :args (@t96)) % 42.63/42.89 (step @p230 :rule reordering :premises (@p229) :args ((or (not @t95) @t94 (not @t96)))) % 42.63/42.89 (step @p231 :rule chain_m_resolution :premises (@p230 @p228 @p98) :args (@t94 @t99 (@list @t95 @t96))) % 42.63/42.89 (step @p232 :rule cnf_and_pos :args (@t94 1)) % 42.63/42.89 (step @p233 :rule reordering :premises (@p232) :args ((or @t93 (not @t94)))) % 42.63/42.89 (step @p234 :rule chain_m_resolution :premises (@p233 @p231) :args (@t93 @t134 (@list @t94))) % 42.63/42.89 (step @p235 :rule not_implies_elim1 :premises (@p68)) % 42.63/42.89 (step @p236 :rule not_implies_elim2 :premises (@p68)) % 42.63/42.89 (step @p237 :rule cnf_or_pos :args (@t153)) % 42.63/42.89 (step @p238 :rule reordering :premises (@p237) :args ((or @t82 @t152 @t154))) % 42.63/42.89 (step @p239 :rule chain_m_resolution :premises (@p238 @p236 @p235) :args (@t154 @t155 (@list @t82 @t83))) % 42.63/42.89 (assume-push @p250 @t93) % 42.63/42.89 (step @p241 :rule instantiate :premises (@p234) :args ((@list tptp.xx))) % 42.63/42.89 (step-pop @p251 :rule scope :premises (@p241)) % 42.63/42.89 (step @p242 :rule process_scope :premises (@p251) :args (@t153)) % 42.63/42.89 (step @p244 :rule implies_elim :premises (@p242)) % 42.63/42.89 (step @p245 false :rule chain_m_resolution :premises (@p244 @p239 @p234) :args (false @t155 (@list @t153 @t93))) % 42.63/42.89 ) % 42.63/42.89 % SZS output end Proof % 42.63/42.89 % cvc5 exiting %------------------------------------------------------------------------------