%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM538+2 : 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 08:39:46 AM UTC 2026 % Result : Theorem 0.45s 0.65s % Output : Proof 0.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM538+2 : 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 : n027.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 11:28:51 EDT 2026 % 0.17/0.35 % CPUTime : % 0.32/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.45/0.65 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.45/0.65 % SZS status Theorem % 0.45/0.65 % SZS output start Proof % 0.45/0.65 ( % 0.45/0.65 (declare-sort $$unsorted 0) % 0.45/0.65 (declare-const tptp.xx $$unsorted) % 0.45/0.65 (declare-const tptp.xS $$unsorted) % 0.45/0.65 (declare-const tptp.sbrdtbr0 (-> $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 0.45/0.65 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 0.45/0.65 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 0.45/0.65 (declare-const tptp.isFinite0 (-> $$unsorted Bool)) % 0.45/0.65 (declare-const tptp.isCountable0 (-> $$unsorted Bool)) % 0.45/0.65 (declare-const tptp.slcrc0 $$unsorted) % 0.45/0.65 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.aSubsetOf0 (-> $$unsorted $$unsorted Bool)) % 0.45/0.65 (declare-const tptp.sdtlseqdt0 (-> $$unsorted $$unsorted Bool)) % 0.45/0.65 (declare-const tptp.szszuzczcdt0 (-> $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.sdtmndt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.65 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 0.45/0.65 (declare-const tptp.szNzAzT0 $$unsorted) % 0.45/0.65 (declare-const tptp.sz00 $$unsorted) % 0.45/0.65 (define @t1 () (@var "W0" $$unsorted)) % 0.45/0.65 (define @t2 () (tptp.aSet0 @t1)) % 0.45/0.65 (define @t3 () (@list @t1)) % 0.45/0.65 (define @t4 () (tptp.aElement0 @t1)) % 0.45/0.65 (define @t5 () (@var "W1" $$unsorted)) % 0.45/0.65 (define @t6 () (tptp.aElement0 @t5)) % 0.45/0.65 (define @t7 () (tptp.aElementOf0 @t5 @t1)) % 0.45/0.65 (define @t8 () (@list @t5)) % 0.45/0.65 (define @t9 () (forall @t8 (=> @t7 @t6))) % 0.45/0.65 (define @t10 () (=> @t2 @t9)) % 0.45/0.65 (define @t11 () (forall @t3 @t10)) % 0.45/0.65 (define @t12 () (tptp.isFinite0 @t1)) % 0.45/0.65 (define @t13 () (= @t1 tptp.slcrc0)) % 0.45/0.65 (define @t14 () (tptp.isCountable0 @t1)) % 0.45/0.65 (define @t15 () (not @t12)) % 0.45/0.65 (define @t16 () (and @t2 @t14)) % 0.45/0.65 (define @t17 () (@var "W2" $$unsorted)) % 0.45/0.65 (define @t18 () (@list @t17)) % 0.45/0.65 (define @t19 () (tptp.aSet0 @t5)) % 0.45/0.65 (define @t20 () (tptp.aSubsetOf0 @t5 @t1)) % 0.45/0.65 (define @t21 () (tptp.isFinite0 @t5)) % 0.45/0.65 (define @t22 () (and @t2 @t12)) % 0.45/0.65 (define @t23 () (= @t1 @t5)) % 0.45/0.65 (define @t24 () (tptp.aSubsetOf0 @t1 @t5)) % 0.45/0.65 (define @t25 () (@list @t1 @t5)) % 0.45/0.65 (define @t26 () (tptp.aSet0 @t17)) % 0.45/0.65 (define @t27 () (@list @t1 @t5 @t17)) % 0.45/0.65 (define @t28 () (@var "W3" $$unsorted)) % 0.45/0.65 (define @t29 () (= @t28 @t5)) % 0.45/0.65 (define @t30 () (tptp.aElementOf0 @t28 @t1)) % 0.45/0.65 (define @t31 () (tptp.aElement0 @t28)) % 0.45/0.65 (define @t32 () (tptp.aElementOf0 @t28 @t17)) % 0.45/0.65 (define @t33 () (@list @t28)) % 0.45/0.65 (define @t34 () (tptp.sdtpldt0 @t1 @t5)) % 0.45/0.65 (define @t35 () (and @t2 @t6)) % 0.45/0.65 (define @t36 () (tptp.sdtmndt0 @t1 @t5)) % 0.45/0.65 (define @t37 () (tptp.sdtpldt0 @t36 @t5)) % 0.45/0.65 (define @t38 () (=> @t7 (= @t37 @t1))) % 0.45/0.65 (define @t39 () (forall @t8 @t38)) % 0.45/0.65 (define @t40 () (=> @t2 @t39)) % 0.45/0.65 (define @t41 () (forall @t3 @t40)) % 0.45/0.65 (define @t42 () (tptp.sdtpldt0 @t5 @t1)) % 0.45/0.65 (define @t43 () (and @t19 (tptp.isCountable0 @t5))) % 0.45/0.65 (define @t44 () (tptp.sdtmndt0 @t5 @t1)) % 0.45/0.65 (define @t45 () (and @t19 @t21)) % 0.45/0.65 (define @t46 () (tptp.isFinite0 @t44)) % 0.45/0.65 (define @t47 () (forall @t8 (=> @t45 @t46))) % 0.45/0.65 (define @t48 () (=> @t4 @t47)) % 0.45/0.65 (define @t49 () (forall @t3 @t48)) % 0.45/0.65 (define @t50 () (tptp.szszuzczcdt0 @t1)) % 0.45/0.65 (define @t51 () (tptp.aElementOf0 @t1 tptp.szNzAzT0)) % 0.45/0.65 (define @t52 () (tptp.szszuzczcdt0 @t5)) % 0.45/0.65 (define @t53 () (tptp.aElementOf0 @t5 tptp.szNzAzT0)) % 0.45/0.65 (define @t54 () (and @t51 @t53)) % 0.45/0.65 (define @t55 () (tptp.sdtlseqdt0 @t1 @t5)) % 0.45/0.65 (define @t56 () (tptp.sbrdtbr0 @t1)) % 0.45/0.65 (define @t57 () (tptp.szszuzczcdt0 @t56)) % 0.45/0.65 (define @t58 () (= (tptp.sbrdtbr0 @t34) @t57)) % 0.45/0.65 (define @t59 () (not @t7)) % 0.45/0.65 (define @t60 () (=> @t59 @t58)) % 0.45/0.65 (define @t61 () (forall @t8 (=> @t6 @t60))) % 0.45/0.65 (define @t62 () (=> @t22 @t61)) % 0.45/0.65 (define @t63 () (forall @t3 @t62)) % 0.45/0.65 (define @t64 () (tptp.aSet0 tptp.xS)) % 0.45/0.65 (define @t65 () (tptp.aElementOf0 tptp.xx tptp.xS)) % 0.45/0.65 (define @t66 () (tptp.isFinite0 tptp.xS)) % 0.45/0.65 (define @t67 () (tptp.sdtmndt0 tptp.xS tptp.xx)) % 0.45/0.65 (define @t68 () (tptp.szszuzczcdt0 (tptp.sbrdtbr0 @t67))) % 0.45/0.65 (define @t69 () (= @t68 (tptp.sbrdtbr0 tptp.xS))) % 0.45/0.65 (define @t70 () (forall @t3 (= (tptp.aElementOf0 @t1 @t67) (and @t4 (tptp.aElementOf0 @t1 tptp.xS) (not (= @t1 tptp.xx)))))) % 0.45/0.65 (define @t71 () (tptp.aSet0 @t67)) % 0.45/0.65 (define @t72 () (@var "BOUND_VARIABLE_7881" $$unsorted)) % 0.45/0.65 (define @t73 () (= @t1 (tptp.sdtpldt0 (tptp.sdtmndt0 @t1 @t72) @t72))) % 0.45/0.65 (define @t74 () (not (tptp.aElementOf0 @t72 @t1))) % 0.45/0.65 (define @t75 () (not @t2)) % 0.45/0.65 (define @t76 () (or @t74 @t73)) % 0.45/0.65 (define @t77 () (or @t75 @t76)) % 0.45/0.65 (define @t78 () (forall (@list @t1 @t72) @t77)) % 0.45/0.65 (define @t79 () (@list @t72)) % 0.45/0.65 (define @t80 () (forall @t79 @t77)) % 0.45/0.65 (define @t81 () (forall @t79 @t76)) % 0.45/0.65 (define @t82 () (@list @t5)) % 0.45/0.65 (define @t83 () (or @t75 @t81)) % 0.45/0.65 (define @t84 () (= @t1 @t37)) % 0.45/0.65 (define @t85 () (forall @t8 (or @t59 @t84))) % 0.45/0.65 (define @t86 () (@list tptp.xS tptp.xx)) % 0.45/0.65 (define @t87 () (tptp.sdtpldt0 @t67 tptp.xx)) % 0.45/0.65 (define @t88 () (= tptp.xS @t87)) % 0.45/0.65 (define @t89 () (not @t65)) % 0.45/0.65 (define @t90 () (not @t64)) % 0.45/0.65 (define @t91 () (or @t90 @t89 @t88)) % 0.45/0.65 (define @t92 () (@list false false false)) % 0.45/0.65 (define @t93 () (@var "BOUND_VARIABLE_8096" $$unsorted)) % 0.45/0.65 (define @t94 () (tptp.sbrdtbr0 (tptp.sdtpldt0 @t1 @t93))) % 0.45/0.65 (define @t95 () (tptp.aElementOf0 @t93 @t1)) % 0.45/0.65 (define @t96 () (not (tptp.aElement0 @t93))) % 0.45/0.65 (define @t97 () (= @t94 @t57)) % 0.45/0.65 (define @t98 () (or @t75 @t15 @t96 @t95 @t97)) % 0.45/0.65 (define @t99 () (or @t96 @t95 @t97)) % 0.45/0.65 (define @t100 () (or @t75 @t15 @t99)) % 0.45/0.65 (define @t101 () (forall (@list @t1 @t93) @t100)) % 0.45/0.65 (define @t102 () (@list @t93)) % 0.45/0.65 (define @t103 () (forall @t102 @t100)) % 0.45/0.65 (define @t104 () (forall @t102 @t99)) % 0.45/0.65 (define @t105 () (or @t75 @t15 @t104)) % 0.45/0.65 (define @t106 () (not @t6)) % 0.45/0.65 (define @t107 () (or @t106 @t7 @t58)) % 0.45/0.65 (define @t108 () (forall @t8 @t107)) % 0.45/0.65 (define @t109 () (or @t75 @t15 @t108)) % 0.45/0.65 (define @t110 () (tptp.aElementOf0 tptp.xx @t67)) % 0.45/0.65 (define @t111 () (tptp.aElement0 tptp.xx)) % 0.45/0.65 (define @t112 () (not (= tptp.xx tptp.xx))) % 0.45/0.65 (define @t113 () (and @t111 @t65 @t112)) % 0.45/0.65 (define @t114 () (= @t110 @t113)) % 0.45/0.65 (define @t115 () (@var "BOUND_VARIABLE_7699" $$unsorted)) % 0.45/0.65 (define @t116 () (tptp.aElement0 @t115)) % 0.45/0.65 (define @t117 () (not (tptp.aElementOf0 @t115 @t1))) % 0.45/0.65 (define @t118 () (or @t117 @t116)) % 0.45/0.65 (define @t119 () (or @t75 @t118)) % 0.45/0.65 (define @t120 () (forall (@list @t1 @t115) @t119)) % 0.45/0.65 (define @t121 () (@list @t115)) % 0.45/0.65 (define @t122 () (forall @t121 @t119)) % 0.45/0.65 (define @t123 () (forall @t121 @t118)) % 0.45/0.65 (define @t124 () (or @t75 @t123)) % 0.45/0.65 (define @t125 () (forall @t8 (or @t59 @t6))) % 0.45/0.65 (define @t126 () (or @t90 @t89 @t111)) % 0.45/0.65 (define @t127 () (@var "BOUND_VARIABLE_7981" $$unsorted)) % 0.45/0.65 (define @t128 () (tptp.isFinite0 (tptp.sdtmndt0 @t127 @t1))) % 0.45/0.65 (define @t129 () (not (tptp.isFinite0 @t127))) % 0.45/0.65 (define @t130 () (not (tptp.aSet0 @t127))) % 0.45/0.65 (define @t131 () (not @t4)) % 0.45/0.65 (define @t132 () (or @t130 @t129 @t128)) % 0.45/0.65 (define @t133 () (or @t131 @t132)) % 0.45/0.65 (define @t134 () (forall (@list @t1 @t127) @t133)) % 0.45/0.65 (define @t135 () (@list @t127)) % 0.45/0.65 (define @t136 () (forall @t135 @t133)) % 0.45/0.65 (define @t137 () (forall @t135 @t132)) % 0.45/0.65 (define @t138 () (or @t131 @t137)) % 0.45/0.65 (define @t139 () (not @t21)) % 0.45/0.65 (define @t140 () (not @t19)) % 0.45/0.65 (define @t141 () (or @t140 @t139 @t46)) % 0.45/0.65 (define @t142 () (forall @t8 @t141)) % 0.45/0.65 (define @t143 () (tptp.isFinite0 @t67)) % 0.45/0.65 (define @t144 () (not @t66)) % 0.45/0.65 (define @t145 () (not @t111)) % 0.45/0.65 (define @t146 () (or @t145 @t90 @t144 @t143)) % 0.45/0.65 (define @t147 () (tptp.sbrdtbr0 @t87)) % 0.45/0.65 (define @t148 () (= @t68 @t147)) % 0.45/0.65 (define @t149 () (not @t143)) % 0.45/0.65 (define @t150 () (not @t71)) % 0.45/0.65 (define @t151 () (or @t150 @t149 @t145 @t110 @t148)) % 0.45/0.65 (define @t152 () (not @t148)) % 0.45/0.65 (define @t153 () (not @t88)) % 0.45/0.65 (define @t154 () (not @t69)) % 0.45/0.65 (define @t155 () (and @t148 @t152)) % 0.45/0.65 (assume @p1 (forall @t3 (=> @t2 true))) % 0.45/0.65 (assume @p2 (forall @t3 (=> @t4 true))) % 0.45/0.65 (assume @p3 @t11) % 0.45/0.65 (assume @p4 (forall @t3 (=> @t2 (=> @t12 true)))) % 0.45/0.65 (assume @p5 (forall @t3 (= @t13 (and @t2 (not (exists @t8 @t7)))))) % 0.45/0.65 (assume @p6 (tptp.isFinite0 tptp.slcrc0)) % 0.45/0.65 (assume @p7 (forall @t3 (=> @t2 (=> @t14 true)))) % 0.45/0.65 (assume @p8 (forall @t3 (=> @t16 @t15))) % 0.45/0.65 (assume @p9 (forall @t3 (=> @t16 (not @t13)))) % 0.45/0.65 (assume @p10 (forall @t3 (=> @t2 (forall @t8 (= @t20 (and @t19 (forall @t18 (=> (tptp.aElementOf0 @t17 @t5) (tptp.aElementOf0 @t17 @t1))))))))) % 0.45/0.65 (assume @p11 (forall @t3 (=> @t22 (forall @t8 (=> @t20 @t21))))) % 0.45/0.65 (assume @p12 (forall @t3 (=> @t2 (tptp.aSubsetOf0 @t1 @t1)))) % 0.45/0.65 (assume @p13 (forall @t25 (=> (and @t2 @t19) (=> (and @t24 @t20) @t23)))) % 0.45/0.65 (assume @p14 (forall @t27 (=> (and @t2 @t19 @t26) (=> (and @t24 (tptp.aSubsetOf0 @t5 @t17)) (tptp.aSubsetOf0 @t1 @t17))))) % 0.45/0.65 (assume @p15 (forall @t25 (=> @t35 (forall @t18 (= (= @t17 @t34) (and @t26 (forall @t33 (= @t32 (and @t31 (or @t30 @t29)))))))))) % 0.45/0.65 (assume @p16 (forall @t25 (=> @t35 (forall @t18 (= (= @t17 @t36) (and @t26 (forall @t33 (= @t32 (and @t31 @t30 (not @t29)))))))))) % 0.45/0.65 (assume @p17 @t41) % 0.45/0.65 (assume @p18 (forall @t25 (=> (and @t4 @t19) (=> (not (tptp.aElementOf0 @t1 @t5)) (= (tptp.sdtmndt0 @t42 @t1) @t5))))) % 0.45/0.65 (assume @p19 (forall @t3 (=> @t4 (forall @t8 (=> @t43 (tptp.isCountable0 @t42)))))) % 0.45/0.65 (assume @p20 (forall @t3 (=> @t4 (forall @t8 (=> @t43 (tptp.isCountable0 @t44)))))) % 0.45/0.65 (assume @p21 (forall @t3 (=> @t4 (forall @t8 (=> @t45 (tptp.isFinite0 @t42)))))) % 0.45/0.65 (assume @p22 @t49) % 0.45/0.65 (assume @p23 (and (tptp.aSet0 tptp.szNzAzT0) (tptp.isCountable0 tptp.szNzAzT0))) % 0.45/0.65 (assume @p24 (tptp.aElementOf0 tptp.sz00 tptp.szNzAzT0)) % 0.45/0.65 (assume @p25 (forall @t3 (=> @t51 (and (tptp.aElementOf0 @t50 tptp.szNzAzT0) (not (= @t50 tptp.sz00)))))) % 0.45/0.65 (assume @p26 (forall @t25 (=> @t54 (=> (= @t50 @t52) @t23)))) % 0.45/0.65 (assume @p27 (forall @t3 (=> @t51 (or (= @t1 tptp.sz00) (exists @t8 (and @t53 (= @t1 @t52))))))) % 0.45/0.65 (assume @p28 (forall @t3 (=> @t51 (not (= @t1 @t50))))) % 0.45/0.65 (assume @p29 (forall @t25 (=> @t54 (=> @t55 true)))) % 0.45/0.65 (assume @p30 (forall @t3 (=> @t51 (tptp.sdtlseqdt0 tptp.sz00 @t1)))) % 0.45/0.65 (assume @p31 (forall @t3 (=> @t51 (not (tptp.sdtlseqdt0 @t50 tptp.sz00))))) % 0.45/0.65 (assume @p32 (forall @t25 (=> @t54 (= @t55 (tptp.sdtlseqdt0 @t50 @t52))))) % 0.45/0.65 (assume @p33 (forall @t3 (=> @t51 (tptp.sdtlseqdt0 @t1 @t50)))) % 0.45/0.65 (assume @p34 (forall @t3 (=> @t51 (tptp.sdtlseqdt0 @t1 @t1)))) % 0.45/0.65 (assume @p35 (forall @t25 (=> @t54 (=> (and @t55 (tptp.sdtlseqdt0 @t5 @t1)) @t23)))) % 0.45/0.65 (assume @p36 (forall @t27 (=> (and @t51 @t53 (tptp.aElementOf0 @t17 tptp.szNzAzT0)) (=> (and @t55 (tptp.sdtlseqdt0 @t5 @t17)) (tptp.sdtlseqdt0 @t1 @t17))))) % 0.45/0.65 (assume @p37 (forall @t25 (=> @t54 (or @t55 (tptp.sdtlseqdt0 @t52 @t1))))) % 0.45/0.65 (assume @p38 (forall @t25 (=> @t54 (=> (tptp.iLess0 @t1 @t5) true)))) % 0.45/0.65 (assume @p39 (forall @t3 (=> @t51 (tptp.iLess0 @t1 @t50)))) % 0.45/0.65 (assume @p40 (forall @t3 (=> @t2 (tptp.aElement0 @t56)))) % 0.45/0.65 (assume @p41 (forall @t3 (=> @t2 (= (tptp.aElementOf0 @t56 tptp.szNzAzT0) @t12)))) % 0.45/0.65 (assume @p42 (forall @t3 (=> @t2 (= (= @t56 tptp.sz00) @t13)))) % 0.45/0.65 (assume @p43 @t63) % 0.45/0.65 (assume @p44 @t64) % 0.45/0.65 (assume @p45 (and @t66 @t65)) % 0.45/0.65 (assume @p46 (not (=> (and @t71 @t70) @t69))) % 0.45/0.65 (assume @p47 true) % 0.45/0.65 (step @p48 :rule not_implies_elim2 :premises (@p46)) % 0.45/0.65 (step @p49 :rule aci_norm :args ((= @t77 (or @t75 @t74 @t73)))) % 0.45/0.65 (step @p50 :rule cong :premises (@p49) :args (@t78)) % 0.45/0.65 (step @p51 :rule quant-merge-prenex :args ((= (forall @t3 @t80) @t78))) % 0.45/0.65 (step @p52 :rule alpha_equiv :args (@t81 (@list @t72) @t82)) % 0.45/0.65 (step @p53 :rule refl :args (@t75)) % 0.45/0.65 (step @p54 :rule nary_cong :premises (@p53 @p52) :args (@t83)) % 0.45/0.65 (step @p55 :rule quant-miniscope-or :args ((= @t80 @t83))) % 0.45/0.65 (step @p56 :rule trans :premises (@p55 @p54)) % 0.45/0.65 (step @p57 :rule symm :premises (@p56)) % 0.45/0.65 (step @p58 :rule cong :premises (@p57) :args ((forall @t3 (or @t75 @t85)))) % 0.45/0.65 (step @p59 :rule trans :premises (@p58 @p51)) % 0.45/0.65 (step @p60 :rule trans :premises (@p59 @p50)) % 0.45/0.65 (step @p61 :rule bool-impl-elim :args (@t2 @t85)) % 0.45/0.65 (step @p62 :rule cong :premises (@p61) :args ((forall @t3 (=> @t2 @t85)))) % 0.45/0.65 (step @p63 :rule trans :premises (@p62 @p60)) % 0.45/0.65 (step @p64 :rule bool-impl-elim :args (@t7 @t84)) % 0.45/0.65 (step @p65 :rule cong :premises (@p64) :args ((forall @t8 (=> @t7 @t84)))) % 0.45/0.65 (step @p66 :rule eq-symm :args (@t37 @t1)) % 0.45/0.65 (step @p67 :rule refl :args (@t7)) % 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(@t95)) % 0.45/0.65 (step @p83 :rule refl :args (@t96)) % 0.45/0.65 (step @p84 :rule refl :args (@t15)) % 0.45/0.65 (step @p85 :rule refl :args (@t75)) % 0.45/0.65 (step @p86 :rule nary_cong :premises (@p85 @p84 @p83 @p82 @p81) :args (@t98)) % 0.45/0.65 (step @p87 :rule aci_norm :args ((= @t100 @t98))) % 0.45/0.65 (step @p88 :rule trans :premises (@p87 @p86)) % 0.45/0.65 (step @p89 :rule cong :premises (@p88) :args (@t101)) % 0.45/0.65 (step @p90 :rule quant-merge-prenex :args ((= (forall @t3 @t103) @t101))) % 0.45/0.65 (step @p91 :rule alpha_equiv :args (@t104 (@list @t93) @t82)) % 0.45/0.65 (step @p92 :rule refl :args (@t15)) % 0.45/0.65 (step @p93 :rule nary_cong :premises (@p53 @p92 @p91) :args (@t105)) % 0.45/0.65 (step @p94 :rule quant-miniscope-or :args ((= @t103 @t105))) % 0.45/0.65 (step @p95 :rule trans :premises (@p94 @p93)) % 0.45/0.65 (step @p96 :rule symm :premises (@p95)) % 0.45/0.65 (step @p97 :rule cong :premises (@p96) :args ((forall @t3 @t109))) % 0.45/0.65 (step 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:args ((or (not @t59) @t58))) % 0.45/0.65 (step @p113 :rule bool-impl-elim :args (@t59 @t58)) % 0.45/0.65 (step @p114 :rule trans :premises (@p113 @p112)) % 0.45/0.65 (step @p115 :rule refl :args (@t106)) % 0.45/0.65 (step @p116 :rule nary_cong :premises (@p115 @p114) :args ((or @t106 @t60))) % 0.45/0.65 (step @p117 :rule trans :premises (@p116 @p109)) % 0.45/0.65 (step @p118 :rule bool-impl-elim :args (@t6 @t60)) % 0.45/0.65 (step @p119 :rule trans :premises (@p118 @p117)) % 0.45/0.65 (step @p120 :rule cong :premises (@p119) :args (@t61)) % 0.45/0.65 (step @p121 :rule refl :args (@t22)) % 0.45/0.65 (step @p122 :rule cong :premises (@p121 @p120) :args (@t62)) % 0.45/0.65 (step @p123 :rule cong :premises (@p122) :args (@t63)) % 0.45/0.65 (step @p124 :rule trans :premises (@p123 @p108)) % 0.45/0.65 (step @p125 :rule eq_resolve :premises (@p43 @p124)) % 0.45/0.65 (step @p126 :rule instantiate :premises (@p125) :args ((@list @t67 tptp.xx))) % 0.45/0.65 (step @p127 :rule not_implies_elim1 :premises (@p46)) % 0.45/0.65 (step @p128 :rule and_elim :premises (@p127) :args (1)) % 0.45/0.65 (step @p129 :rule bool-eq-false :args (@t110)) % 0.45/0.65 (step @p130 :rule absorb :args ((= (and @t111 @t65 false) false))) % 0.45/0.65 (step @p131 :rule evaluate :args ((not true))) % 0.45/0.65 (step @p132 :rule eq-refl :args (tptp.xx)) % 0.45/0.65 (step @p133 :rule cong :premises (@p132) :args (@t112)) % 0.45/0.65 (step @p134 :rule trans :premises (@p133 @p131)) % 0.45/0.65 (step @p135 :rule refl :args (@t65)) % 0.45/0.65 (step @p136 :rule refl :args (@t111)) % 0.45/0.65 (step @p137 :rule nary_cong :premises (@p136 @p135 @p134) :args (@t113)) % 0.45/0.65 (step @p138 :rule trans :premises (@p137 @p130)) % 0.45/0.65 (step @p139 :rule refl :args (@t110)) % 0.45/0.65 (step @p140 :rule cong :premises (@p139 @p138) :args (@t114)) % 0.45/0.65 (step @p141 :rule trans :premises (@p140 @p129)) % 0.45/0.65 (step @p142 :rule refl :args (@t70)) % 0.45/0.65 (step @p143 :rule cong :premises (@p142 @p141) :args ((=> @t70 @t114))) % 0.45/0.65 (assume-push @p247 @t70) % 0.45/0.65 (step @p145 :rule instantiate :premises (@p128) :args ((@list tptp.xx))) % 0.45/0.65 (step-pop @p248 :rule scope :premises (@p145)) % 0.45/0.65 (step @p146 :rule process_scope :premises (@p248) :args (@t114)) % 0.45/0.65 (step @p148 :rule eq_resolve :premises (@p146 @p143)) % 0.45/0.65 (step @p149 :rule implies_elim :premises (@p148)) % 0.45/0.65 (step @p150 :rule chain_m_resolution :premises (@p149 @p128) :args ((not @t110) (@list false) (@list @t70))) % 0.45/0.65 (step @p151 :rule aci_norm :args ((= @t119 (or @t75 @t117 @t116)))) % 0.45/0.65 (step @p152 :rule cong :premises (@p151) :args (@t120)) % 0.45/0.65 (step @p153 :rule quant-merge-prenex :args ((= (forall @t3 @t122) @t120))) % 0.45/0.65 (step @p154 :rule alpha_equiv :args (@t123 (@list @t115) @t82)) % 0.45/0.65 (step @p155 :rule nary_cong :premises (@p53 @p154) :args (@t124)) % 0.45/0.65 (step @p156 :rule quant-miniscope-or :args ((= @t122 @t124))) % 0.45/0.65 (step @p157 :rule trans :premises (@p156 @p155)) % 0.45/0.65 (step @p158 :rule symm :premises (@p157)) % 0.45/0.65 (step @p159 :rule cong :premises (@p158) :args ((forall @t3 (or @t75 @t125)))) % 0.45/0.65 (step @p160 :rule trans :premises (@p159 @p153)) % 0.45/0.65 (step @p161 :rule trans :premises (@p160 @p152)) % 0.45/0.65 (step @p162 :rule bool-impl-elim :args (@t2 @t125)) % 0.45/0.65 (step @p163 :rule cong :premises (@p162) :args ((forall @t3 (=> @t2 @t125)))) % 0.45/0.65 (step @p164 :rule trans :premises (@p163 @p161)) % 0.45/0.65 (step @p165 :rule bool-impl-elim :args (@t7 @t6)) % 0.45/0.65 (step @p166 :rule cong :premises (@p165) :args (@t9)) % 0.45/0.65 (step @p167 :rule cong :premises (@p71 @p166) :args (@t10)) % 0.45/0.65 (step @p168 :rule cong :premises (@p167) :args (@t11)) % 0.45/0.65 (step @p169 :rule trans :premises (@p168 @p164)) % 0.45/0.65 (step @p170 :rule eq_resolve :premises (@p3 @p169)) % 0.45/0.65 (step @p171 :rule instantiate :premises (@p170) :args (@t86)) % 0.45/0.65 (step @p172 :rule cnf_or_pos :args (@t126)) % 0.45/0.65 (step @p173 :rule reordering :premises (@p172) :args ((or @t90 @t89 @t111 (not @t126)))) % 0.45/0.65 (step @p174 :rule chain_m_resolution :premises (@p173 @p44 @p77 @p171) :args (@t111 @t92 (@list @t64 @t65 @t126))) % 0.45/0.65 (step @p175 :rule aci_norm :args ((= @t133 (or @t131 @t130 @t129 @t128)))) % 0.45/0.65 (step @p176 :rule cong :premises (@p175) :args (@t134)) % 0.45/0.65 (step @p177 :rule quant-merge-prenex :args ((= (forall @t3 @t136) @t134))) % 0.45/0.65 (step @p178 :rule alpha_equiv :args (@t137 (@list @t127) @t82)) % 0.45/0.65 (step @p179 :rule refl :args (@t131)) % 0.45/0.65 (step @p180 :rule nary_cong :premises (@p179 @p178) :args (@t138)) % 0.45/0.65 (step @p181 :rule quant-miniscope-or :args ((= @t136 @t138))) % 0.45/0.65 (step @p182 :rule trans :premises (@p181 @p180)) % 0.45/0.65 (step @p183 :rule symm :premises (@p182)) % 0.45/0.65 (step @p184 :rule cong :premises (@p183) :args ((forall @t3 (or @t131 @t142)))) % 0.45/0.65 (step @p185 :rule trans :premises (@p184 @p177)) % 0.45/0.65 (step @p186 :rule trans :premises (@p185 @p176)) % 0.45/0.65 (step @p187 :rule bool-impl-elim :args (@t4 @t142)) % 0.45/0.65 (step @p188 :rule cong :premises (@p187) :args ((forall @t3 (=> @t4 @t142)))) % 0.45/0.65 (step @p189 :rule trans :premises (@p188 @p186)) % 0.45/0.65 (step @p190 :rule aci_norm :args ((= (or (or @t140 @t139) @t46) @t141))) % 0.45/0.65 (step @p191 :rule refl :args (@t46)) % 0.45/0.65 (step @p192 :rule bool-and-de-morgan :args (@t19 @t21 true)) % 0.45/0.65 (step @p193 :rule nary_cong :premises (@p192 @p191) :args ((or (not @t45) @t46))) % 0.45/0.65 (step @p194 :rule trans :premises (@p193 @p190)) % 0.45/0.65 (step @p195 :rule bool-impl-elim :args (@t45 @t46)) % 0.45/0.65 (step @p196 :rule trans :premises (@p195 @p194)) % 0.45/0.65 (step @p197 :rule cong :premises (@p196) :args (@t47)) % 0.45/0.65 (step @p198 :rule refl :args (@t4)) % 0.45/0.65 (step @p199 :rule cong :premises (@p198 @p197) :args (@t48)) % 0.45/0.65 (step @p200 :rule cong :premises (@p199) :args (@t49)) % 0.45/0.65 (step @p201 :rule trans :premises (@p200 @p189)) % 0.45/0.65 (step @p202 :rule eq_resolve :premises (@p22 @p201)) % 0.45/0.65 (step @p203 :rule instantiate :premises (@p202) :args ((@list tptp.xx tptp.xS))) % 0.45/0.65 (step @p204 :rule and_elim :premises (@p45) :args (0)) % 0.45/0.65 (step @p205 :rule cnf_or_pos :args (@t146)) % 0.45/0.65 (step @p206 :rule reordering :premises (@p205) :args ((or @t90 @t144 @t143 @t145 (not @t146)))) % 0.45/0.65 (step @p207 :rule chain_m_resolution :premises (@p206 @p44 @p204 @p174 @p203) :args (@t143 (@list false false false false) (@list @t64 @t66 @t111 @t146))) % 0.45/0.65 (step @p208 :rule and_elim :premises (@p127) :args (0)) % 0.45/0.65 (step @p209 :rule cnf_or_pos :args (@t151)) % 0.45/0.65 (step @p210 :rule reordering :premises (@p209) :args ((or @t150 @t149 @t145 @t110 @t148 (not @t151)))) % 0.45/0.65 (step @p211 :rule chain_m_resolution :premises (@p210 @p208 @p207 @p174 @p150 @p126) :args (@t148 (@list false false false true false) (@list @t71 @t143 @t111 @t110 @t151))) % 0.45/0.65 (step @p212 :rule refl :args (@t152)) % 0.45/0.65 (step @p213 :rule refl :args (@t153)) % 0.45/0.65 (step @p214 :rule bool-double-not-elim :args (@t69)) % 0.45/0.65 (step @p215 :rule nary_cong :premises (@p214 @p213 @p212) :args ((or (not @t154) @t153 @t152))) % 0.45/0.65 (assume-push @p249 @t148) % 0.45/0.65 (assume-push @p250 @t152) % 0.45/0.65 (step @p218 :rule evaluate :args ((= false true))) % 0.45/0.65 (step @p219 :rule true_intro :premises (@p211)) % 0.45/0.65 (step @p220 :rule false_intro :premises (@p48)) % 0.45/0.65 (step @p221 :rule symm :premises (@p80)) % 0.45/0.65 (step @p222 :rule cong :premises (@p221) :args (@t147)) % 0.45/0.65 (step @p223 :rule refl :args (@t68)) % 0.45/0.65 (step @p224 :rule cong :premises (@p223 @p222) :args (@t148)) % 0.45/0.65 (step @p225 :rule trans :premises (@p224 @p220)) % 0.45/0.65 (step @p226 :rule symm :premises (@p225)) % 0.45/0.65 (step @p227 :rule trans :premises (@p226 @p219)) % 0.45/0.65 (step @p228 false :rule eq_resolve :premises (@p227 @p218)) % 0.45/0.65 (step-pop @p251 :rule scope :premises (@p228)) % 0.45/0.65 (step-pop @p252 :rule scope :premises (@p251)) % 0.45/0.65 (step @p229 :rule process_scope :premises (@p252) :args (false)) % 0.45/0.65 (assume-push @p253 @t154) % 0.45/0.65 (assume-push @p254 @t88) % 0.45/0.65 (assume-push @p255 @t148) % 0.45/0.65 (step @p220 :rule false_intro :premises (@p48)) % 0.45/0.65 (step @p221 :rule symm :premises (@p80)) % 0.45/0.65 (step @p222 :rule cong :premises (@p221) :args (@t147)) % 0.45/0.65 (step @p223 :rule refl :args (@t68)) % 0.45/0.65 (step @p224 :rule cong :premises (@p223 @p222) :args (@t148)) % 0.45/0.65 (step @p235 :rule trans :premises (@p224 @p220)) % 0.45/0.65 (step @p236 :rule false_elim :premises (@p235)) % 0.45/0.65 (step @p237 :rule and_intro :premises (@p211 @p236)) % 0.45/0.65 (step-pop @p256 :rule scope :premises (@p237)) % 0.45/0.65 (step-pop @p257 :rule scope :premises (@p256)) % 0.45/0.65 (step-pop @p258 :rule scope :premises (@p257)) % 0.45/0.65 (step @p238 :rule process_scope :premises (@p258) :args (@t155)) % 0.45/0.65 (step @p242 :rule implies_elim :premises (@p238)) % 0.45/0.65 (step @p243 :rule resolution :premises (@p242 @p229) :args (true @t155)) % 0.45/0.65 (step @p244 :rule not_and :premises (@p243)) % 0.45/0.65 (step @p245 :rule eq_resolve :premises (@p244 @p215)) % 0.45/0.65 (step @p246 false :rule chain_m_resolution :premises (@p245 @p211 @p80 @p48) :args (false (@list false false true) (@list @t148 @t88 @t69))) % 0.45/0.65 ) % 0.45/0.65 % SZS output end Proof % 0.45/0.65 % cvc5 exiting %------------------------------------------------------------------------------