%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM548+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 : n027.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 08:39:48 AM UTC 2026 % Result : Theorem 17.70s 17.97s % Output : Proof 17.70s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM548+1 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n027.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 11:29:06 EDT 2026 % 0.16/0.34 % CPUTime : % 0.26/0.50 %----Proving TF0_NAR, FOF, or CNF % 17.70/17.97 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 17.70/17.97 --- Run --no-e-matching --full-saturate-quant at 6... % 17.70/17.97 % SZS status Theorem % 17.70/17.97 % SZS output start Proof % 17.70/17.97 ( % 17.70/17.97 (declare-sort $$unsorted 0) % 17.70/17.97 (declare-const tptp.xT $$unsorted) % 17.70/17.97 (declare-const tptp.slbdtsldtrb0 (-> $$unsorted $$unsorted $$unsorted)) % 17.70/17.97 (declare-const tptp.slbdtrb0 (-> $$unsorted $$unsorted)) % 17.70/17.97 (declare-const tptp.szmzazxdt0 (-> $$unsorted $$unsorted)) % 17.70/17.97 (declare-const tptp.szmzizndt0 (-> $$unsorted $$unsorted)) % 17.70/17.97 (declare-const tptp.sbrdtbr0 (-> $$unsorted $$unsorted)) % 17.70/17.97 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 17.70/17.97 (declare-const tptp.xQ $$unsorted) % 17.70/17.97 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 17.70/17.97 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 17.70/17.97 (declare-const tptp.xS $$unsorted) % 17.70/17.97 (declare-const tptp.isFinite0 (-> $$unsorted Bool)) % 17.70/17.97 (declare-const tptp.xx $$unsorted) % 17.70/17.97 (declare-const tptp.isCountable0 (-> $$unsorted Bool)) % 17.70/17.97 (declare-const tptp.slcrc0 $$unsorted) % 17.70/17.97 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 17.70/17.97 (declare-const tptp.aSubsetOf0 (-> $$unsorted $$unsorted Bool)) % 17.70/17.97 (declare-const tptp.sdtlseqdt0 (-> $$unsorted $$unsorted Bool)) % 17.70/17.97 (declare-const tptp.xk $$unsorted) % 17.70/17.97 (declare-const tptp.szszuzczcdt0 (-> $$unsorted $$unsorted)) % 17.70/17.97 (declare-const tptp.sdtmndt0 (-> $$unsorted $$unsorted $$unsorted)) % 17.70/17.97 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 17.70/17.97 (declare-const tptp.szNzAzT0 $$unsorted) % 17.70/17.97 (declare-const tptp.sz00 $$unsorted) % 17.70/17.97 (define @t1 () (@var "W0" $$unsorted)) % 17.70/17.97 (define @t2 () (tptp.aSet0 @t1)) % 17.70/17.97 (define @t3 () (@list @t1)) % 17.70/17.97 (define @t4 () (tptp.aElement0 @t1)) % 17.70/17.97 (define @t5 () (@var "W1" $$unsorted)) % 17.70/17.97 (define @t6 () (tptp.aElement0 @t5)) % 17.70/17.97 (define @t7 () (tptp.aElementOf0 @t5 @t1)) % 17.70/17.97 (define @t8 () (@list @t5)) % 17.70/17.97 (define @t9 () (tptp.isFinite0 @t1)) % 17.70/17.97 (define @t10 () (= @t1 tptp.slcrc0)) % 17.70/17.97 (define @t11 () (tptp.isCountable0 @t1)) % 17.70/17.97 (define @t12 () (not @t9)) % 17.70/17.97 (define @t13 () (and @t2 @t11)) % 17.70/17.97 (define @t14 () (not @t10)) % 17.70/17.97 (define @t15 () (@var "W2" $$unsorted)) % 17.70/17.97 (define @t16 () (tptp.aElementOf0 @t15 @t1)) % 17.70/17.97 (define @t17 () (tptp.aElementOf0 @t15 @t5)) % 17.70/17.97 (define @t18 () (@list @t15)) % 17.70/17.97 (define @t19 () (forall @t18 (=> @t17 @t16))) % 17.70/17.97 (define @t20 () (tptp.aSet0 @t5)) % 17.70/17.97 (define @t21 () (and @t20 @t19)) % 17.70/17.97 (define @t22 () (tptp.aSubsetOf0 @t5 @t1)) % 17.70/17.97 (define @t23 () (= @t22 @t21)) % 17.70/17.97 (define @t24 () (forall @t8 @t23)) % 17.70/17.97 (define @t25 () (=> @t2 @t24)) % 17.70/17.97 (define @t26 () (forall @t3 @t25)) % 17.70/17.97 (define @t27 () (tptp.isFinite0 @t5)) % 17.70/17.97 (define @t28 () (and @t2 @t9)) % 17.70/17.97 (define @t29 () (= @t1 @t5)) % 17.70/17.97 (define @t30 () (tptp.aSubsetOf0 @t1 @t5)) % 17.70/17.97 (define @t31 () (@list @t1 @t5)) % 17.70/17.97 (define @t32 () (tptp.aSet0 @t15)) % 17.70/17.97 (define @t33 () (@list @t1 @t5 @t15)) % 17.70/17.97 (define @t34 () (@var "W3" $$unsorted)) % 17.70/17.97 (define @t35 () (= @t34 @t5)) % 17.70/17.97 (define @t36 () (tptp.aElementOf0 @t34 @t1)) % 17.70/17.97 (define @t37 () (tptp.aElement0 @t34)) % 17.70/17.97 (define @t38 () (tptp.aElementOf0 @t34 @t15)) % 17.70/17.97 (define @t39 () (@list @t34)) % 17.70/17.97 (define @t40 () (tptp.sdtpldt0 @t1 @t5)) % 17.70/17.97 (define @t41 () (and @t2 @t6)) % 17.70/17.97 (define @t42 () (tptp.sdtmndt0 @t1 @t5)) % 17.70/17.97 (define @t43 () (tptp.sdtpldt0 @t5 @t1)) % 17.70/17.97 (define @t44 () (and @t20 (tptp.isCountable0 @t5))) % 17.70/17.97 (define @t45 () (tptp.sdtmndt0 @t5 @t1)) % 17.70/17.97 (define @t46 () (and @t20 @t27)) % 17.70/17.97 (define @t47 () (tptp.szszuzczcdt0 @t1)) % 17.70/17.97 (define @t48 () (tptp.aElementOf0 @t1 tptp.szNzAzT0)) % 17.70/17.97 (define @t49 () (tptp.szszuzczcdt0 @t5)) % 17.70/17.97 (define @t50 () (tptp.aElementOf0 @t5 tptp.szNzAzT0)) % 17.70/17.97 (define @t51 () (and @t48 @t50)) % 17.70/17.97 (define @t52 () (tptp.sdtlseqdt0 @t1 @t5)) % 17.70/17.97 (define @t53 () (tptp.sdtlseqdt0 @t5 @t15)) % 17.70/17.97 (define @t54 () (tptp.aElementOf0 @t15 tptp.szNzAzT0)) % 17.70/17.97 (define @t55 () (tptp.sbrdtbr0 @t1)) % 17.70/17.97 (define @t56 () (tptp.aElementOf0 @t55 tptp.szNzAzT0)) % 17.70/17.97 (define @t57 () (=> @t2 (= @t56 @t9))) % 17.70/17.97 (define @t58 () (forall @t3 @t57)) % 17.70/17.97 (define @t59 () (and @t2 @t50)) % 17.70/17.97 (define @t60 () (tptp.szmzizndt0 @t1)) % 17.70/17.97 (define @t61 () (tptp.aSubsetOf0 @t1 tptp.szNzAzT0)) % 17.70/17.97 (define @t62 () (tptp.szmzizndt0 @t5)) % 17.70/17.97 (define @t63 () (tptp.slbdtrb0 @t1)) % 17.70/17.97 (define @t64 () (tptp.slbdtrb0 @t5)) % 17.70/17.97 (define @t65 () (tptp.sbrdtbr0 @t34)) % 17.70/17.97 (define @t66 () (tptp.aSubsetOf0 @t34 @t1)) % 17.70/17.97 (define @t67 () (and @t66 (= @t65 @t5))) % 17.70/17.97 (define @t68 () (= @t38 @t67)) % 17.70/17.97 (define @t69 () (forall @t39 @t68)) % 17.70/17.97 (define @t70 () (and @t32 @t69)) % 17.70/17.97 (define @t71 () (tptp.slbdtsldtrb0 @t1 @t5)) % 17.70/17.97 (define @t72 () (= @t15 @t71)) % 17.70/17.97 (define @t73 () (= @t72 @t70)) % 17.70/17.97 (define @t74 () (forall @t18 @t73)) % 17.70/17.97 (define @t75 () (=> @t59 @t74)) % 17.70/17.97 (define @t76 () (forall @t31 @t75)) % 17.70/17.97 (define @t77 () (tptp.aElementOf0 tptp.xk tptp.szNzAzT0)) % 17.70/17.97 (define @t78 () (tptp.aSet0 tptp.xS)) % 17.70/17.97 (define @t79 () (tptp.slbdtsldtrb0 tptp.xS tptp.xk)) % 17.70/17.97 (define @t80 () (tptp.aElementOf0 tptp.xQ @t79)) % 17.70/17.97 (define @t81 () (tptp.isFinite0 tptp.xQ)) % 17.70/17.97 (define @t82 () (@var "BOUND_VARIABLE_7887" $$unsorted)) % 17.70/17.97 (define @t83 () (= (tptp.aSubsetOf0 @t82 @t1) (and (tptp.aSet0 @t82) (forall @t18 (or (not (tptp.aElementOf0 @t15 @t82)) @t16))))) % 17.70/17.97 (define @t84 () (not @t2)) % 17.70/17.97 (define @t85 () (or @t84 @t83)) % 17.70/17.97 (define @t86 () (@list @t82)) % 17.70/17.97 (define @t87 () (forall @t86 @t85)) % 17.70/17.97 (define @t88 () (forall @t86 @t83)) % 17.70/17.97 (define @t89 () (or @t84 @t88)) % 17.70/17.97 (define @t90 () (forall @t8 (= @t22 (and @t20 (forall @t18 (or (not @t17) @t16)))))) % 17.70/17.97 (define @t91 () (= @t9 @t56)) % 17.70/17.98 (define @t92 () (@list tptp.xQ)) % 17.70/17.98 (define @t93 () (@var "BOUND_VARIABLE_8463" $$unsorted)) % 17.70/17.98 (define @t94 () (tptp.aElementOf0 @t34 @t93)) % 17.70/17.98 (define @t95 () (and @t66 (= @t5 @t65))) % 17.70/17.98 (define @t96 () (forall @t39 (= @t94 @t95))) % 17.70/17.98 (define @t97 () (tptp.aSet0 @t93)) % 17.70/17.98 (define @t98 () (and @t97 @t96)) % 17.70/17.98 (define @t99 () (= (= @t93 @t71) @t98)) % 17.70/17.98 (define @t100 () (not @t50)) % 17.70/17.98 (define @t101 () (or @t84 @t100 @t99)) % 17.70/17.98 (define @t102 () (@list @t1 @t5 @t93)) % 17.70/17.98 (define @t103 () (forall @t102 @t101)) % 17.70/17.98 (define @t104 () (@list @t93)) % 17.70/17.98 (define @t105 () (forall @t104 @t101)) % 17.70/17.98 (define @t106 () (forall @t104 @t99)) % 17.70/17.98 (define @t107 () (or @t84 @t100 @t106)) % 17.70/17.98 (define @t108 () (forall @t18 (= @t72 (and @t32 (forall @t39 (= @t38 @t95)))))) % 17.70/17.98 (define @t109 () (or @t84 @t100 @t108)) % 17.70/17.98 (define @t110 () (tptp.aSubsetOf0 @t34 tptp.xS)) % 17.70/17.98 (define @t111 () (and @t110 (= @t65 tptp.xk))) % 17.70/17.98 (define @t112 () (tptp.aElementOf0 @t34 @t79)) % 17.70/17.98 (define @t113 () (forall @t39 (= @t112 @t111))) % 17.70/17.98 (define @t114 () (tptp.aSet0 @t79)) % 17.70/17.98 (define @t115 () (and @t114 @t113)) % 17.70/17.98 (define @t116 () (and @t110 (= tptp.xk @t65))) % 17.70/17.98 (define @t117 () (= @t116 @t112)) % 17.70/17.98 (define @t118 () (forall @t39 @t117)) % 17.70/17.98 (define @t119 () (and @t114 @t118)) % 17.70/17.98 (define @t120 () (= (= @t79 @t79) @t119)) % 17.70/17.98 (define @t121 () (not @t77)) % 17.70/17.98 (define @t122 () (not @t78)) % 17.70/17.98 (define @t123 () (or @t122 @t121 @t120)) % 17.70/17.98 (define @t124 () (forall @t102 (or @t84 @t100 (= (= @t71 @t93) (and @t97 (forall @t39 (= @t95 @t94))))))) % 17.70/17.98 (define @t125 () (or @t122 @t121 @t115)) % 17.70/17.98 (define @t126 () (@list false)) % 17.70/17.98 (define @t127 () (tptp.sbrdtbr0 tptp.xQ)) % 17.70/17.98 (define @t128 () (tptp.aSubsetOf0 tptp.xQ tptp.xS)) % 17.70/17.98 (define @t129 () (and @t128 (= @t127 tptp.xk))) % 17.70/17.98 (define @t130 () (= @t80 @t129)) % 17.70/17.98 (define @t131 () (= tptp.xk @t127)) % 17.70/17.98 (define @t132 () (and @t128 @t131)) % 17.70/17.98 (define @t133 () (= @t80 @t132)) % 17.70/17.98 (define @t134 () (not @t132)) % 17.70/17.98 (define @t135 () (@list @t132)) % 17.70/17.98 (define @t136 () (tptp.aElementOf0 @t127 tptp.szNzAzT0)) % 17.70/17.98 (define @t137 () (= @t81 @t136)) % 17.70/17.98 (define @t138 () (not @t137)) % 17.70/17.98 (define @t139 () (@list true false)) % 17.70/17.98 (define @t140 () (tptp.aSet0 tptp.xQ)) % 17.70/17.98 (define @t141 () (not @t140)) % 17.70/17.98 (define @t142 () (or @t141 @t137)) % 17.70/17.98 (define @t143 () (and @t140 (forall @t18 (or (not (tptp.aElementOf0 @t15 tptp.xQ)) (tptp.aElementOf0 @t15 tptp.xS))))) % 17.70/17.98 (define @t144 () (not @t143)) % 17.70/17.98 (define @t145 () (= @t128 @t143)) % 17.70/17.98 (define @t146 () (not @t145)) % 17.70/17.98 (define @t147 () (or @t122 @t145)) % 17.70/17.98 (assume @p1 (forall @t3 (=> @t2 true))) % 17.70/17.98 (assume @p2 (forall @t3 (=> @t4 true))) % 17.70/17.98 (assume @p3 (forall @t3 (=> @t2 (forall @t8 (=> @t7 @t6))))) % 17.70/17.98 (assume @p4 (forall @t3 (=> @t2 (=> @t9 true)))) % 17.70/17.98 (assume @p5 (forall @t3 (= @t10 (and @t2 (not (exists @t8 @t7)))))) % 17.70/17.98 (assume @p6 (tptp.isFinite0 tptp.slcrc0)) % 17.70/17.98 (assume @p7 (forall @t3 (=> @t2 (=> @t11 true)))) % 17.70/17.98 (assume @p8 (forall @t3 (=> @t13 @t12))) % 17.70/17.98 (assume @p9 (forall @t3 (=> @t13 @t14))) % 17.70/17.98 (assume @p10 @t26) % 17.70/17.98 (assume @p11 (forall @t3 (=> @t28 (forall @t8 (=> @t22 @t27))))) % 17.70/17.98 (assume @p12 (forall @t3 (=> @t2 (tptp.aSubsetOf0 @t1 @t1)))) % 17.70/17.98 (assume @p13 (forall @t31 (=> (and @t2 @t20) (=> (and @t30 @t22) @t29)))) % 17.70/17.98 (assume @p14 (forall @t33 (=> (and @t2 @t20 @t32) (=> (and @t30 (tptp.aSubsetOf0 @t5 @t15)) (tptp.aSubsetOf0 @t1 @t15))))) % 17.70/17.98 (assume @p15 (forall @t31 (=> @t41 (forall @t18 (= (= @t15 @t40) (and @t32 (forall @t39 (= @t38 (and @t37 (or @t36 @t35)))))))))) % 17.70/17.98 (assume @p16 (forall @t31 (=> @t41 (forall @t18 (= (= @t15 @t42) (and @t32 (forall @t39 (= @t38 (and @t37 @t36 (not @t35)))))))))) % 17.70/17.98 (assume @p17 (forall @t3 (=> @t2 (forall @t8 (=> @t7 (= (tptp.sdtpldt0 @t42 @t5) @t1)))))) % 17.70/17.98 (assume @p18 (forall @t31 (=> (and @t4 @t20) (=> (not (tptp.aElementOf0 @t1 @t5)) (= (tptp.sdtmndt0 @t43 @t1) @t5))))) % 17.70/17.98 (assume @p19 (forall @t3 (=> @t4 (forall @t8 (=> @t44 (tptp.isCountable0 @t43)))))) % 17.70/17.98 (assume @p20 (forall @t3 (=> @t4 (forall @t8 (=> @t44 (tptp.isCountable0 @t45)))))) % 17.70/17.98 (assume @p21 (forall @t3 (=> @t4 (forall @t8 (=> @t46 (tptp.isFinite0 @t43)))))) % 17.70/17.98 (assume @p22 (forall @t3 (=> @t4 (forall @t8 (=> @t46 (tptp.isFinite0 @t45)))))) % 17.70/17.98 (assume @p23 (and (tptp.aSet0 tptp.szNzAzT0) (tptp.isCountable0 tptp.szNzAzT0))) % 17.70/17.98 (assume @p24 (tptp.aElementOf0 tptp.sz00 tptp.szNzAzT0)) % 17.70/17.98 (assume @p25 (forall @t3 (=> @t48 (and (tptp.aElementOf0 @t47 tptp.szNzAzT0) (not (= @t47 tptp.sz00)))))) % 17.70/17.98 (assume @p26 (forall @t31 (=> @t51 (=> (= @t47 @t49) @t29)))) % 17.70/17.98 (assume @p27 (forall @t3 (=> @t48 (or (= @t1 tptp.sz00) (exists @t8 (and @t50 (= @t1 @t49))))))) % 17.70/17.98 (assume @p28 (forall @t3 (=> @t48 (not (= @t1 @t47))))) % 17.70/17.98 (assume @p29 (forall @t31 (=> @t51 (=> @t52 true)))) % 17.70/17.98 (assume @p30 (forall @t3 (=> @t48 (tptp.sdtlseqdt0 tptp.sz00 @t1)))) % 17.70/17.98 (assume @p31 (forall @t3 (=> @t48 (not (tptp.sdtlseqdt0 @t47 tptp.sz00))))) % 17.70/17.98 (assume @p32 (forall @t31 (=> @t51 (= @t52 (tptp.sdtlseqdt0 @t47 @t49))))) % 17.70/17.98 (assume @p33 (forall @t3 (=> @t48 (tptp.sdtlseqdt0 @t1 @t47)))) % 17.70/17.98 (assume @p34 (forall @t3 (=> @t48 (tptp.sdtlseqdt0 @t1 @t1)))) % 17.70/17.98 (assume @p35 (forall @t31 (=> @t51 (=> (and @t52 (tptp.sdtlseqdt0 @t5 @t1)) @t29)))) % 17.70/17.98 (assume @p36 (forall @t33 (=> (and @t48 @t50 @t54) (=> (and @t52 @t53) (tptp.sdtlseqdt0 @t1 @t15))))) % 17.70/17.98 (assume @p37 (forall @t31 (=> @t51 (or @t52 (tptp.sdtlseqdt0 @t49 @t1))))) % 17.70/17.98 (assume @p38 (forall @t31 (=> @t51 (=> (tptp.iLess0 @t1 @t5) true)))) % 17.70/17.98 (assume @p39 (forall @t3 (=> @t48 (tptp.iLess0 @t1 @t47)))) % 17.70/17.98 (assume @p40 (forall @t3 (=> @t2 (tptp.aElement0 @t55)))) % 17.70/17.98 (assume @p41 @t58) % 17.70/17.98 (assume @p42 (forall @t3 (=> @t2 (= (= @t55 tptp.sz00) @t10)))) % 17.70/17.98 (assume @p43 (forall @t3 (=> @t28 (forall @t8 (=> @t6 (=> (not @t7) (= (tptp.sbrdtbr0 @t40) (tptp.szszuzczcdt0 @t55)))))))) % 17.70/17.98 (assume @p44 (forall @t3 (=> @t2 (forall @t8 (=> (and @t9 @t7) (= (tptp.szszuzczcdt0 (tptp.sbrdtbr0 @t42)) @t55)))))) % 17.70/17.98 (assume @p45 (forall @t3 (=> @t2 (forall @t8 (=> (and @t9 @t22) (tptp.sdtlseqdt0 (tptp.sbrdtbr0 @t5) @t55)))))) % 17.70/17.98 (assume @p46 (forall @t31 (=> @t59 (=> (and @t9 (tptp.sdtlseqdt0 @t5 @t55)) (exists @t18 (and (tptp.aSubsetOf0 @t15 @t1) (= (tptp.sbrdtbr0 @t15) @t5))))))) % 17.70/17.98 (assume @p47 (forall @t3 (=> (and @t61 @t14) (forall @t8 (= (= @t5 @t60) (and @t7 (forall @t18 (=> @t16 @t53)))))))) % 17.70/17.98 (assume @p48 (forall @t3 (=> (and @t61 @t9 @t14) (forall @t8 (= (= @t5 (tptp.szmzazxdt0 @t1)) (and @t7 (forall @t18 (=> @t16 (tptp.sdtlseqdt0 @t15 @t5))))))))) % 17.70/17.98 (assume @p49 (forall @t31 (=> (and @t61 (tptp.aSubsetOf0 @t5 tptp.szNzAzT0) @t14 (not (= @t5 tptp.slcrc0))) (=> (and (tptp.aElementOf0 @t60 @t5) (tptp.aElementOf0 @t62 @t1)) (= @t60 @t62))))) % 17.70/17.98 (assume @p50 (forall @t3 (=> @t48 (forall @t8 (= (= @t5 @t63) (and @t20 (forall @t18 (= @t17 (and @t54 (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 @t15) @t1)))))))))) % 17.70/17.98 (assume @p51 (forall @t3 (=> @t48 (tptp.isFinite0 @t63)))) % 17.70/17.98 (assume @p52 (= (tptp.slbdtrb0 tptp.sz00) tptp.slcrc0)) % 17.70/17.98 (assume @p53 (forall @t31 (=> @t51 (= (tptp.aElementOf0 @t1 (tptp.slbdtrb0 @t49)) (or (tptp.aElementOf0 @t1 @t64) @t29))))) % 17.70/17.98 (assume @p54 (forall @t31 (=> @t51 (= @t52 (tptp.aSubsetOf0 @t63 @t64))))) % 17.70/17.98 (assume @p55 (forall @t3 (=> (and @t61 @t9) (exists @t8 (and @t50 (tptp.aSubsetOf0 @t1 @t64)))))) % 17.70/17.98 (assume @p56 (forall @t3 (=> @t48 (= (tptp.sbrdtbr0 @t63) @t1)))) % 17.70/17.98 (assume @p57 @t76) % 17.70/17.98 (assume @p58 (forall @t3 (=> @t28 (forall @t8 (=> @t50 (tptp.isFinite0 @t71)))))) % 17.70/17.98 (assume @p59 (forall @t3 (=> (and @t2 @t12) (forall @t8 (=> @t50 (not (= @t71 tptp.slcrc0))))))) % 17.70/17.98 (assume @p60 (forall @t3 (=> @t13 (forall @t8 (=> (and @t50 (not (= @t5 tptp.sz00))) (tptp.isCountable0 @t71)))))) % 17.70/17.98 (assume @p61 @t77) % 17.70/17.98 (assume @p62 (and @t78 (tptp.aSet0 tptp.xT) (not (= tptp.xk tptp.sz00)))) % 17.70/17.98 (assume @p63 (and (tptp.aSubsetOf0 @t79 (tptp.slbdtsldtrb0 tptp.xT tptp.xk)) (not (= @t79 tptp.slcrc0)))) % 17.70/17.98 (assume @p64 (tptp.aElementOf0 tptp.xx tptp.xS)) % 17.70/17.98 (assume @p65 @t80) % 17.70/17.98 (assume @p66 (not @t81)) % 17.70/17.98 (assume @p67 true) % 17.70/17.98 (step @p68 :rule and_elim :premises (@p62) :args (0)) % 17.70/17.98 (step @p69 :rule quant-merge-prenex :args ((= (forall @t3 @t87) (forall (@list @t1 @t82) @t85)))) % 17.70/17.98 (step @p70 :rule alpha_equiv :args (@t88 (@list @t82) (@list @t5))) % 17.70/17.98 (step @p71 :rule refl :args (@t84)) % 17.70/17.98 (step @p72 :rule nary_cong :premises (@p71 @p70) :args (@t89)) % 17.70/17.98 (step @p73 :rule quant-miniscope-or :args ((= @t87 @t89))) % 17.70/17.98 (step @p74 :rule trans :premises (@p73 @p72)) % 17.70/17.98 (step @p75 :rule symm :premises (@p74)) % 17.70/17.98 (step @p76 :rule cong :premises (@p75) :args ((forall @t3 (or @t84 @t90)))) % 17.70/17.98 (step @p77 :rule trans :premises (@p76 @p69)) % 17.70/17.98 (step @p78 :rule bool-impl-elim :args (@t2 @t90)) % 17.70/17.98 (step @p79 :rule cong :premises (@p78) :args ((forall @t3 (=> @t2 @t90)))) % 17.70/17.98 (step @p80 :rule trans :premises (@p79 @p77)) % 17.70/17.98 (step @p81 :rule bool-impl-elim :args (@t17 @t16)) % 17.70/17.98 (step @p82 :rule cong :premises (@p81) :args (@t19)) % 17.70/17.98 (step @p83 :rule refl :args (@t20)) % 17.70/17.98 (step @p84 :rule nary_cong :premises (@p83 @p82) :args (@t21)) % 17.70/17.98 (step @p85 :rule refl :args (@t22)) % 17.70/17.98 (step @p86 :rule cong :premises (@p85 @p84) :args (@t23)) % 17.70/17.98 (step @p87 :rule cong :premises (@p86) :args (@t24)) % 17.70/17.98 (step @p88 :rule refl :args (@t2)) % 17.70/17.98 (step @p89 :rule cong :premises (@p88 @p87) :args (@t25)) % 17.70/17.98 (step @p90 :rule cong :premises (@p89) :args (@t26)) % 17.70/17.98 (step @p91 :rule trans :premises (@p90 @p80)) % 17.70/17.98 (step @p92 :rule eq_resolve :premises (@p10 @p91)) % 17.70/17.98 (step @p93 :rule instantiate :premises (@p92) :args ((@list tptp.xS tptp.xQ))) % 17.70/17.98 (step @p94 :rule bool-impl-elim :args (@t2 @t91)) % 17.70/17.98 (step @p95 :rule cong :premises (@p94) :args ((forall @t3 (=> @t2 @t91)))) % 17.70/17.98 (step @p96 :rule eq-symm :args (@t56 @t9)) % 17.70/17.98 (step @p97 :rule cong :premises (@p88 @p96) :args (@t57)) % 17.70/17.98 (step @p98 :rule cong :premises (@p97) :args (@t58)) % 17.70/17.98 (step @p99 :rule trans :premises (@p98 @p95)) % 17.70/17.98 (step @p100 :rule eq_resolve :premises (@p41 @p99)) % 17.70/17.98 (step @p101 :rule instantiate :premises (@p100) :args (@t92)) % 17.70/17.98 (step @p102 :rule true_intro :premises (@p61)) % 17.70/17.98 (step @p103 :rule refl :args (tptp.szNzAzT0)) % 17.70/17.98 (step @p104 :rule eq-symm :args (@t94 @t95)) % 17.70/17.98 (step @p105 :rule cong :premises (@p104) :args (@t96)) % 17.70/17.98 (step @p106 :rule refl :args (@t97)) % 17.70/17.98 (step @p107 :rule nary_cong :premises (@p106 @p105) :args (@t98)) % 17.70/17.98 (step @p108 :rule eq-symm :args (@t93 @t71)) % 17.70/17.98 (step @p109 :rule cong :premises (@p108 @p107) :args (@t99)) % 17.70/17.98 (step @p110 :rule refl :args (@t100)) % 17.70/17.98 (step @p111 :rule refl :args (@t84)) % 17.70/17.98 (step @p112 :rule nary_cong :premises (@p111 @p110 @p109) :args (@t101)) % 17.70/17.98 (step @p113 :rule cong :premises (@p112) :args (@t103)) % 17.70/17.98 (step @p114 :rule quant-merge-prenex :args ((= (forall @t31 @t105) @t103))) % 17.70/17.98 (step @p115 :rule alpha_equiv :args (@t106 (@list @t93) (@list @t15))) % 17.70/17.98 (step @p116 :rule refl :args (@t100)) % 17.70/17.98 (step @p117 :rule nary_cong :premises (@p71 @p116 @p115) :args (@t107)) % 17.70/17.98 (step @p118 :rule quant-miniscope-or :args ((= @t105 @t107))) % 17.70/17.98 (step @p119 :rule trans :premises (@p118 @p117)) % 17.70/17.98 (step @p120 :rule symm :premises (@p119)) % 17.70/17.98 (step @p121 :rule cong :premises (@p120) :args ((forall @t31 @t109))) % 17.70/17.98 (step @p122 :rule trans :premises (@p121 @p114)) % 17.70/17.98 (step @p123 :rule trans :premises (@p122 @p113)) % 17.70/17.98 (step @p124 :rule aci_norm :args ((= (or (or @t84 @t100) @t108) @t109))) % 17.70/17.98 (step @p125 :rule refl :args (@t108)) % 17.70/17.98 (step @p126 :rule bool-and-de-morgan :args (@t2 @t50 true)) % 17.70/17.98 (step @p127 :rule nary_cong :premises (@p126 @p125) :args ((or (not @t59) @t108))) % 17.70/17.98 (step @p128 :rule trans :premises (@p127 @p124)) % 17.70/17.98 (step @p129 :rule bool-impl-elim :args (@t59 @t108)) % 17.70/17.98 (step @p130 :rule trans :premises (@p129 @p128)) % 17.70/17.98 (step @p131 :rule cong :premises (@p130) :args ((forall @t31 (=> @t59 @t108)))) % 17.70/17.98 (step @p132 :rule trans :premises (@p131 @p123)) % 17.70/17.98 (step @p133 :rule eq-symm :args (@t65 @t5)) % 17.70/17.98 (step @p134 :rule refl :args (@t66)) % 17.70/17.98 (step @p135 :rule nary_cong :premises (@p134 @p133) :args (@t67)) % 17.70/17.98 (step @p136 :rule refl :args (@t38)) % 17.70/17.98 (step @p137 :rule cong :premises (@p136 @p135) :args (@t68)) % 17.70/17.98 (step @p138 :rule cong :premises (@p137) :args (@t69)) % 17.70/17.98 (step @p139 :rule refl :args (@t32)) % 17.70/17.98 (step @p140 :rule nary_cong :premises (@p139 @p138) :args (@t70)) % 17.70/17.98 (step @p141 :rule refl :args (@t72)) % 17.70/17.98 (step @p142 :rule cong :premises (@p141 @p140) :args (@t73)) % 17.70/17.98 (step @p143 :rule cong :premises (@p142) :args (@t74)) % 17.70/17.98 (step @p144 :rule refl :args (@t59)) % 17.70/17.98 (step @p145 :rule cong :premises (@p144 @p143) :args (@t75)) % 17.70/17.98 (step @p146 :rule cong :premises (@p145) :args (@t76)) % 17.70/17.98 (step @p147 :rule trans :premises (@p146 @p132)) % 17.70/17.98 (step @p148 :rule eq_resolve :premises (@p57 @p147)) % 17.70/17.98 (step @p149 :rule bool-eq-true :args (@t115)) % 17.70/17.98 (step @p150 :rule eq-symm :args (true @t115)) % 17.70/17.98 (step @p151 :rule trans :premises (@p150 @p149)) % 17.70/17.98 (step @p152 :rule eq-symm :args (@t111 @t112)) % 17.70/17.98 (step @p153 :rule refl :args (@t112)) % 17.70/17.98 (step @p154 :rule eq-symm :args (tptp.xk @t65)) % 17.70/17.98 (step @p155 :rule refl :args (@t110)) % 17.70/17.98 (step @p156 :rule nary_cong :premises (@p155 @p154) :args (@t116)) % 17.70/17.98 (step @p157 :rule cong :premises (@p156 @p153) :args (@t117)) % 17.70/17.98 (step @p158 :rule trans :premises (@p157 @p152)) % 17.70/17.98 (step @p159 :rule cong :premises (@p158) :args (@t118)) % 17.70/17.98 (step @p160 :rule refl :args (@t114)) % 17.70/17.98 (step @p161 :rule nary_cong :premises (@p160 @p159) :args (@t119)) % 17.70/17.98 (step @p162 :rule eq-refl :args (@t79)) % 17.70/17.98 (step @p163 :rule cong :premises (@p162 @p161) :args (@t120)) % 17.70/17.98 (step @p164 :rule trans :premises (@p163 @p151)) % 17.70/17.98 (step @p165 :rule refl :args (@t121)) % 17.70/17.98 (step @p166 :rule refl :args (@t122)) % 17.70/17.98 (step @p167 :rule nary_cong :premises (@p166 @p165 @p164) :args (@t123)) % 17.70/17.98 (step @p168 :rule refl :args (@t124)) % 17.70/17.98 (step @p169 :rule cong :premises (@p168 @p167) :args ((=> @t124 @t123))) % 17.70/17.98 (assume-push @p225 @t124) % 17.70/17.98 (step @p171 :rule instantiate :premises (@p148) :args ((@list tptp.xS tptp.xk @t79))) % 17.70/17.98 (step-pop @p226 :rule scope :premises (@p171)) % 17.70/17.98 (step @p172 :rule process_scope :premises (@p226) :args (@t123)) % 17.70/17.98 (step @p174 :rule eq_resolve :premises (@p172 @p169)) % 17.70/17.98 (step @p175 :rule implies_elim :premises (@p174)) % 17.70/17.98 (step @p176 :rule chain_m_resolution :premises (@p175 @p148) :args (@t125 @t126 (@list @t124))) % 17.70/17.98 (step @p177 :rule cnf_or_pos :args (@t125)) % 17.70/17.98 (step @p178 :rule reordering :premises (@p177) :args ((or @t121 @t122 @t115 (not @t125)))) % 17.70/17.98 (step @p179 :rule chain_m_resolution :premises (@p178 @p61 @p68 @p176) :args (@t115 (@list false false false) (@list @t77 @t78 @t125))) % 17.70/17.98 (step @p180 :rule cnf_and_pos :args (@t115 1)) % 17.70/17.98 (step @p181 :rule reordering :premises (@p180) :args ((or @t113 (not @t115)))) % 17.70/17.98 (step @p182 :rule chain_m_resolution :premises (@p181 @p179) :args (@t113 @t126 (@list @t115))) % 17.70/17.98 (step @p183 :rule eq-symm :args (@t127 tptp.xk)) % 17.70/17.98 (step @p184 :rule refl :args (@t128)) % 17.70/17.98 (step @p185 :rule nary_cong :premises (@p184 @p183) :args (@t129)) % 17.70/17.98 (step @p186 :rule refl :args (@t80)) % 17.70/17.98 (step @p187 :rule cong :premises (@p186 @p185) :args (@t130)) % 17.70/17.98 (step @p188 :rule refl :args (@t113)) % 17.70/17.98 (step @p189 :rule cong :premises (@p188 @p187) :args ((=> @t113 @t130))) % 17.70/17.98 (assume-push @p227 @t113) % 17.70/17.98 (step @p191 :rule instantiate :premises (@p182) :args (@t92)) % 17.70/17.98 (step-pop @p228 :rule scope :premises (@p191)) % 17.70/17.98 (step @p192 :rule process_scope :premises (@p228) :args (@t130)) % 17.70/17.98 (step @p194 :rule eq_resolve :premises (@p192 @p189)) % 17.70/17.98 (step @p195 :rule implies_elim :premises (@p194)) % 17.70/17.98 (step @p196 :rule chain_m_resolution :premises (@p195 @p182) :args (@t133 @t126 (@list @t113))) % 17.70/17.98 (step @p197 :rule cnf_equiv_pos1 :args (@t133)) % 17.70/17.98 (step @p198 :rule reordering :premises (@p197) :args ((or (not @t80) @t132 (not @t133)))) % 17.70/17.98 (step @p199 :rule chain_m_resolution :premises (@p198 @p65 @p196) :args (@t132 (@list false false) (@list @t80 @t133))) % 17.70/17.98 (step @p200 :rule cnf_and_pos :args (@t132 1)) % 17.70/17.98 (step @p201 :rule reordering :premises (@p200) :args ((or @t131 @t134))) % 17.70/17.98 (step @p202 :rule chain_m_resolution :premises (@p201 @p199) :args (@t131 @t126 @t135)) % 17.70/17.98 (step @p203 :rule symm :premises (@p202)) % 17.70/17.98 (step @p204 :rule cong :premises (@p203 @p103) :args (@t136)) % 17.70/17.98 (step @p205 :rule trans :premises (@p204 @p102)) % 17.70/17.98 (step @p206 :rule true_elim :premises (@p205)) % 17.70/17.98 (step @p207 :rule cnf_equiv_pos2 :args (@t137)) % 17.70/17.98 (step @p208 :rule reordering :premises (@p207) :args ((or @t81 (not @t136) @t138))) % 17.70/17.98 (step @p209 :rule chain_m_resolution :premises (@p208 @p66 @p206) :args (@t138 @t139 (@list @t81 @t136))) % 17.70/17.98 (step @p210 :rule cnf_or_pos :args (@t142)) % 17.70/17.98 (step @p211 :rule reordering :premises (@p210) :args ((or @t141 @t137 (not @t142)))) % 17.70/17.98 (step @p212 :rule chain_m_resolution :premises (@p211 @p209 @p101) :args (@t141 @t139 (@list @t137 @t142))) % 17.70/17.98 (step @p213 :rule cnf_and_pos :args (@t143 0)) % 17.70/17.98 (step @p214 :rule reordering :premises (@p213) :args ((or @t140 @t144))) % 17.70/17.98 (step @p215 :rule chain_m_resolution :premises (@p214 @p212) :args (@t144 (@list true) (@list @t140))) % 17.70/17.98 (step @p216 :rule cnf_and_pos :args (@t132 0)) % 17.70/17.98 (step @p217 :rule reordering :premises (@p216) :args ((or @t128 @t134))) % 17.70/17.98 (step @p218 :rule chain_m_resolution :premises (@p217 @p199) :args (@t128 @t126 @t135)) % 17.70/17.98 (step @p219 :rule cnf_equiv_pos1 :args (@t145)) % 17.70/17.98 (step @p220 :rule reordering :premises (@p219) :args ((or (not @t128) @t143 @t146))) % 17.70/17.98 (step @p221 :rule chain_m_resolution :premises (@p220 @p218 @p215) :args (@t146 (@list false true) (@list @t128 @t143))) % 17.70/17.98 (step @p222 :rule cnf_or_pos :args (@t147)) % 17.70/17.98 (step @p223 :rule reordering :premises (@p222) :args ((or @t122 @t145 (not @t147)))) % 17.70/17.98 (step @p224 false :rule chain_m_resolution :premises (@p223 @p221 @p93 @p68) :args (false (@list true false false) (@list @t145 @t147 @t78))) % 17.70/17.98 ) % 17.70/17.98 % SZS output end Proof % 17.70/17.98 % cvc5 exiting %------------------------------------------------------------------------------