%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM557+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 : n013.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 16.32s 16.57s % Output : Proof 16.32s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM557+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 % 0.17/0.35 % Computer : n013.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Tue Jun 2 11:29:15 EDT 2026 % 0.17/0.35 % CPUTime : % 0.32/0.51 %----Proving TF0_NAR, FOF, or CNF % 16.32/16.57 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 16.32/16.57 --- Run --no-e-matching --full-saturate-quant at 6... % 16.32/16.57 % SZS status Theorem % 16.32/16.57 % SZS output start Proof % 16.32/16.57 ( % 16.32/16.57 (declare-sort $$unsorted 0) % 16.32/16.57 (declare-const tptp.xP $$unsorted) % 16.32/16.57 (declare-const tptp.xT $$unsorted) % 16.32/16.57 (declare-const tptp.xy $$unsorted) % 16.32/16.57 (declare-const tptp.slbdtsldtrb0 (-> $$unsorted $$unsorted $$unsorted)) % 16.32/16.57 (declare-const tptp.slbdtrb0 (-> $$unsorted $$unsorted)) % 16.32/16.57 (declare-const tptp.szmzazxdt0 (-> $$unsorted $$unsorted)) % 16.32/16.57 (declare-const tptp.szmzizndt0 (-> $$unsorted $$unsorted)) % 16.32/16.57 (declare-const tptp.sbrdtbr0 (-> $$unsorted $$unsorted)) % 16.32/16.57 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 16.32/16.57 (declare-const tptp.xQ $$unsorted) % 16.32/16.57 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 16.32/16.57 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 16.32/16.57 (declare-const tptp.xS $$unsorted) % 16.32/16.57 (declare-const tptp.isFinite0 (-> $$unsorted Bool)) % 16.32/16.57 (declare-const tptp.xx $$unsorted) % 16.32/16.57 (declare-const tptp.isCountable0 (-> $$unsorted Bool)) % 16.32/16.57 (declare-const tptp.slcrc0 $$unsorted) % 16.32/16.57 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 16.32/16.57 (declare-const tptp.aSubsetOf0 (-> $$unsorted $$unsorted Bool)) % 16.32/16.57 (declare-const tptp.sdtlseqdt0 (-> $$unsorted $$unsorted Bool)) % 16.32/16.57 (declare-const tptp.xk $$unsorted) % 16.32/16.57 (declare-const tptp.szszuzczcdt0 (-> $$unsorted $$unsorted)) % 16.32/16.57 (declare-const tptp.sdtmndt0 (-> $$unsorted $$unsorted $$unsorted)) % 16.32/16.57 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 16.32/16.57 (declare-const tptp.szNzAzT0 $$unsorted) % 16.32/16.57 (declare-const tptp.sz00 $$unsorted) % 16.32/16.57 (define @t1 () (@var "W0" $$unsorted)) % 16.32/16.57 (define @t2 () (tptp.aSet0 @t1)) % 16.32/16.57 (define @t3 () (@list @t1)) % 16.32/16.57 (define @t4 () (tptp.aElement0 @t1)) % 16.32/16.57 (define @t5 () (@var "W1" $$unsorted)) % 16.32/16.57 (define @t6 () (tptp.aElement0 @t5)) % 16.32/16.57 (define @t7 () (tptp.aElementOf0 @t5 @t1)) % 16.32/16.57 (define @t8 () (@list @t5)) % 16.32/16.57 (define @t9 () (tptp.isFinite0 @t1)) % 16.32/16.57 (define @t10 () (= @t1 tptp.slcrc0)) % 16.32/16.57 (define @t11 () (tptp.isCountable0 @t1)) % 16.32/16.57 (define @t12 () (not @t9)) % 16.32/16.57 (define @t13 () (and @t2 @t11)) % 16.32/16.57 (define @t14 () (not @t10)) % 16.32/16.57 (define @t15 () (@var "W2" $$unsorted)) % 16.32/16.57 (define @t16 () (tptp.aElementOf0 @t15 @t1)) % 16.32/16.57 (define @t17 () (tptp.aElementOf0 @t15 @t5)) % 16.32/16.57 (define @t18 () (@list @t15)) % 16.32/16.57 (define @t19 () (tptp.aSet0 @t5)) % 16.32/16.57 (define @t20 () (tptp.aSubsetOf0 @t5 @t1)) % 16.32/16.57 (define @t21 () (tptp.isFinite0 @t5)) % 16.32/16.57 (define @t22 () (and @t2 @t9)) % 16.32/16.57 (define @t23 () (= @t1 @t5)) % 16.32/16.57 (define @t24 () (tptp.aSubsetOf0 @t1 @t5)) % 16.32/16.57 (define @t25 () (@list @t1 @t5)) % 16.32/16.57 (define @t26 () (tptp.aSet0 @t15)) % 16.32/16.57 (define @t27 () (@list @t1 @t5 @t15)) % 16.32/16.57 (define @t28 () (@var "W3" $$unsorted)) % 16.32/16.57 (define @t29 () (= @t28 @t5)) % 16.32/16.57 (define @t30 () (tptp.aElementOf0 @t28 @t1)) % 16.32/16.57 (define @t31 () (tptp.aElement0 @t28)) % 16.32/16.57 (define @t32 () (tptp.aElementOf0 @t28 @t15)) % 16.32/16.57 (define @t33 () (@list @t28)) % 16.32/16.57 (define @t34 () (tptp.sdtpldt0 @t1 @t5)) % 16.32/16.57 (define @t35 () (and @t2 @t6)) % 16.32/16.57 (define @t36 () (tptp.sdtmndt0 @t1 @t5)) % 16.32/16.57 (define @t37 () (tptp.sdtpldt0 @t5 @t1)) % 16.32/16.57 (define @t38 () (and @t19 (tptp.isCountable0 @t5))) % 16.32/16.57 (define @t39 () (tptp.sdtmndt0 @t5 @t1)) % 16.32/16.57 (define @t40 () (and @t19 @t21)) % 16.32/16.57 (define @t41 () (tptp.szszuzczcdt0 @t1)) % 16.32/16.57 (define @t42 () (tptp.aElementOf0 @t1 tptp.szNzAzT0)) % 16.32/16.57 (define @t43 () (tptp.szszuzczcdt0 @t5)) % 16.32/16.57 (define @t44 () (tptp.aElementOf0 @t5 tptp.szNzAzT0)) % 16.32/16.57 (define @t45 () (and @t42 @t44)) % 16.32/16.57 (define @t46 () (tptp.sdtlseqdt0 @t1 @t5)) % 16.32/16.57 (define @t47 () (tptp.sdtlseqdt0 @t5 @t15)) % 16.32/16.57 (define @t48 () (tptp.aElementOf0 @t15 tptp.szNzAzT0)) % 16.32/16.57 (define @t49 () (tptp.sbrdtbr0 @t1)) % 16.32/16.57 (define @t50 () (and @t2 @t44)) % 16.32/16.57 (define @t51 () (tptp.szmzizndt0 @t1)) % 16.32/16.57 (define @t52 () (tptp.aSubsetOf0 @t1 tptp.szNzAzT0)) % 16.32/16.57 (define @t53 () (tptp.szmzizndt0 @t5)) % 16.32/16.57 (define @t54 () (tptp.slbdtrb0 @t1)) % 16.32/16.57 (define @t55 () (tptp.slbdtrb0 @t5)) % 16.32/16.57 (define @t56 () (tptp.sbrdtbr0 @t28)) % 16.32/16.57 (define @t57 () (tptp.aSubsetOf0 @t28 @t1)) % 16.32/16.57 (define @t58 () (and @t57 (= @t56 @t5))) % 16.32/16.57 (define @t59 () (= @t32 @t58)) % 16.32/16.57 (define @t60 () (forall @t33 @t59)) % 16.32/16.57 (define @t61 () (and @t26 @t60)) % 16.32/16.57 (define @t62 () (tptp.slbdtsldtrb0 @t1 @t5)) % 16.32/16.57 (define @t63 () (= @t15 @t62)) % 16.32/16.57 (define @t64 () (= @t63 @t61)) % 16.32/16.57 (define @t65 () (forall @t18 @t64)) % 16.32/16.57 (define @t66 () (=> @t50 @t65)) % 16.32/16.57 (define @t67 () (forall @t25 @t66)) % 16.32/16.57 (define @t68 () (tptp.aElementOf0 tptp.xk tptp.szNzAzT0)) % 16.32/16.57 (define @t69 () (tptp.aSet0 tptp.xS)) % 16.32/16.57 (define @t70 () (tptp.slbdtsldtrb0 tptp.xS tptp.xk)) % 16.32/16.57 (define @t71 () (tptp.sbrdtbr0 tptp.xQ)) % 16.32/16.57 (define @t72 () (tptp.sdtmndt0 tptp.xQ tptp.xy)) % 16.32/16.57 (define @t73 () (tptp.sdtpldt0 @t72 tptp.xx)) % 16.32/16.57 (define @t74 () (tptp.sbrdtbr0 tptp.xP)) % 16.32/16.57 (define @t75 () (tptp.aSubsetOf0 tptp.xP tptp.xS)) % 16.32/16.57 (define @t76 () (tptp.aElementOf0 tptp.xP @t70)) % 16.32/16.57 (define @t77 () (not @t76)) % 16.32/16.57 (define @t78 () (tptp.sbrdtbr0 @t73)) % 16.32/16.57 (define @t79 () (= @t71 @t78)) % 16.32/16.57 (define @t80 () (tptp.aSubsetOf0 @t73 tptp.xS)) % 16.32/16.57 (define @t81 () (and @t80 @t79)) % 16.32/16.57 (define @t82 () (@var "BOUND_VARIABLE_8491" $$unsorted)) % 16.32/16.57 (define @t83 () (tptp.aElementOf0 @t28 @t82)) % 16.32/16.57 (define @t84 () (and @t57 (= @t5 @t56))) % 16.32/16.57 (define @t85 () (forall @t33 (= @t83 @t84))) % 16.32/16.57 (define @t86 () (tptp.aSet0 @t82)) % 16.32/16.57 (define @t87 () (and @t86 @t85)) % 16.32/16.57 (define @t88 () (= (= @t82 @t62) @t87)) % 16.32/16.57 (define @t89 () (not @t44)) % 16.32/16.57 (define @t90 () (not @t2)) % 16.32/16.57 (define @t91 () (or @t90 @t89 @t88)) % 16.32/16.57 (define @t92 () (@list @t1 @t5 @t82)) % 16.32/16.57 (define @t93 () (forall @t92 @t91)) % 16.32/16.57 (define @t94 () (@list @t82)) % 16.32/16.57 (define @t95 () (forall @t94 @t91)) % 16.32/16.57 (define @t96 () (forall @t94 @t88)) % 16.32/16.57 (define @t97 () (or @t90 @t89 @t96)) % 16.32/16.57 (define @t98 () (forall @t18 (= @t63 (and @t26 (forall @t33 (= @t32 @t84)))))) % 16.32/16.57 (define @t99 () (or @t90 @t89 @t98)) % 16.32/16.57 (define @t100 () (tptp.aSubsetOf0 @t28 tptp.xS)) % 16.32/16.57 (define @t101 () (and @t100 (= @t56 @t71))) % 16.32/16.57 (define @t102 () (tptp.slbdtsldtrb0 tptp.xS @t71)) % 16.32/16.57 (define @t103 () (tptp.aElementOf0 @t28 @t102)) % 16.32/16.57 (define @t104 () (forall @t33 (= @t103 @t101))) % 16.32/16.57 (define @t105 () (tptp.aSet0 @t102)) % 16.32/16.57 (define @t106 () (and @t105 @t104)) % 16.32/16.57 (define @t107 () (and @t100 (= @t71 @t56))) % 16.32/16.57 (define @t108 () (= @t107 @t103)) % 16.32/16.57 (define @t109 () (forall @t33 @t108)) % 16.32/16.57 (define @t110 () (and @t105 @t109)) % 16.32/16.57 (define @t111 () (= (= @t102 @t102) @t110)) % 16.32/16.57 (define @t112 () (tptp.aElementOf0 @t71 tptp.szNzAzT0)) % 16.32/16.57 (define @t113 () (not @t112)) % 16.32/16.57 (define @t114 () (not @t69)) % 16.32/16.57 (define @t115 () (or @t114 @t113 @t111)) % 16.32/16.57 (define @t116 () (forall @t92 (or @t90 @t89 (= (= @t62 @t82) (and @t86 (forall @t33 (= @t84 @t83))))))) % 16.32/16.57 (define @t117 () (or @t114 @t113 @t106)) % 16.32/16.57 (define @t118 () (@list false)) % 16.32/16.57 (define @t119 () (and @t80 (= @t78 @t71))) % 16.32/16.57 (define @t120 () (tptp.aElementOf0 @t73 @t102)) % 16.32/16.57 (define @t121 () (= @t120 @t119)) % 16.32/16.57 (define @t122 () (= @t120 @t81)) % 16.32/16.57 (assume @p1 (forall @t3 (=> @t2 true))) % 16.32/16.57 (assume @p2 (forall @t3 (=> @t4 true))) % 16.32/16.57 (assume @p3 (forall @t3 (=> @t2 (forall @t8 (=> @t7 @t6))))) % 16.32/16.57 (assume @p4 (forall @t3 (=> @t2 (=> @t9 true)))) % 16.32/16.57 (assume @p5 (forall @t3 (= @t10 (and @t2 (not (exists @t8 @t7)))))) % 16.32/16.57 (assume @p6 (tptp.isFinite0 tptp.slcrc0)) % 16.32/16.57 (assume @p7 (forall @t3 (=> @t2 (=> @t11 true)))) % 16.32/16.57 (assume @p8 (forall @t3 (=> @t13 @t12))) % 16.32/16.57 (assume @p9 (forall @t3 (=> @t13 @t14))) % 16.32/16.57 (assume @p10 (forall @t3 (=> @t2 (forall @t8 (= @t20 (and @t19 (forall @t18 (=> @t17 @t16)))))))) % 16.32/16.57 (assume @p11 (forall @t3 (=> @t22 (forall @t8 (=> @t20 @t21))))) % 16.32/16.57 (assume @p12 (forall @t3 (=> @t2 (tptp.aSubsetOf0 @t1 @t1)))) % 16.32/16.57 (assume @p13 (forall @t25 (=> (and @t2 @t19) (=> (and @t24 @t20) @t23)))) % 16.32/16.57 (assume @p14 (forall @t27 (=> (and @t2 @t19 @t26) (=> (and @t24 (tptp.aSubsetOf0 @t5 @t15)) (tptp.aSubsetOf0 @t1 @t15))))) % 16.32/16.57 (assume @p15 (forall @t25 (=> @t35 (forall @t18 (= (= @t15 @t34) (and @t26 (forall @t33 (= @t32 (and @t31 (or @t30 @t29)))))))))) % 16.32/16.57 (assume @p16 (forall @t25 (=> @t35 (forall @t18 (= (= @t15 @t36) (and @t26 (forall @t33 (= @t32 (and @t31 @t30 (not @t29)))))))))) % 16.32/16.57 (assume @p17 (forall @t3 (=> @t2 (forall @t8 (=> @t7 (= (tptp.sdtpldt0 @t36 @t5) @t1)))))) % 16.32/16.57 (assume @p18 (forall @t25 (=> (and @t4 @t19) (=> (not (tptp.aElementOf0 @t1 @t5)) (= (tptp.sdtmndt0 @t37 @t1) @t5))))) % 16.32/16.57 (assume @p19 (forall @t3 (=> @t4 (forall @t8 (=> @t38 (tptp.isCountable0 @t37)))))) % 16.32/16.57 (assume @p20 (forall @t3 (=> @t4 (forall @t8 (=> @t38 (tptp.isCountable0 @t39)))))) % 16.32/16.57 (assume @p21 (forall @t3 (=> @t4 (forall @t8 (=> @t40 (tptp.isFinite0 @t37)))))) % 16.32/16.57 (assume @p22 (forall @t3 (=> @t4 (forall @t8 (=> @t40 (tptp.isFinite0 @t39)))))) % 16.32/16.57 (assume @p23 (and (tptp.aSet0 tptp.szNzAzT0) (tptp.isCountable0 tptp.szNzAzT0))) % 16.32/16.57 (assume @p24 (tptp.aElementOf0 tptp.sz00 tptp.szNzAzT0)) % 16.32/16.57 (assume @p25 (forall @t3 (=> @t42 (and (tptp.aElementOf0 @t41 tptp.szNzAzT0) (not (= @t41 tptp.sz00)))))) % 16.32/16.57 (assume @p26 (forall @t25 (=> @t45 (=> (= @t41 @t43) @t23)))) % 16.32/16.57 (assume @p27 (forall @t3 (=> @t42 (or (= @t1 tptp.sz00) (exists @t8 (and @t44 (= @t1 @t43))))))) % 16.32/16.57 (assume @p28 (forall @t3 (=> @t42 (not (= @t1 @t41))))) % 16.32/16.57 (assume @p29 (forall @t25 (=> @t45 (=> @t46 true)))) % 16.32/16.57 (assume @p30 (forall @t3 (=> @t42 (tptp.sdtlseqdt0 tptp.sz00 @t1)))) % 16.32/16.57 (assume @p31 (forall @t3 (=> @t42 (not (tptp.sdtlseqdt0 @t41 tptp.sz00))))) % 16.32/16.57 (assume @p32 (forall @t25 (=> @t45 (= @t46 (tptp.sdtlseqdt0 @t41 @t43))))) % 16.32/16.57 (assume @p33 (forall @t3 (=> @t42 (tptp.sdtlseqdt0 @t1 @t41)))) % 16.32/16.57 (assume @p34 (forall @t3 (=> @t42 (tptp.sdtlseqdt0 @t1 @t1)))) % 16.32/16.57 (assume @p35 (forall @t25 (=> @t45 (=> (and @t46 (tptp.sdtlseqdt0 @t5 @t1)) @t23)))) % 16.32/16.57 (assume @p36 (forall @t27 (=> (and @t42 @t44 @t48) (=> (and @t46 @t47) (tptp.sdtlseqdt0 @t1 @t15))))) % 16.32/16.57 (assume @p37 (forall @t25 (=> @t45 (or @t46 (tptp.sdtlseqdt0 @t43 @t1))))) % 16.32/16.57 (assume @p38 (forall @t25 (=> @t45 (=> (tptp.iLess0 @t1 @t5) true)))) % 16.32/16.57 (assume @p39 (forall @t3 (=> @t42 (tptp.iLess0 @t1 @t41)))) % 16.32/16.57 (assume @p40 (forall @t3 (=> @t2 (tptp.aElement0 @t49)))) % 16.32/16.57 (assume @p41 (forall @t3 (=> @t2 (= (tptp.aElementOf0 @t49 tptp.szNzAzT0) @t9)))) % 16.32/16.57 (assume @p42 (forall @t3 (=> @t2 (= (= @t49 tptp.sz00) @t10)))) % 16.32/16.57 (assume @p43 (forall @t3 (=> @t22 (forall @t8 (=> @t6 (=> (not @t7) (= (tptp.sbrdtbr0 @t34) (tptp.szszuzczcdt0 @t49)))))))) % 16.32/16.57 (assume @p44 (forall @t3 (=> @t2 (forall @t8 (=> (and @t9 @t7) (= (tptp.szszuzczcdt0 (tptp.sbrdtbr0 @t36)) @t49)))))) % 16.32/16.57 (assume @p45 (forall @t3 (=> @t2 (forall @t8 (=> (and @t9 @t20) (tptp.sdtlseqdt0 (tptp.sbrdtbr0 @t5) @t49)))))) % 16.32/16.57 (assume @p46 (forall @t25 (=> @t50 (=> (and @t9 (tptp.sdtlseqdt0 @t5 @t49)) (exists @t18 (and (tptp.aSubsetOf0 @t15 @t1) (= (tptp.sbrdtbr0 @t15) @t5))))))) % 16.32/16.57 (assume @p47 (forall @t3 (=> (and @t52 @t14) (forall @t8 (= (= @t5 @t51) (and @t7 (forall @t18 (=> @t16 @t47)))))))) % 16.32/16.57 (assume @p48 (forall @t3 (=> (and @t52 @t9 @t14) (forall @t8 (= (= @t5 (tptp.szmzazxdt0 @t1)) (and @t7 (forall @t18 (=> @t16 (tptp.sdtlseqdt0 @t15 @t5))))))))) % 16.32/16.57 (assume @p49 (forall @t25 (=> (and @t52 (tptp.aSubsetOf0 @t5 tptp.szNzAzT0) @t14 (not (= @t5 tptp.slcrc0))) (=> (and (tptp.aElementOf0 @t51 @t5) (tptp.aElementOf0 @t53 @t1)) (= @t51 @t53))))) % 16.32/16.57 (assume @p50 (forall @t3 (=> @t42 (forall @t8 (= (= @t5 @t54) (and @t19 (forall @t18 (= @t17 (and @t48 (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 @t15) @t1)))))))))) % 16.32/16.57 (assume @p51 (forall @t3 (=> @t42 (tptp.isFinite0 @t54)))) % 16.32/16.57 (assume @p52 (= (tptp.slbdtrb0 tptp.sz00) tptp.slcrc0)) % 16.32/16.57 (assume @p53 (forall @t25 (=> @t45 (= (tptp.aElementOf0 @t1 (tptp.slbdtrb0 @t43)) (or (tptp.aElementOf0 @t1 @t55) @t23))))) % 16.32/16.57 (assume @p54 (forall @t25 (=> @t45 (= @t46 (tptp.aSubsetOf0 @t54 @t55))))) % 16.32/16.57 (assume @p55 (forall @t3 (=> (and @t52 @t9) (exists @t8 (and @t44 (tptp.aSubsetOf0 @t1 @t55)))))) % 16.32/16.57 (assume @p56 (forall @t3 (=> @t42 (= (tptp.sbrdtbr0 @t54) @t1)))) % 16.32/16.57 (assume @p57 @t67) % 16.32/16.57 (assume @p58 (forall @t3 (=> @t22 (forall @t8 (=> @t44 (tptp.isFinite0 @t62)))))) % 16.32/16.57 (assume @p59 (forall @t3 (=> (and @t2 @t12) (forall @t8 (=> @t44 (not (= @t62 tptp.slcrc0))))))) % 16.32/16.57 (assume @p60 (forall @t3 (=> @t13 (forall @t8 (=> (and @t44 (not (= @t5 tptp.sz00))) (tptp.isCountable0 @t62)))))) % 16.32/16.57 (assume @p61 @t68) % 16.32/16.57 (assume @p62 (and @t69 (tptp.aSet0 tptp.xT) (not (= tptp.xk tptp.sz00)))) % 16.32/16.57 (assume @p63 (and (tptp.aSubsetOf0 @t70 (tptp.slbdtsldtrb0 tptp.xT tptp.xk)) (not (= @t70 tptp.slcrc0)))) % 16.32/16.57 (assume @p64 (tptp.aElementOf0 tptp.xx tptp.xS)) % 16.32/16.57 (assume @p65 (tptp.aElementOf0 tptp.xQ @t70)) % 16.32/16.57 (assume @p66 (and (tptp.aSet0 tptp.xQ) (tptp.isFinite0 tptp.xQ) (= @t71 tptp.xk))) % 16.32/16.57 (assume @p67 (and (tptp.aElement0 tptp.xy) (tptp.aElementOf0 tptp.xy tptp.xQ))) % 16.32/16.57 (assume @p68 (not (tptp.aElementOf0 tptp.xx tptp.xQ))) % 16.32/16.57 (assume @p69 (= tptp.xP @t73)) % 16.32/16.57 (assume @p70 (and (not (tptp.aElementOf0 tptp.xx @t72)) (= (tptp.szszuzczcdt0 (tptp.sbrdtbr0 @t72)) tptp.xk))) % 16.32/16.57 (assume @p71 (and @t75 (= @t74 tptp.xk))) % 16.32/16.57 (assume @p72 @t77) % 16.32/16.57 (assume @p73 true) % 16.32/16.57 (step @p74 :rule and_elim :premises (@p66) :args (2)) % 16.32/16.57 (step @p75 :rule symm :premises (@p74)) % 16.32/16.57 (step @p76 :rule refl :args (tptp.xS)) % 16.32/16.57 (step @p77 :rule cong :premises (@p76 @p75) :args (@t70)) % 16.32/16.57 (step @p78 :rule cong :premises (@p69 @p77) :args (@t76)) % 16.32/16.57 (step @p79 :rule cong :premises (@p78) :args (@t77)) % 16.32/16.57 (step @p80 :rule eq_resolve :premises (@p72 @p79)) % 16.32/16.57 (step @p81 :rule cong :premises (@p69) :args (@t74)) % 16.32/16.57 (step @p82 :rule cong :premises (@p75 @p81) :args ((= tptp.xk @t74))) % 16.32/16.57 (step @p83 :rule eq-symm :args (@t74 tptp.xk)) % 16.32/16.57 (step @p84 :rule trans :premises (@p83 @p82)) % 16.32/16.57 (step @p85 :rule and_elim :premises (@p71) :args (1)) % 16.32/16.57 (step @p86 :rule eq_resolve :premises (@p85 @p84)) % 16.32/16.57 (step @p87 :rule cong :premises (@p69 @p76) :args (@t75)) % 16.32/16.57 (step @p88 :rule and_elim :premises (@p71) :args (0)) % 16.32/16.57 (step @p89 :rule eq_resolve :premises (@p88 @p87)) % 16.32/16.57 (step @p90 :rule cnf_and_neg :args (@t81)) % 16.32/16.57 (step @p91 :rule reordering :premises (@p90) :args ((or (not @t80) (not @t79) @t81))) % 16.32/16.57 (step @p92 :rule chain_m_resolution :premises (@p91 @p89 @p86) :args (@t81 (@list false false) (@list @t80 @t79))) % 16.32/16.57 (step @p93 :rule eq-symm :args (@t83 @t84)) % 16.32/16.57 (step @p94 :rule cong :premises (@p93) :args (@t85)) % 16.32/16.57 (step @p95 :rule refl :args (@t86)) % 16.32/16.57 (step @p96 :rule nary_cong :premises (@p95 @p94) :args (@t87)) % 16.32/16.57 (step @p97 :rule eq-symm :args (@t82 @t62)) % 16.32/16.57 (step @p98 :rule cong :premises (@p97 @p96) :args (@t88)) % 16.32/16.57 (step @p99 :rule refl :args (@t89)) % 16.32/16.57 (step @p100 :rule refl :args (@t90)) % 16.32/16.57 (step @p101 :rule nary_cong :premises (@p100 @p99 @p98) :args (@t91)) % 16.32/16.57 (step @p102 :rule cong :premises (@p101) :args (@t93)) % 16.32/16.57 (step @p103 :rule quant-merge-prenex :args ((= (forall @t25 @t95) @t93))) % 16.32/16.57 (step @p104 :rule alpha_equiv :args (@t96 (@list @t82) (@list @t15))) % 16.32/16.57 (step @p105 :rule refl :args (@t89)) % 16.32/16.57 (step @p106 :rule refl :args (@t90)) % 16.32/16.57 (step @p107 :rule nary_cong :premises (@p106 @p105 @p104) :args (@t97)) % 16.32/16.57 (step @p108 :rule quant-miniscope-or :args ((= @t95 @t97))) % 16.32/16.57 (step @p109 :rule trans :premises (@p108 @p107)) % 16.32/16.57 (step @p110 :rule symm :premises (@p109)) % 16.32/16.57 (step @p111 :rule cong :premises (@p110) :args ((forall @t25 @t99))) % 16.32/16.57 (step @p112 :rule trans :premises (@p111 @p103)) % 16.32/16.57 (step @p113 :rule trans :premises (@p112 @p102)) % 16.32/16.57 (step @p114 :rule aci_norm :args ((= (or (or @t90 @t89) @t98) @t99))) % 16.32/16.57 (step @p115 :rule refl :args (@t98)) % 16.32/16.57 (step @p116 :rule bool-and-de-morgan :args (@t2 @t44 true)) % 16.32/16.57 (step @p117 :rule nary_cong :premises (@p116 @p115) :args ((or (not @t50) @t98))) % 16.32/16.57 (step @p118 :rule trans :premises (@p117 @p114)) % 16.32/16.57 (step @p119 :rule bool-impl-elim :args (@t50 @t98)) % 16.32/16.57 (step @p120 :rule trans :premises (@p119 @p118)) % 16.32/16.57 (step @p121 :rule cong :premises (@p120) :args ((forall @t25 (=> @t50 @t98)))) % 16.32/16.57 (step @p122 :rule trans :premises (@p121 @p113)) % 16.32/16.57 (step @p123 :rule eq-symm :args (@t56 @t5)) % 16.32/16.57 (step @p124 :rule refl :args (@t57)) % 16.32/16.57 (step @p125 :rule nary_cong :premises (@p124 @p123) :args (@t58)) % 16.32/16.57 (step @p126 :rule refl :args (@t32)) % 16.32/16.57 (step @p127 :rule cong :premises (@p126 @p125) :args (@t59)) % 16.32/16.57 (step @p128 :rule cong :premises (@p127) :args (@t60)) % 16.32/16.57 (step @p129 :rule refl :args (@t26)) % 16.32/16.57 (step @p130 :rule nary_cong :premises (@p129 @p128) :args (@t61)) % 16.32/16.57 (step @p131 :rule refl :args (@t63)) % 16.32/16.57 (step @p132 :rule cong :premises (@p131 @p130) :args (@t64)) % 16.32/16.57 (step @p133 :rule cong :premises (@p132) :args (@t65)) % 16.32/16.57 (step @p134 :rule refl :args (@t50)) % 16.32/16.57 (step @p135 :rule cong :premises (@p134 @p133) :args (@t66)) % 16.32/16.57 (step @p136 :rule cong :premises (@p135) :args (@t67)) % 16.32/16.57 (step @p137 :rule trans :premises (@p136 @p122)) % 16.32/16.57 (step @p138 :rule eq_resolve :premises (@p57 @p137)) % 16.32/16.57 (step @p139 :rule bool-eq-true :args (@t106)) % 16.32/16.57 (step @p140 :rule eq-symm :args (true @t106)) % 16.32/16.57 (step @p141 :rule trans :premises (@p140 @p139)) % 16.32/16.57 (step @p142 :rule eq-symm :args (@t101 @t103)) % 16.32/16.57 (step @p143 :rule refl :args (@t103)) % 16.32/16.57 (step @p144 :rule eq-symm :args (@t71 @t56)) % 16.32/16.57 (step @p145 :rule refl :args (@t100)) % 16.32/16.57 (step @p146 :rule nary_cong :premises (@p145 @p144) :args (@t107)) % 16.32/16.57 (step @p147 :rule cong :premises (@p146 @p143) :args (@t108)) % 16.32/16.57 (step @p148 :rule trans :premises (@p147 @p142)) % 16.32/16.57 (step @p149 :rule cong :premises (@p148) :args (@t109)) % 16.32/16.57 (step @p150 :rule refl :args (@t105)) % 16.32/16.57 (step @p151 :rule nary_cong :premises (@p150 @p149) :args (@t110)) % 16.32/16.57 (step @p152 :rule eq-refl :args (@t102)) % 16.32/16.57 (step @p153 :rule cong :premises (@p152 @p151) :args (@t111)) % 16.32/16.57 (step @p154 :rule trans :premises (@p153 @p141)) % 16.32/16.57 (step @p155 :rule refl :args (@t113)) % 16.32/16.57 (step @p156 :rule refl :args (@t114)) % 16.32/16.57 (step @p157 :rule nary_cong :premises (@p156 @p155 @p154) :args (@t115)) % 16.32/16.57 (step @p158 :rule refl :args (@t116)) % 16.32/16.57 (step @p159 :rule cong :premises (@p158 @p157) :args ((=> @t116 @t115))) % 16.32/16.57 (assume-push @p194 @t116) % 16.32/16.57 (step @p161 :rule instantiate :premises (@p138) :args ((@list tptp.xS @t71 @t102))) % 16.32/16.57 (step-pop @p195 :rule scope :premises (@p161)) % 16.32/16.57 (step @p162 :rule process_scope :premises (@p195) :args (@t115)) % 16.32/16.57 (step @p164 :rule eq_resolve :premises (@p162 @p159)) % 16.32/16.57 (step @p165 :rule implies_elim :premises (@p164)) % 16.32/16.57 (step @p166 :rule chain_m_resolution :premises (@p165 @p138) :args (@t117 @t118 (@list @t116))) % 16.32/16.57 (step @p167 :rule and_elim :premises (@p62) :args (0)) % 16.32/16.57 (step @p168 :rule refl :args (tptp.szNzAzT0)) % 16.32/16.57 (step @p169 :rule cong :premises (@p75 @p168) :args (@t68)) % 16.32/16.57 (step @p170 :rule eq_resolve :premises (@p61 @p169)) % 16.32/16.57 (step @p171 :rule cnf_or_pos :args (@t117)) % 16.32/16.57 (step @p172 :rule reordering :premises (@p171) :args ((or @t113 @t114 @t106 (not @t117)))) % 16.32/16.57 (step @p173 :rule chain_m_resolution :premises (@p172 @p170 @p167 @p166) :args (@t106 (@list false false false) (@list @t112 @t69 @t117))) % 16.32/16.57 (step @p174 :rule cnf_and_pos :args (@t106 1)) % 16.32/16.57 (step @p175 :rule reordering :premises (@p174) :args ((or @t104 (not @t106)))) % 16.32/16.57 (step @p176 :rule chain_m_resolution :premises (@p175 @p173) :args (@t104 @t118 (@list @t106))) % 16.32/16.57 (step @p177 :rule eq-symm :args (@t78 @t71)) % 16.32/16.57 (step @p178 :rule refl :args (@t80)) % 16.32/16.57 (step @p179 :rule nary_cong :premises (@p178 @p177) :args (@t119)) % 16.32/16.57 (step @p180 :rule refl :args (@t120)) % 16.32/16.57 (step @p181 :rule cong :premises (@p180 @p179) :args (@t121)) % 16.32/16.57 (step @p182 :rule refl :args (@t104)) % 16.32/16.57 (step @p183 :rule cong :premises (@p182 @p181) :args ((=> @t104 @t121))) % 16.32/16.57 (assume-push @p196 @t104) % 16.32/16.57 (step @p185 :rule instantiate :premises (@p176) :args ((@list @t73))) % 16.32/16.57 (step-pop @p197 :rule scope :premises (@p185)) % 16.32/16.57 (step @p186 :rule process_scope :premises (@p197) :args (@t121)) % 16.32/16.57 (step @p188 :rule eq_resolve :premises (@p186 @p183)) % 16.32/16.57 (step @p189 :rule implies_elim :premises (@p188)) % 16.32/16.57 (step @p190 :rule chain_m_resolution :premises (@p189 @p176) :args (@t122 @t118 (@list @t104))) % 16.32/16.57 (step @p191 :rule cnf_equiv_pos2 :args (@t122)) % 16.32/16.57 (step @p192 :rule reordering :premises (@p191) :args ((or @t120 (not @t81) (not @t122)))) % 16.32/16.57 (step @p193 false :rule chain_m_resolution :premises (@p192 @p190 @p92 @p80) :args (false (@list false false true) (@list @t122 @t81 @t120))) % 16.32/16.57 ) % 16.32/16.57 % SZS output end Proof % 16.32/16.57 % cvc5 exiting %------------------------------------------------------------------------------