%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM561+1 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n019.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 08:39:50 AM UTC 2026 % Result : Theorem 16.23s 16.43s % Output : Proof 16.23s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM561+1 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n019.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 11:29:34 EDT 2026 % 0.16/0.34 % CPUTime : % 0.30/0.50 %----Proving TF0_NAR, FOF, or CNF % 16.23/16.43 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 16.23/16.43 --- Run --no-e-matching --full-saturate-quant at 6... % 16.23/16.43 % SZS status Theorem % 16.23/16.43 % SZS output start Proof % 16.23/16.43 ( % 16.23/16.43 (declare-sort $$unsorted 0) % 16.23/16.43 (declare-const tptp.xx $$unsorted) % 16.23/16.43 (declare-const tptp.xF $$unsorted) % 16.23/16.43 (declare-const tptp.sdtlcdtrc0 (-> $$unsorted $$unsorted $$unsorted)) % 16.23/16.43 (declare-const tptp.sdtlbdtrb0 (-> $$unsorted $$unsorted $$unsorted)) % 16.23/16.43 (declare-const tptp.szDzozmdt0 (-> $$unsorted $$unsorted)) % 16.23/16.43 (declare-const tptp.slbdtsldtrb0 (-> $$unsorted $$unsorted $$unsorted)) % 16.23/16.43 (declare-const tptp.slbdtrb0 (-> $$unsorted $$unsorted)) % 16.23/16.43 (declare-const tptp.szmzazxdt0 (-> $$unsorted $$unsorted)) % 16.23/16.43 (declare-const tptp.sdtlpdtrp0 (-> $$unsorted $$unsorted $$unsorted)) % 16.23/16.43 (declare-const tptp.szmzizndt0 (-> $$unsorted $$unsorted)) % 16.23/16.43 (declare-const tptp.sbrdtbr0 (-> $$unsorted $$unsorted)) % 16.23/16.43 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 16.23/16.43 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 16.23/16.43 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 16.23/16.43 (declare-const tptp.isFinite0 (-> $$unsorted Bool)) % 16.23/16.43 (declare-const tptp.isCountable0 (-> $$unsorted Bool)) % 16.23/16.43 (declare-const tptp.slcrc0 $$unsorted) % 16.23/16.43 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 16.23/16.43 (declare-const tptp.aSubsetOf0 (-> $$unsorted $$unsorted Bool)) % 16.23/16.43 (declare-const tptp.sdtlseqdt0 (-> $$unsorted $$unsorted Bool)) % 16.23/16.43 (declare-const tptp.szszuzczcdt0 (-> $$unsorted $$unsorted)) % 16.23/16.43 (declare-const tptp.sdtmndt0 (-> $$unsorted $$unsorted $$unsorted)) % 16.23/16.43 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 16.23/16.43 (declare-const tptp.szNzAzT0 $$unsorted) % 16.23/16.43 (declare-const tptp.aFunction0 (-> $$unsorted Bool)) % 16.23/16.43 (declare-const tptp.sz00 $$unsorted) % 16.23/16.43 (define @t1 () (@var "W0" $$unsorted)) % 16.23/16.43 (define @t2 () (tptp.aSet0 @t1)) % 16.23/16.43 (define @t3 () (@list @t1)) % 16.23/16.43 (define @t4 () (tptp.aElement0 @t1)) % 16.23/16.43 (define @t5 () (@var "W1" $$unsorted)) % 16.23/16.43 (define @t6 () (tptp.aElement0 @t5)) % 16.23/16.43 (define @t7 () (tptp.aElementOf0 @t5 @t1)) % 16.23/16.43 (define @t8 () (@list @t5)) % 16.23/16.43 (define @t9 () (tptp.isFinite0 @t1)) % 16.23/16.43 (define @t10 () (= @t1 tptp.slcrc0)) % 16.23/16.43 (define @t11 () (tptp.isCountable0 @t1)) % 16.23/16.43 (define @t12 () (not @t9)) % 16.23/16.43 (define @t13 () (and @t2 @t11)) % 16.23/16.43 (define @t14 () (not @t10)) % 16.23/16.43 (define @t15 () (@var "W2" $$unsorted)) % 16.23/16.43 (define @t16 () (tptp.aElementOf0 @t15 @t1)) % 16.23/16.43 (define @t17 () (tptp.aElementOf0 @t15 @t5)) % 16.23/16.43 (define @t18 () (@list @t15)) % 16.23/16.43 (define @t19 () (tptp.aSet0 @t5)) % 16.23/16.43 (define @t20 () (tptp.aSubsetOf0 @t5 @t1)) % 16.23/16.43 (define @t21 () (tptp.isFinite0 @t5)) % 16.23/16.43 (define @t22 () (and @t2 @t9)) % 16.23/16.43 (define @t23 () (tptp.aSubsetOf0 @t1 @t1)) % 16.23/16.43 (define @t24 () (forall @t3 (=> @t2 @t23))) % 16.23/16.43 (define @t25 () (= @t1 @t5)) % 16.23/16.43 (define @t26 () (tptp.aSubsetOf0 @t1 @t5)) % 16.23/16.43 (define @t27 () (@list @t1 @t5)) % 16.23/16.43 (define @t28 () (tptp.aSubsetOf0 @t5 @t15)) % 16.23/16.43 (define @t29 () (tptp.aSet0 @t15)) % 16.23/16.43 (define @t30 () (@list @t1 @t5 @t15)) % 16.23/16.43 (define @t31 () (@var "W3" $$unsorted)) % 16.23/16.43 (define @t32 () (= @t31 @t5)) % 16.23/16.43 (define @t33 () (tptp.aElementOf0 @t31 @t1)) % 16.23/16.43 (define @t34 () (tptp.aElement0 @t31)) % 16.23/16.43 (define @t35 () (tptp.aElementOf0 @t31 @t15)) % 16.23/16.43 (define @t36 () (@list @t31)) % 16.23/16.43 (define @t37 () (tptp.sdtpldt0 @t1 @t5)) % 16.23/16.43 (define @t38 () (and @t2 @t6)) % 16.23/16.43 (define @t39 () (tptp.sdtmndt0 @t1 @t5)) % 16.23/16.43 (define @t40 () (tptp.sdtpldt0 @t5 @t1)) % 16.23/16.43 (define @t41 () (and @t19 (tptp.isCountable0 @t5))) % 16.23/16.43 (define @t42 () (tptp.sdtmndt0 @t5 @t1)) % 16.23/16.43 (define @t43 () (and @t19 @t21)) % 16.23/16.43 (define @t44 () (tptp.szszuzczcdt0 @t1)) % 16.23/16.43 (define @t45 () (tptp.aElementOf0 @t1 tptp.szNzAzT0)) % 16.23/16.43 (define @t46 () (tptp.szszuzczcdt0 @t5)) % 16.23/16.43 (define @t47 () (tptp.aElementOf0 @t5 tptp.szNzAzT0)) % 16.23/16.43 (define @t48 () (and @t45 @t47)) % 16.23/16.43 (define @t49 () (= @t1 tptp.sz00)) % 16.23/16.43 (define @t50 () (tptp.sdtlseqdt0 @t1 @t5)) % 16.23/16.43 (define @t51 () (tptp.sdtlseqdt0 @t5 @t15)) % 16.23/16.43 (define @t52 () (tptp.aElementOf0 @t15 tptp.szNzAzT0)) % 16.23/16.43 (define @t53 () (tptp.sbrdtbr0 @t1)) % 16.23/16.43 (define @t54 () (and @t2 @t47)) % 16.23/16.43 (define @t55 () (tptp.szmzizndt0 @t1)) % 16.23/16.43 (define @t56 () (tptp.aSubsetOf0 @t1 tptp.szNzAzT0)) % 16.23/16.43 (define @t57 () (tptp.szmzizndt0 @t5)) % 16.23/16.43 (define @t58 () (tptp.slbdtrb0 @t1)) % 16.23/16.43 (define @t59 () (tptp.slbdtrb0 @t5)) % 16.23/16.43 (define @t60 () (tptp.aSubsetOf0 @t31 @t1)) % 16.23/16.43 (define @t61 () (tptp.slbdtsldtrb0 @t1 @t5)) % 16.23/16.43 (define @t62 () (tptp.slbdtsldtrb0 @t5 @t1)) % 16.23/16.43 (define @t63 () (tptp.aFunction0 @t1)) % 16.23/16.43 (define @t64 () (tptp.szDzozmdt0 @t1)) % 16.23/16.43 (define @t65 () (tptp.aSet0 @t64)) % 16.23/16.43 (define @t66 () (forall @t3 (=> @t63 @t65))) % 16.23/16.43 (define @t67 () (tptp.sdtlbdtrb0 @t1 @t5)) % 16.23/16.43 (define @t68 () (and @t63 @t6)) % 16.23/16.43 (define @t69 () (@var "W4" $$unsorted)) % 16.23/16.43 (define @t70 () (tptp.sdtlpdtrp0 @t1 @t69)) % 16.23/16.43 (define @t71 () (tptp.aElementOf0 @t69 @t5)) % 16.23/16.43 (define @t72 () (and @t71 (= @t70 @t31))) % 16.23/16.43 (define @t73 () (@list @t69)) % 16.23/16.43 (define @t74 () (exists @t73 @t72)) % 16.23/16.43 (define @t75 () (= @t35 @t74)) % 16.23/16.43 (define @t76 () (forall @t36 @t75)) % 16.23/16.43 (define @t77 () (and @t29 @t76)) % 16.23/16.43 (define @t78 () (tptp.sdtlcdtrc0 @t1 @t5)) % 16.23/16.43 (define @t79 () (= @t15 @t78)) % 16.23/16.43 (define @t80 () (= @t79 @t77)) % 16.23/16.43 (define @t81 () (forall @t18 @t80)) % 16.23/16.43 (define @t82 () (tptp.aSubsetOf0 @t5 @t64)) % 16.23/16.43 (define @t83 () (=> @t82 @t81)) % 16.23/16.43 (define @t84 () (forall @t8 @t83)) % 16.23/16.43 (define @t85 () (=> @t63 @t84)) % 16.23/16.43 (define @t86 () (forall @t3 @t85)) % 16.23/16.43 (define @t87 () (tptp.aFunction0 tptp.xF)) % 16.23/16.43 (define @t88 () (tptp.szDzozmdt0 tptp.xF)) % 16.23/16.43 (define @t89 () (tptp.aElementOf0 tptp.xx @t88)) % 16.23/16.43 (define @t90 () (tptp.sdtlcdtrc0 tptp.xF @t88)) % 16.23/16.43 (define @t91 () (tptp.sdtlpdtrp0 tptp.xF tptp.xx)) % 16.23/16.43 (define @t92 () (tptp.aElementOf0 @t91 @t90)) % 16.23/16.43 (define @t93 () (@var "BOUND_VARIABLE_8803" $$unsorted)) % 16.23/16.43 (define @t94 () (tptp.sdtlcdtrc0 @t1 @t93)) % 16.23/16.43 (define @t95 () (@var "BOUND_VARIABLE_8805" $$unsorted)) % 16.23/16.43 (define @t96 () (= @t95 @t94)) % 16.23/16.43 (define @t97 () (= @t31 @t70)) % 16.23/16.43 (define @t98 () (not @t97)) % 16.23/16.43 (define @t99 () (and (tptp.aSet0 @t95) (forall @t36 (= (not (forall @t73 (or (not (tptp.aElementOf0 @t69 @t93)) @t98))) (tptp.aElementOf0 @t31 @t95))))) % 16.23/16.43 (define @t100 () (= (= @t94 @t95) @t99)) % 16.23/16.43 (define @t101 () (not (tptp.aSubsetOf0 @t93 @t64))) % 16.23/16.43 (define @t102 () (not @t63)) % 16.23/16.43 (define @t103 () (or @t102 @t101 @t100)) % 16.23/16.43 (define @t104 () (or @t101 @t100)) % 16.23/16.43 (define @t105 () (or @t102 @t104)) % 16.23/16.43 (define @t106 () (@list @t1 @t93 @t95)) % 16.23/16.43 (define @t107 () (forall @t106 @t105)) % 16.23/16.43 (define @t108 () (@list @t93 @t95)) % 16.23/16.43 (define @t109 () (forall @t108 @t105)) % 16.23/16.43 (define @t110 () (forall @t108 @t104)) % 16.23/16.43 (define @t111 () (@var "BOUND_VARIABLE_8780" $$unsorted)) % 16.23/16.43 (define @t112 () (or @t102 @t110)) % 16.23/16.43 (define @t113 () (tptp.aElementOf0 @t31 @t111)) % 16.23/16.43 (define @t114 () (not (forall @t73 (or (not @t71) @t98)))) % 16.23/16.43 (define @t115 () (tptp.aSet0 @t111)) % 16.23/16.43 (define @t116 () (not @t82)) % 16.23/16.43 (define @t117 () (@list @t5 @t111)) % 16.23/16.43 (define @t118 () (forall @t117 (or @t116 (= (= @t78 @t111) (and @t115 (forall @t36 (= @t114 @t113))))))) % 16.23/16.43 (define @t119 () (forall @t36 (= @t113 @t114))) % 16.23/16.43 (define @t120 () (and @t115 @t119)) % 16.23/16.43 (define @t121 () (= (= @t111 @t78) @t120)) % 16.23/16.43 (define @t122 () (or @t116 @t121)) % 16.23/16.43 (define @t123 () (forall @t117 @t122)) % 16.23/16.43 (define @t124 () (@list @t111)) % 16.23/16.43 (define @t125 () (forall @t124 @t122)) % 16.23/16.43 (define @t126 () (forall @t124 @t121)) % 16.23/16.43 (define @t127 () (or @t116 @t126)) % 16.23/16.43 (define @t128 () (forall @t18 (= @t79 (and @t29 (forall @t36 (= @t35 @t114)))))) % 16.23/16.43 (define @t129 () (and @t71 @t97)) % 16.23/16.43 (define @t130 () (forall @t73 (not @t129))) % 16.23/16.43 (define @t131 () (not @t130)) % 16.23/16.43 (define @t132 () (tptp.sdtlpdtrp0 tptp.xF @t69)) % 16.23/16.43 (define @t133 () (not (tptp.aElementOf0 @t69 @t88))) % 16.23/16.43 (define @t134 () (forall @t36 (= (not (forall @t73 (or @t133 (not (= @t31 @t132))))) (tptp.aElementOf0 @t31 @t90)))) % 16.23/16.43 (define @t135 () (and (tptp.aSet0 @t90) @t134)) % 16.23/16.43 (define @t136 () (= @t135 (= @t90 @t90))) % 16.23/16.43 (define @t137 () (tptp.aSubsetOf0 @t88 @t88)) % 16.23/16.43 (define @t138 () (not @t137)) % 16.23/16.43 (define @t139 () (not @t87)) % 16.23/16.43 (define @t140 () (or @t139 @t138 @t136)) % 16.23/16.43 (define @t141 () (forall @t106 (or @t102 @t101 (= @t99 @t96)))) % 16.23/16.43 (define @t142 () (or @t139 @t138 @t135)) % 16.23/16.43 (define @t143 () (@list false)) % 16.23/16.43 (define @t144 () (tptp.aSet0 @t88)) % 16.23/16.43 (define @t145 () (or @t139 @t144)) % 16.23/16.43 (define @t146 () (@list false false)) % 16.23/16.43 (define @t147 () (not @t144)) % 16.23/16.43 (define @t148 () (or @t147 @t137)) % 16.23/16.43 (define @t149 () (forall @t73 (or @t133 (not (= @t91 @t132))))) % 16.23/16.43 (define @t150 () (not @t149)) % 16.23/16.43 (define @t151 () (= @t150 @t92)) % 16.23/16.43 (define @t152 () (= @t92 @t150)) % 16.23/16.43 (define @t153 () (not @t152)) % 16.23/16.43 (define @t154 () (not @t89)) % 16.23/16.43 (define @t155 () (not (= @t91 @t91))) % 16.23/16.43 (define @t156 () (or @t154 @t155)) % 16.23/16.43 (assume @p1 (forall @t3 (=> @t2 true))) % 16.23/16.43 (assume @p2 (forall @t3 (=> @t4 true))) % 16.23/16.43 (assume @p3 (forall @t3 (=> @t2 (forall @t8 (=> @t7 @t6))))) % 16.23/16.43 (assume @p4 (forall @t3 (=> @t2 (=> @t9 true)))) % 16.23/16.43 (assume @p5 (forall @t3 (= @t10 (and @t2 (not (exists @t8 @t7)))))) % 16.23/16.43 (assume @p6 (tptp.isFinite0 tptp.slcrc0)) % 16.23/16.43 (assume @p7 (forall @t3 (=> @t2 (=> @t11 true)))) % 16.23/16.43 (assume @p8 (forall @t3 (=> @t13 @t12))) % 16.23/16.43 (assume @p9 (forall @t3 (=> @t13 @t14))) % 16.23/16.43 (assume @p10 (forall @t3 (=> @t2 (forall @t8 (= @t20 (and @t19 (forall @t18 (=> @t17 @t16)))))))) % 16.23/16.43 (assume @p11 (forall @t3 (=> @t22 (forall @t8 (=> @t20 @t21))))) % 16.23/16.43 (assume @p12 @t24) % 16.23/16.43 (assume @p13 (forall @t27 (=> (and @t2 @t19) (=> (and @t26 @t20) @t25)))) % 16.23/16.43 (assume @p14 (forall @t30 (=> (and @t2 @t19 @t29) (=> (and @t26 @t28) (tptp.aSubsetOf0 @t1 @t15))))) % 16.23/16.43 (assume @p15 (forall @t27 (=> @t38 (forall @t18 (= (= @t15 @t37) (and @t29 (forall @t36 (= @t35 (and @t34 (or @t33 @t32)))))))))) % 16.23/16.43 (assume @p16 (forall @t27 (=> @t38 (forall @t18 (= (= @t15 @t39) (and @t29 (forall @t36 (= @t35 (and @t34 @t33 (not @t32)))))))))) % 16.23/16.43 (assume @p17 (forall @t3 (=> @t2 (forall @t8 (=> @t7 (= (tptp.sdtpldt0 @t39 @t5) @t1)))))) % 16.23/16.43 (assume @p18 (forall @t27 (=> (and @t4 @t19) (=> (not (tptp.aElementOf0 @t1 @t5)) (= (tptp.sdtmndt0 @t40 @t1) @t5))))) % 16.23/16.43 (assume @p19 (forall @t3 (=> @t4 (forall @t8 (=> @t41 (tptp.isCountable0 @t40)))))) % 16.23/16.43 (assume @p20 (forall @t3 (=> @t4 (forall @t8 (=> @t41 (tptp.isCountable0 @t42)))))) % 16.23/16.43 (assume @p21 (forall @t3 (=> @t4 (forall @t8 (=> @t43 (tptp.isFinite0 @t40)))))) % 16.23/16.43 (assume @p22 (forall @t3 (=> @t4 (forall @t8 (=> @t43 (tptp.isFinite0 @t42)))))) % 16.23/16.43 (assume @p23 (and (tptp.aSet0 tptp.szNzAzT0) (tptp.isCountable0 tptp.szNzAzT0))) % 16.23/16.43 (assume @p24 (tptp.aElementOf0 tptp.sz00 tptp.szNzAzT0)) % 16.23/16.43 (assume @p25 (forall @t3 (=> @t45 (and (tptp.aElementOf0 @t44 tptp.szNzAzT0) (not (= @t44 tptp.sz00)))))) % 16.23/16.43 (assume @p26 (forall @t27 (=> @t48 (=> (= @t44 @t46) @t25)))) % 16.23/16.43 (assume @p27 (forall @t3 (=> @t45 (or @t49 (exists @t8 (and @t47 (= @t1 @t46))))))) % 16.23/16.43 (assume @p28 (forall @t3 (=> @t45 (not (= @t1 @t44))))) % 16.23/16.43 (assume @p29 (forall @t27 (=> @t48 (=> @t50 true)))) % 16.23/16.43 (assume @p30 (forall @t3 (=> @t45 (tptp.sdtlseqdt0 tptp.sz00 @t1)))) % 16.23/16.43 (assume @p31 (forall @t3 (=> @t45 (not (tptp.sdtlseqdt0 @t44 tptp.sz00))))) % 16.23/16.43 (assume @p32 (forall @t27 (=> @t48 (= @t50 (tptp.sdtlseqdt0 @t44 @t46))))) % 16.23/16.43 (assume @p33 (forall @t3 (=> @t45 (tptp.sdtlseqdt0 @t1 @t44)))) % 16.23/16.43 (assume @p34 (forall @t3 (=> @t45 (tptp.sdtlseqdt0 @t1 @t1)))) % 16.23/16.43 (assume @p35 (forall @t27 (=> @t48 (=> (and @t50 (tptp.sdtlseqdt0 @t5 @t1)) @t25)))) % 16.23/16.43 (assume @p36 (forall @t30 (=> (and @t45 @t47 @t52) (=> (and @t50 @t51) (tptp.sdtlseqdt0 @t1 @t15))))) % 16.23/16.43 (assume @p37 (forall @t27 (=> @t48 (or @t50 (tptp.sdtlseqdt0 @t46 @t1))))) % 16.23/16.43 (assume @p38 (forall @t27 (=> @t48 (=> (tptp.iLess0 @t1 @t5) true)))) % 16.23/16.43 (assume @p39 (forall @t3 (=> @t45 (tptp.iLess0 @t1 @t44)))) % 16.23/16.43 (assume @p40 (forall @t3 (=> @t2 (tptp.aElement0 @t53)))) % 16.23/16.43 (assume @p41 (forall @t3 (=> @t2 (= (tptp.aElementOf0 @t53 tptp.szNzAzT0) @t9)))) % 16.23/16.43 (assume @p42 (forall @t3 (=> @t2 (= (= @t53 tptp.sz00) @t10)))) % 16.23/16.43 (assume @p43 (forall @t3 (=> @t22 (forall @t8 (=> @t6 (=> (not @t7) (= (tptp.sbrdtbr0 @t37) (tptp.szszuzczcdt0 @t53)))))))) % 16.23/16.43 (assume @p44 (forall @t3 (=> @t2 (forall @t8 (=> (and @t9 @t7) (= (tptp.szszuzczcdt0 (tptp.sbrdtbr0 @t39)) @t53)))))) % 16.23/16.43 (assume @p45 (forall @t3 (=> @t2 (forall @t8 (=> (and @t9 @t20) (tptp.sdtlseqdt0 (tptp.sbrdtbr0 @t5) @t53)))))) % 16.23/16.43 (assume @p46 (forall @t27 (=> @t54 (=> (and @t9 (tptp.sdtlseqdt0 @t5 @t53)) (exists @t18 (and (tptp.aSubsetOf0 @t15 @t1) (= (tptp.sbrdtbr0 @t15) @t5))))))) % 16.23/16.43 (assume @p47 (forall @t3 (=> (and @t56 @t14) (forall @t8 (= (= @t5 @t55) (and @t7 (forall @t18 (=> @t16 @t51)))))))) % 16.23/16.43 (assume @p48 (forall @t3 (=> (and @t56 @t9 @t14) (forall @t8 (= (= @t5 (tptp.szmzazxdt0 @t1)) (and @t7 (forall @t18 (=> @t16 (tptp.sdtlseqdt0 @t15 @t5))))))))) % 16.23/16.43 (assume @p49 (forall @t27 (=> (and @t56 (tptp.aSubsetOf0 @t5 tptp.szNzAzT0) @t14 (not (= @t5 tptp.slcrc0))) (=> (and (tptp.aElementOf0 @t55 @t5) (tptp.aElementOf0 @t57 @t1)) (= @t55 @t57))))) % 16.23/16.43 (assume @p50 (forall @t3 (=> @t45 (forall @t8 (= (= @t5 @t58) (and @t19 (forall @t18 (= @t17 (and @t52 (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 @t15) @t1)))))))))) % 16.23/16.43 (assume @p51 (forall @t3 (=> @t45 (tptp.isFinite0 @t58)))) % 16.23/16.43 (assume @p52 (= (tptp.slbdtrb0 tptp.sz00) tptp.slcrc0)) % 16.23/16.43 (assume @p53 (forall @t27 (=> @t48 (= (tptp.aElementOf0 @t1 (tptp.slbdtrb0 @t46)) (or (tptp.aElementOf0 @t1 @t59) @t25))))) % 16.23/16.43 (assume @p54 (forall @t27 (=> @t48 (= @t50 (tptp.aSubsetOf0 @t58 @t59))))) % 16.23/16.43 (assume @p55 (forall @t3 (=> (and @t56 @t9) (exists @t8 (and @t47 (tptp.aSubsetOf0 @t1 @t59)))))) % 16.23/16.43 (assume @p56 (forall @t3 (=> @t45 (= (tptp.sbrdtbr0 @t58) @t1)))) % 16.23/16.43 (assume @p57 (forall @t27 (=> @t54 (forall @t18 (= (= @t15 @t61) (and @t29 (forall @t36 (= @t35 (and @t60 (= (tptp.sbrdtbr0 @t31) @t5)))))))))) % 16.23/16.43 (assume @p58 (forall @t3 (=> @t22 (forall @t8 (=> @t47 (tptp.isFinite0 @t61)))))) % 16.23/16.43 (assume @p59 (forall @t3 (=> (and @t2 @t12) (forall @t8 (=> @t47 (not (= @t61 tptp.slcrc0))))))) % 16.23/16.43 (assume @p60 (forall @t3 (=> @t13 (forall @t8 (=> (and @t47 (not (= @t5 tptp.sz00))) (tptp.isCountable0 @t61)))))) % 16.23/16.43 (assume @p61 (forall @t3 (=> @t45 (forall (@list @t5 @t15) (=> (and @t19 @t29 (not @t49)) (=> (and (tptp.aSubsetOf0 @t62 (tptp.slbdtsldtrb0 @t15 @t1)) (not (= @t62 tptp.slcrc0))) @t28)))))) % 16.23/16.43 (assume @p62 (forall @t27 (=> @t54 (forall @t18 (=> (and (tptp.aSubsetOf0 @t15 @t61) (tptp.isFinite0 @t15)) (exists @t36 (and @t60 (tptp.isFinite0 @t31) (tptp.aSubsetOf0 @t15 (tptp.slbdtsldtrb0 @t31 @t5))))))))) % 16.23/16.43 (assume @p63 (forall @t3 (=> @t63 true))) % 16.23/16.43 (assume @p64 @t66) % 16.23/16.43 (assume @p65 (forall @t3 (=> @t63 (forall @t8 (=> (tptp.aElementOf0 @t5 @t64) (tptp.aElement0 (tptp.sdtlpdtrp0 @t1 @t5))))))) % 16.23/16.43 (assume @p66 (forall @t27 (=> @t68 (forall @t18 (= (= @t15 @t67) (and @t29 (forall @t36 (= @t35 (and (tptp.aElementOf0 @t31 @t64) (= (tptp.sdtlpdtrp0 @t1 @t31) @t5)))))))))) % 16.23/16.43 (assume @p67 (forall @t27 (=> @t68 (tptp.aSubsetOf0 @t67 @t64)))) % 16.23/16.43 (assume @p68 @t86) % 16.23/16.43 (assume @p69 @t87) % 16.23/16.43 (assume @p70 @t89) % 16.23/16.43 (assume @p71 (not @t92)) % 16.23/16.43 (assume @p72 true) % 16.23/16.43 (step @p73 :rule eq-symm :args (@t96 @t99)) % 16.23/16.43 (step @p74 :rule refl :args (@t99)) % 16.23/16.43 (step @p75 :rule eq-symm :args (@t94 @t95)) % 16.23/16.43 (step @p76 :rule cong :premises (@p75 @p74) :args (@t100)) % 16.23/16.43 (step @p77 :rule trans :premises (@p76 @p73)) % 16.23/16.43 (step @p78 :rule refl :args (@t101)) % 16.23/16.43 (step @p79 :rule refl :args (@t102)) % 16.23/16.43 (step @p80 :rule nary_cong :premises (@p79 @p78 @p77) :args (@t103)) % 16.23/16.43 (step @p81 :rule aci_norm :args ((= @t105 @t103))) % 16.23/16.43 (step @p82 :rule trans :premises (@p81 @p80)) % 16.23/16.43 (step @p83 :rule cong :premises (@p82) :args (@t107)) % 16.23/16.43 (step @p84 :rule quant-merge-prenex :args ((= (forall @t3 @t109) @t107))) % 16.23/16.43 (step @p85 :rule alpha_equiv :args (@t110 (@list @t93 @t95) (@list @t5 @t111))) % 16.23/16.43 (step @p86 :rule refl :args (@t102)) % 16.23/16.43 (step @p87 :rule nary_cong :premises (@p86 @p85) :args (@t112)) % 16.23/16.43 (step @p88 :rule quant-miniscope-or :args ((= @t109 @t112))) % 16.23/16.43 (step @p89 :rule trans :premises (@p88 @p87)) % 16.23/16.43 (step @p90 :rule symm :premises (@p89)) % 16.23/16.43 (step @p91 :rule cong :premises (@p90) :args ((forall @t3 (or @t102 @t118)))) % 16.23/16.43 (step @p92 :rule trans :premises (@p91 @p84)) % 16.23/16.43 (step @p93 :rule trans :premises (@p92 @p83)) % 16.23/16.43 (step @p94 :rule bool-impl-elim :args (@t63 @t118)) % 16.23/16.43 (step @p95 :rule cong :premises (@p94) :args ((forall @t3 (=> @t63 @t118)))) % 16.23/16.43 (step @p96 :rule trans :premises (@p95 @p93)) % 16.23/16.43 (step @p97 :rule eq-symm :args (@t113 @t114)) % 16.23/16.43 (step @p98 :rule cong :premises (@p97) :args (@t119)) % 16.23/16.43 (step @p99 :rule refl :args (@t115)) % 16.23/16.43 (step @p100 :rule nary_cong :premises (@p99 @p98) :args (@t120)) % 16.23/16.43 (step @p101 :rule eq-symm :args (@t111 @t78)) % 16.23/16.43 (step @p102 :rule cong :premises (@p101 @p100) :args (@t121)) % 16.23/16.43 (step @p103 :rule refl :args (@t116)) % 16.23/16.43 (step @p104 :rule nary_cong :premises (@p103 @p102) :args (@t122)) % 16.23/16.43 (step @p105 :rule cong :premises (@p104) :args (@t123)) % 16.23/16.43 (step @p106 :rule quant-merge-prenex :args ((= (forall @t8 @t125) @t123))) % 16.23/16.43 (step @p107 :rule alpha_equiv :args (@t126 (@list @t111) (@list @t15))) % 16.23/16.43 (step @p108 :rule refl :args (@t116)) % 16.23/16.43 (step @p109 :rule nary_cong :premises (@p108 @p107) :args (@t127)) % 16.23/16.43 (step @p110 :rule quant-miniscope-or :args ((= @t125 @t127))) % 16.23/16.43 (step @p111 :rule trans :premises (@p110 @p109)) % 16.23/16.43 (step @p112 :rule symm :premises (@p111)) % 16.23/16.43 (step @p113 :rule cong :premises (@p112) :args ((forall @t8 (or @t116 @t128)))) % 16.23/16.43 (step @p114 :rule trans :premises (@p113 @p106)) % 16.23/16.43 (step @p115 :rule trans :premises (@p114 @p105)) % 16.23/16.43 (step @p116 :rule bool-impl-elim :args (@t82 @t128)) % 16.23/16.43 (step @p117 :rule cong :premises (@p116) :args ((forall @t8 (=> @t82 @t128)))) % 16.23/16.43 (step @p118 :rule trans :premises (@p117 @p115)) % 16.23/16.43 (step @p119 :rule bool-and-de-morgan :args (@t71 @t97 true)) % 16.23/16.43 (step @p120 :rule cong :premises (@p119) :args (@t130)) % 16.23/16.43 (step @p121 :rule cong :premises (@p120) :args (@t131)) % 16.23/16.43 (step @p122 :rule exists-elim :args ((= (exists @t73 @t129) @t131))) % 16.23/16.43 (step @p123 :rule trans :premises (@p122 @p121)) % 16.23/16.43 (step @p124 :rule eq-symm :args (@t70 @t31)) % 16.23/16.43 (step @p125 :rule refl :args (@t71)) % 16.23/16.43 (step @p126 :rule nary_cong :premises (@p125 @p124) :args (@t72)) % 16.23/16.43 (step @p127 :rule cong :premises (@p126) :args (@t74)) % 16.23/16.43 (step @p128 :rule trans :premises (@p127 @p123)) % 16.23/16.43 (step @p129 :rule refl :args (@t35)) % 16.23/16.43 (step @p130 :rule cong :premises (@p129 @p128) :args (@t75)) % 16.23/16.43 (step @p131 :rule cong :premises (@p130) :args (@t76)) % 16.23/16.43 (step @p132 :rule refl :args (@t29)) % 16.23/16.43 (step @p133 :rule nary_cong :premises (@p132 @p131) :args (@t77)) % 16.23/16.43 (step @p134 :rule refl :args (@t79)) % 16.23/16.43 (step @p135 :rule cong :premises (@p134 @p133) :args (@t80)) % 16.23/16.43 (step @p136 :rule cong :premises (@p135) :args (@t81)) % 16.23/16.43 (step @p137 :rule refl :args (@t82)) % 16.23/16.43 (step @p138 :rule cong :premises (@p137 @p136) :args (@t83)) % 16.23/16.43 (step @p139 :rule cong :premises (@p138) :args (@t84)) % 16.23/16.43 (step @p140 :rule trans :premises (@p139 @p118)) % 16.23/16.43 (step @p141 :rule refl :args (@t63)) % 16.23/16.43 (step @p142 :rule cong :premises (@p141 @p140) :args (@t85)) % 16.23/16.43 (step @p143 :rule cong :premises (@p142) :args (@t86)) % 16.23/16.43 (step @p144 :rule trans :premises (@p143 @p96)) % 16.23/16.43 (step @p145 :rule eq_resolve :premises (@p68 @p144)) % 16.23/16.43 (step @p146 :rule bool-eq-true :args (@t135)) % 16.23/16.43 (step @p147 :rule eq-refl :args (@t90)) % 16.23/16.43 (step @p148 :rule refl :args (@t135)) % 16.23/16.43 (step @p149 :rule cong :premises (@p148 @p147) :args (@t136)) % 16.23/16.43 (step @p150 :rule trans :premises (@p149 @p146)) % 16.23/16.43 (step @p151 :rule refl :args (@t138)) % 16.23/16.43 (step @p152 :rule refl :args (@t139)) % 16.23/16.43 (step @p153 :rule nary_cong :premises (@p152 @p151 @p150) :args (@t140)) % 16.23/16.43 (step @p154 :rule refl :args (@t141)) % 16.23/16.43 (step @p155 :rule cong :premises (@p154 @p153) :args ((=> @t141 @t140))) % 16.23/16.43 (assume-push @p219 @t141) % 16.23/16.43 (step @p157 :rule instantiate :premises (@p145) :args ((@list tptp.xF @t88 @t90))) % 16.23/16.43 (step-pop @p220 :rule scope :premises (@p157)) % 16.23/16.43 (step @p158 :rule process_scope :premises (@p220) :args (@t140)) % 16.23/16.43 (step @p160 :rule eq_resolve :premises (@p158 @p155)) % 16.23/16.43 (step @p161 :rule implies_elim :premises (@p160)) % 16.23/16.43 (step @p162 :rule chain_m_resolution :premises (@p161 @p145) :args (@t142 @t143 (@list @t141))) % 16.23/16.43 (step @p163 :rule bool-impl-elim :args (@t2 @t23)) % 16.23/16.43 (step @p164 :rule cong :premises (@p163) :args (@t24)) % 16.23/16.43 (step @p165 :rule eq_resolve :premises (@p12 @p164)) % 16.23/16.43 (step @p166 :rule instantiate :premises (@p165) :args ((@list @t88))) % 16.23/16.43 (step @p167 :rule bool-impl-elim :args (@t63 @t65)) % 16.23/16.43 (step @p168 :rule cong :premises (@p167) :args (@t66)) % 16.23/16.43 (step @p169 :rule eq_resolve :premises (@p64 @p168)) % 16.23/16.43 (step @p170 :rule instantiate :premises (@p169) :args ((@list tptp.xF))) % 16.23/16.43 (step @p171 :rule cnf_or_pos :args (@t145)) % 16.23/16.43 (step @p172 :rule reordering :premises (@p171) :args ((or @t139 @t144 (not @t145)))) % 16.23/16.43 (step @p173 :rule chain_m_resolution :premises (@p172 @p69 @p170) :args (@t144 @t146 (@list @t87 @t145))) % 16.23/16.43 (step @p174 :rule cnf_or_pos :args (@t148)) % 16.23/16.43 (step @p175 :rule reordering :premises (@p174) :args ((or @t147 @t137 (not @t148)))) % 16.23/16.43 (step @p176 :rule chain_m_resolution :premises (@p175 @p173 @p166) :args (@t137 @t146 (@list @t144 @t148))) % 16.23/16.43 (step @p177 :rule cnf_or_pos :args (@t142)) % 16.23/16.43 (step @p178 :rule reordering :premises (@p177) :args ((or @t139 @t138 @t135 (not @t142)))) % 16.23/16.43 (step @p179 :rule chain_m_resolution :premises (@p178 @p69 @p176 @p162) :args (@t135 (@list false false false) (@list @t87 @t137 @t142))) % 16.23/16.43 (step @p180 :rule cnf_and_pos :args (@t135 1)) % 16.23/16.43 (step @p181 :rule reordering :premises (@p180) :args ((or @t134 (not @t135)))) % 16.23/16.43 (step @p182 :rule chain_m_resolution :premises (@p181 @p179) :args (@t134 @t143 (@list @t135))) % 16.23/16.43 (step @p183 :rule eq-symm :args (@t150 @t92)) % 16.23/16.43 (step @p184 :rule refl :args (@t134)) % 16.23/16.43 (step @p185 :rule cong :premises (@p184 @p183) :args ((=> @t134 @t151))) % 16.23/16.43 (assume-push @p221 @t134) % 16.23/16.43 (step @p187 :rule instantiate :premises (@p182) :args ((@list @t91))) % 16.23/16.43 (step-pop @p222 :rule scope :premises (@p187)) % 16.23/16.43 (step @p188 :rule process_scope :premises (@p222) :args (@t151)) % 16.23/16.43 (step @p190 :rule eq_resolve :premises (@p188 @p185)) % 16.23/16.43 (step @p191 :rule implies_elim :premises (@p190)) % 16.23/16.43 (step @p192 :rule chain_m_resolution :premises (@p191 @p182) :args (@t152 @t143 (@list @t134))) % 16.23/16.43 (step @p193 :rule bool-double-not-elim :args (@t149)) % 16.23/16.43 (step @p194 :rule refl :args (@t92)) % 16.23/16.43 (step @p195 :rule refl :args (@t153)) % 16.23/16.43 (step @p196 :rule nary_cong :premises (@p195 @p194 @p193) :args ((or @t153 @t92 (not @t150)))) % 16.23/16.43 (step @p197 :rule cnf_equiv_pos2 :args (@t152)) % 16.23/16.43 (step @p198 :rule eq_resolve :premises (@p197 @p196)) % 16.23/16.43 (step @p199 :rule reordering :premises (@p198) :args ((or @t92 @t149 @t153))) % 16.23/16.43 (step @p200 :rule chain_m_resolution :premises (@p199 @p71 @p192) :args (@t149 (@list true false) (@list @t92 @t152))) % 16.23/16.43 (step @p201 :rule aci_norm :args ((= (or @t154 false) @t154))) % 16.23/16.43 (step @p202 :rule evaluate :args ((not true))) % 16.23/16.43 (step @p203 :rule eq-refl :args (@t91)) % 16.23/16.43 (step @p204 :rule cong :premises (@p203) :args (@t155)) % 16.23/16.43 (step @p205 :rule trans :premises (@p204 @p202)) % 16.23/16.43 (step @p206 :rule refl :args (@t154)) % 16.23/16.43 (step @p207 :rule nary_cong :premises (@p206 @p205) :args (@t156)) % 16.23/16.43 (step @p208 :rule trans :premises (@p207 @p201)) % 16.23/16.43 (step @p209 :rule refl :args (@t149)) % 16.23/16.43 (step @p210 :rule cong :premises (@p209 @p208) :args ((=> @t149 @t156))) % 16.23/16.43 (assume-push @p223 @t149) % 16.23/16.43 (step @p212 :rule instantiate :premises (@p200) :args ((@list tptp.xx))) % 16.23/16.43 (step-pop @p224 :rule scope :premises (@p212)) % 16.23/16.43 (step @p213 :rule process_scope :premises (@p224) :args (@t156)) % 16.23/16.43 (step @p215 :rule eq_resolve :premises (@p213 @p210)) % 16.23/16.43 (step @p216 :rule implies_elim :premises (@p215)) % 16.23/16.43 (step @p217 :rule reordering :premises (@p216) :args ((or @t154 @t150))) % 16.23/16.43 (step @p218 false :rule chain_m_resolution :premises (@p217 @p200 @p70) :args (false @t146 (@list @t149 @t89))) % 16.23/16.43 ) % 16.23/16.43 % SZS output end Proof % 16.23/16.43 % cvc5 exiting %------------------------------------------------------------------------------