%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM539+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 : n005.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 16.42s 16.65s % Output : Proof 16.42s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.13/0.13 % Problem : NUM539+1 : TPTP v9.2.1. Released v4.0.0. % 0.13/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.18/0.35 % Computer : n005.cluster.edu % 0.18/0.35 % Model : x86_64 x86_64 % 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.35 % Memory : 8042.1875MB % 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.35 % CPULimit : 300 % 0.18/0.35 % WCLimit : 300 % 0.18/0.35 % DateTime : Tue Jun 2 11:28:33 EDT 2026 % 0.18/0.35 % CPUTime : % 0.33/0.50 %----Proving TF0_NAR, FOF, or CNF % 16.42/16.65 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 16.42/16.65 --- Run --no-e-matching --full-saturate-quant at 6... % 16.42/16.65 % SZS status Theorem % 16.42/16.65 % SZS output start Proof % 16.42/16.65 ( % 16.42/16.65 (declare-sort $$unsorted 0) % 16.42/16.65 (declare-const tptp.xS $$unsorted) % 16.42/16.65 (declare-const tptp.szmzazxdt0 (-> $$unsorted $$unsorted)) % 16.42/16.65 (declare-const tptp.szmzizndt0 (-> $$unsorted $$unsorted)) % 16.42/16.65 (declare-const tptp.sbrdtbr0 (-> $$unsorted $$unsorted)) % 16.42/16.65 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 16.42/16.65 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 16.42/16.65 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 16.42/16.65 (declare-const tptp.xT $$unsorted) % 16.42/16.65 (declare-const tptp.isFinite0 (-> $$unsorted Bool)) % 16.42/16.65 (declare-const tptp.isCountable0 (-> $$unsorted Bool)) % 16.42/16.65 (declare-const tptp.slcrc0 $$unsorted) % 16.42/16.65 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 16.42/16.65 (declare-const tptp.aSubsetOf0 (-> $$unsorted $$unsorted Bool)) % 16.42/16.65 (declare-const tptp.sdtlseqdt0 (-> $$unsorted $$unsorted Bool)) % 16.42/16.65 (declare-const tptp.szszuzczcdt0 (-> $$unsorted $$unsorted)) % 16.42/16.65 (declare-const tptp.sdtmndt0 (-> $$unsorted $$unsorted $$unsorted)) % 16.42/16.65 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 16.42/16.65 (declare-const tptp.szNzAzT0 $$unsorted) % 16.42/16.65 (declare-const tptp.sz00 $$unsorted) % 16.42/16.65 (define @t1 () (@var "W0" $$unsorted)) % 16.42/16.65 (define @t2 () (tptp.aSet0 @t1)) % 16.42/16.65 (define @t3 () (@list @t1)) % 16.42/16.65 (define @t4 () (tptp.aElement0 @t1)) % 16.42/16.65 (define @t5 () (@var "W1" $$unsorted)) % 16.42/16.65 (define @t6 () (tptp.aElement0 @t5)) % 16.42/16.65 (define @t7 () (tptp.aElementOf0 @t5 @t1)) % 16.42/16.65 (define @t8 () (@list @t5)) % 16.42/16.65 (define @t9 () (tptp.isFinite0 @t1)) % 16.42/16.65 (define @t10 () (= @t1 tptp.slcrc0)) % 16.42/16.65 (define @t11 () (tptp.isCountable0 @t1)) % 16.42/16.65 (define @t12 () (and @t2 @t11)) % 16.42/16.65 (define @t13 () (not @t10)) % 16.42/16.65 (define @t14 () (@var "W2" $$unsorted)) % 16.42/16.65 (define @t15 () (tptp.aElementOf0 @t14 @t1)) % 16.42/16.65 (define @t16 () (tptp.aElementOf0 @t14 @t5)) % 16.42/16.65 (define @t17 () (@list @t14)) % 16.42/16.65 (define @t18 () (forall @t17 (=> @t16 @t15))) % 16.42/16.65 (define @t19 () (tptp.aSet0 @t5)) % 16.42/16.65 (define @t20 () (and @t19 @t18)) % 16.42/16.65 (define @t21 () (tptp.aSubsetOf0 @t5 @t1)) % 16.42/16.65 (define @t22 () (= @t21 @t20)) % 16.42/16.65 (define @t23 () (forall @t8 @t22)) % 16.42/16.65 (define @t24 () (=> @t2 @t23)) % 16.42/16.65 (define @t25 () (forall @t3 @t24)) % 16.42/16.65 (define @t26 () (tptp.isFinite0 @t5)) % 16.42/16.65 (define @t27 () (and @t2 @t9)) % 16.42/16.65 (define @t28 () (= @t1 @t5)) % 16.42/16.65 (define @t29 () (tptp.aSubsetOf0 @t1 @t5)) % 16.42/16.65 (define @t30 () (@list @t1 @t5)) % 16.42/16.65 (define @t31 () (tptp.aSet0 @t14)) % 16.42/16.65 (define @t32 () (@list @t1 @t5 @t14)) % 16.42/16.65 (define @t33 () (@var "W3" $$unsorted)) % 16.42/16.65 (define @t34 () (= @t33 @t5)) % 16.42/16.65 (define @t35 () (tptp.aElementOf0 @t33 @t1)) % 16.42/16.65 (define @t36 () (tptp.aElement0 @t33)) % 16.42/16.65 (define @t37 () (tptp.aElementOf0 @t33 @t14)) % 16.42/16.65 (define @t38 () (@list @t33)) % 16.42/16.65 (define @t39 () (tptp.sdtpldt0 @t1 @t5)) % 16.42/16.65 (define @t40 () (and @t2 @t6)) % 16.42/16.65 (define @t41 () (tptp.sdtmndt0 @t1 @t5)) % 16.42/16.65 (define @t42 () (tptp.sdtpldt0 @t5 @t1)) % 16.42/16.65 (define @t43 () (and @t19 (tptp.isCountable0 @t5))) % 16.42/16.65 (define @t44 () (tptp.sdtmndt0 @t5 @t1)) % 16.42/16.65 (define @t45 () (and @t19 @t26)) % 16.42/16.65 (define @t46 () (tptp.aSet0 tptp.szNzAzT0)) % 16.42/16.65 (define @t47 () (tptp.szszuzczcdt0 @t1)) % 16.42/16.65 (define @t48 () (tptp.aElementOf0 @t1 tptp.szNzAzT0)) % 16.42/16.65 (define @t49 () (tptp.szszuzczcdt0 @t5)) % 16.42/16.65 (define @t50 () (tptp.aElementOf0 @t5 tptp.szNzAzT0)) % 16.42/16.65 (define @t51 () (and @t48 @t50)) % 16.42/16.65 (define @t52 () (tptp.sdtlseqdt0 @t1 @t5)) % 16.42/16.65 (define @t53 () (tptp.sdtlseqdt0 @t5 @t1)) % 16.42/16.65 (define @t54 () (and @t52 @t53)) % 16.42/16.65 (define @t55 () (=> @t54 @t28)) % 16.42/16.65 (define @t56 () (forall @t30 (=> @t51 @t55))) % 16.42/16.65 (define @t57 () (tptp.sdtlseqdt0 @t5 @t14)) % 16.42/16.65 (define @t58 () (tptp.aElementOf0 @t14 tptp.szNzAzT0)) % 16.42/16.65 (define @t59 () (tptp.sbrdtbr0 @t1)) % 16.42/16.65 (define @t60 () (forall @t17 (=> @t15 @t57))) % 16.42/16.65 (define @t61 () (and @t7 @t60)) % 16.42/16.65 (define @t62 () (tptp.szmzizndt0 @t1)) % 16.42/16.65 (define @t63 () (= @t5 @t62)) % 16.42/16.65 (define @t64 () (= @t63 @t61)) % 16.42/16.65 (define @t65 () (forall @t8 @t64)) % 16.42/16.65 (define @t66 () (tptp.aSubsetOf0 @t1 tptp.szNzAzT0)) % 16.42/16.65 (define @t67 () (and @t66 @t13)) % 16.42/16.65 (define @t68 () (=> @t67 @t65)) % 16.42/16.65 (define @t69 () (forall @t3 @t68)) % 16.42/16.65 (define @t70 () (= tptp.xT tptp.slcrc0)) % 16.42/16.65 (define @t71 () (= tptp.xS tptp.slcrc0)) % 16.42/16.65 (define @t72 () (tptp.aSubsetOf0 tptp.xT tptp.szNzAzT0)) % 16.42/16.65 (define @t73 () (tptp.aSubsetOf0 tptp.xS tptp.szNzAzT0)) % 16.42/16.65 (define @t74 () (tptp.szmzizndt0 tptp.xT)) % 16.42/16.65 (define @t75 () (tptp.aElementOf0 @t74 tptp.xS)) % 16.42/16.65 (define @t76 () (tptp.szmzizndt0 tptp.xS)) % 16.42/16.65 (define @t77 () (tptp.aElementOf0 @t76 tptp.xT)) % 16.42/16.65 (define @t78 () (= @t76 @t74)) % 16.42/16.65 (define @t79 () (@var "BOUND_VARIABLE_8251" $$unsorted)) % 16.42/16.65 (define @t80 () (= @t62 @t79)) % 16.42/16.65 (define @t81 () (not @t15)) % 16.42/16.65 (define @t82 () (and (tptp.aElementOf0 @t79 @t1) (forall @t17 (or @t81 (tptp.sdtlseqdt0 @t79 @t14))))) % 16.42/16.65 (define @t83 () (= (= @t79 @t62) @t82)) % 16.42/16.65 (define @t84 () (not @t66)) % 16.42/16.65 (define @t85 () (or @t84 @t10 @t83)) % 16.42/16.65 (define @t86 () (@list @t1 @t79)) % 16.42/16.65 (define @t87 () (forall @t86 @t85)) % 16.42/16.65 (define @t88 () (@list @t79)) % 16.42/16.65 (define @t89 () (forall @t88 @t85)) % 16.42/16.65 (define @t90 () (forall @t88 @t83)) % 16.42/16.65 (define @t91 () (@list @t5)) % 16.42/16.65 (define @t92 () (or @t84 @t10 @t90)) % 16.42/16.65 (define @t93 () (forall @t8 (= @t63 (and @t7 (forall @t17 (or @t81 @t57)))))) % 16.42/16.65 (define @t94 () (or @t84 @t10 @t93)) % 16.42/16.65 (define @t95 () (forall @t17 (or (not (tptp.aElementOf0 @t14 tptp.xT)) (tptp.sdtlseqdt0 @t74 @t14)))) % 16.42/16.65 (define @t96 () (and (tptp.aElementOf0 @t74 tptp.xT) @t95)) % 16.42/16.65 (define @t97 () (= @t74 @t74)) % 16.42/16.65 (define @t98 () (not @t72)) % 16.42/16.65 (define @t99 () (or @t98 @t70 (= @t96 @t97))) % 16.42/16.65 (define @t100 () (forall @t86 (or @t84 @t10 (= @t82 @t80)))) % 16.42/16.65 (define @t101 () (= tptp.slcrc0 tptp.xT)) % 16.42/16.65 (define @t102 () (or @t98 @t101 @t96)) % 16.42/16.65 (define @t103 () (@list false)) % 16.42/16.65 (define @t104 () (@list @t100)) % 16.42/16.65 (define @t105 () (@list true false false)) % 16.42/16.65 (define @t106 () (not @t53)) % 16.42/16.65 (define @t107 () (not @t52)) % 16.42/16.65 (define @t108 () (not @t50)) % 16.42/16.65 (define @t109 () (not @t48)) % 16.42/16.65 (define @t110 () (or @t107 @t106 @t28)) % 16.42/16.65 (define @t111 () (not (tptp.aElementOf0 @t14 tptp.xS))) % 16.42/16.65 (define @t112 () (forall @t17 (or @t111 (tptp.sdtlseqdt0 @t76 @t14)))) % 16.42/16.65 (define @t113 () (tptp.aElementOf0 @t76 tptp.xS)) % 16.42/16.65 (define @t114 () (and @t113 @t112)) % 16.42/16.65 (define @t115 () (= @t114 (= @t76 @t76))) % 16.42/16.65 (define @t116 () (not @t73)) % 16.42/16.65 (define @t117 () (or @t116 @t71 @t115)) % 16.42/16.65 (define @t118 () (= tptp.slcrc0 tptp.xS)) % 16.42/16.65 (define @t119 () (or @t116 @t118 @t114)) % 16.42/16.65 (define @t120 () (not @t114)) % 16.42/16.65 (define @t121 () (@list @t114)) % 16.42/16.65 (define @t122 () (@list @t74)) % 16.42/16.65 (define @t123 () (tptp.sdtlseqdt0 @t76 @t74)) % 16.42/16.65 (define @t124 () (not @t75)) % 16.42/16.65 (define @t125 () (or @t124 @t123)) % 16.42/16.65 (define @t126 () (@list false false)) % 16.42/16.65 (define @t127 () (@var "BOUND_VARIABLE_7797" $$unsorted)) % 16.42/16.65 (define @t128 () (= (tptp.aSubsetOf0 @t127 @t1) (and (tptp.aSet0 @t127) (forall @t17 (or (not (tptp.aElementOf0 @t14 @t127)) @t15))))) % 16.42/16.65 (define @t129 () (not @t2)) % 16.42/16.65 (define @t130 () (or @t129 @t128)) % 16.42/16.65 (define @t131 () (@list @t127)) % 16.42/16.65 (define @t132 () (forall @t131 @t130)) % 16.42/16.65 (define @t133 () (forall @t131 @t128)) % 16.42/16.65 (define @t134 () (or @t129 @t133)) % 16.42/16.65 (define @t135 () (forall @t8 (= @t21 (and @t19 (forall @t17 (or (not @t16) @t15)))))) % 16.42/16.65 (define @t136 () (forall @t17 (or @t111 @t58))) % 16.42/16.65 (define @t137 () (and (tptp.aSet0 tptp.xS) @t136)) % 16.42/16.65 (define @t138 () (= @t73 @t137)) % 16.42/16.65 (define @t139 () (not @t46)) % 16.42/16.65 (define @t140 () (or @t139 @t138)) % 16.42/16.65 (define @t141 () (tptp.aElementOf0 @t74 tptp.szNzAzT0)) % 16.42/16.65 (define @t142 () (or @t124 @t141)) % 16.42/16.65 (define @t143 () (@list @t76)) % 16.42/16.65 (define @t144 () (tptp.aElementOf0 @t76 tptp.szNzAzT0)) % 16.42/16.65 (define @t145 () (not @t113)) % 16.42/16.65 (define @t146 () (or @t145 @t144)) % 16.42/16.65 (define @t147 () (tptp.sdtlseqdt0 @t74 @t76)) % 16.42/16.65 (define @t148 () (not @t147)) % 16.42/16.65 (define @t149 () (not @t123)) % 16.42/16.65 (define @t150 () (not @t141)) % 16.42/16.65 (define @t151 () (not @t144)) % 16.42/16.65 (define @t152 () (or @t151 @t150 @t149 @t148 @t78)) % 16.42/16.65 (define @t153 () (not @t77)) % 16.42/16.65 (define @t154 () (or @t153 @t147)) % 16.42/16.65 (define @t155 () (not @t154)) % 16.42/16.65 (assume @p1 (forall @t3 (=> @t2 true))) % 16.42/16.65 (assume @p2 (forall @t3 (=> @t4 true))) % 16.42/16.65 (assume @p3 (forall @t3 (=> @t2 (forall @t8 (=> @t7 @t6))))) % 16.42/16.65 (assume @p4 (forall @t3 (=> @t2 (=> @t9 true)))) % 16.42/16.65 (assume @p5 (forall @t3 (= @t10 (and @t2 (not (exists @t8 @t7)))))) % 16.42/16.65 (assume @p6 (tptp.isFinite0 tptp.slcrc0)) % 16.42/16.65 (assume @p7 (forall @t3 (=> @t2 (=> @t11 true)))) % 16.42/16.65 (assume @p8 (forall @t3 (=> @t12 (not @t9)))) % 16.42/16.65 (assume @p9 (forall @t3 (=> @t12 @t13))) % 16.42/16.65 (assume @p10 @t25) % 16.42/16.65 (assume @p11 (forall @t3 (=> @t27 (forall @t8 (=> @t21 @t26))))) % 16.42/16.65 (assume @p12 (forall @t3 (=> @t2 (tptp.aSubsetOf0 @t1 @t1)))) % 16.42/16.65 (assume @p13 (forall @t30 (=> (and @t2 @t19) (=> (and @t29 @t21) @t28)))) % 16.42/16.65 (assume @p14 (forall @t32 (=> (and @t2 @t19 @t31) (=> (and @t29 (tptp.aSubsetOf0 @t5 @t14)) (tptp.aSubsetOf0 @t1 @t14))))) % 16.42/16.65 (assume @p15 (forall @t30 (=> @t40 (forall @t17 (= (= @t14 @t39) (and @t31 (forall @t38 (= @t37 (and @t36 (or @t35 @t34)))))))))) % 16.42/16.65 (assume @p16 (forall @t30 (=> @t40 (forall @t17 (= (= @t14 @t41) (and @t31 (forall @t38 (= @t37 (and @t36 @t35 (not @t34)))))))))) % 16.42/16.65 (assume @p17 (forall @t3 (=> @t2 (forall @t8 (=> @t7 (= (tptp.sdtpldt0 @t41 @t5) @t1)))))) % 16.42/16.65 (assume @p18 (forall @t30 (=> (and @t4 @t19) (=> (not (tptp.aElementOf0 @t1 @t5)) (= (tptp.sdtmndt0 @t42 @t1) @t5))))) % 16.42/16.65 (assume @p19 (forall @t3 (=> @t4 (forall @t8 (=> @t43 (tptp.isCountable0 @t42)))))) % 16.42/16.65 (assume @p20 (forall @t3 (=> @t4 (forall @t8 (=> @t43 (tptp.isCountable0 @t44)))))) % 16.42/16.65 (assume @p21 (forall @t3 (=> @t4 (forall @t8 (=> @t45 (tptp.isFinite0 @t42)))))) % 16.42/16.65 (assume @p22 (forall @t3 (=> @t4 (forall @t8 (=> @t45 (tptp.isFinite0 @t44)))))) % 16.42/16.65 (assume @p23 (and @t46 (tptp.isCountable0 tptp.szNzAzT0))) % 16.42/16.65 (assume @p24 (tptp.aElementOf0 tptp.sz00 tptp.szNzAzT0)) % 16.42/16.65 (assume @p25 (forall @t3 (=> @t48 (and (tptp.aElementOf0 @t47 tptp.szNzAzT0) (not (= @t47 tptp.sz00)))))) % 16.42/16.65 (assume @p26 (forall @t30 (=> @t51 (=> (= @t47 @t49) @t28)))) % 16.42/16.65 (assume @p27 (forall @t3 (=> @t48 (or (= @t1 tptp.sz00) (exists @t8 (and @t50 (= @t1 @t49))))))) % 16.42/16.65 (assume @p28 (forall @t3 (=> @t48 (not (= @t1 @t47))))) % 16.42/16.65 (assume @p29 (forall @t30 (=> @t51 (=> @t52 true)))) % 16.42/16.65 (assume @p30 (forall @t3 (=> @t48 (tptp.sdtlseqdt0 tptp.sz00 @t1)))) % 16.42/16.65 (assume @p31 (forall @t3 (=> @t48 (not (tptp.sdtlseqdt0 @t47 tptp.sz00))))) % 16.42/16.65 (assume @p32 (forall @t30 (=> @t51 (= @t52 (tptp.sdtlseqdt0 @t47 @t49))))) % 16.42/16.65 (assume @p33 (forall @t3 (=> @t48 (tptp.sdtlseqdt0 @t1 @t47)))) % 16.42/16.65 (assume @p34 (forall @t3 (=> @t48 (tptp.sdtlseqdt0 @t1 @t1)))) % 16.42/16.65 (assume @p35 @t56) % 16.42/16.65 (assume @p36 (forall @t32 (=> (and @t48 @t50 @t58) (=> (and @t52 @t57) (tptp.sdtlseqdt0 @t1 @t14))))) % 16.42/16.65 (assume @p37 (forall @t30 (=> @t51 (or @t52 (tptp.sdtlseqdt0 @t49 @t1))))) % 16.42/16.65 (assume @p38 (forall @t30 (=> @t51 (=> (tptp.iLess0 @t1 @t5) true)))) % 16.42/16.65 (assume @p39 (forall @t3 (=> @t48 (tptp.iLess0 @t1 @t47)))) % 16.42/16.65 (assume @p40 (forall @t3 (=> @t2 (tptp.aElement0 @t59)))) % 16.42/16.65 (assume @p41 (forall @t3 (=> @t2 (= (tptp.aElementOf0 @t59 tptp.szNzAzT0) @t9)))) % 16.42/16.65 (assume @p42 (forall @t3 (=> @t2 (= (= @t59 tptp.sz00) @t10)))) % 16.42/16.65 (assume @p43 (forall @t3 (=> @t27 (forall @t8 (=> @t6 (=> (not @t7) (= (tptp.sbrdtbr0 @t39) (tptp.szszuzczcdt0 @t59)))))))) % 16.42/16.65 (assume @p44 (forall @t3 (=> @t2 (forall @t8 (=> (and @t9 @t7) (= (tptp.szszuzczcdt0 (tptp.sbrdtbr0 @t41)) @t59)))))) % 16.42/16.65 (assume @p45 (forall @t3 (=> @t2 (forall @t8 (=> (and @t9 @t21) (tptp.sdtlseqdt0 (tptp.sbrdtbr0 @t5) @t59)))))) % 16.42/16.65 (assume @p46 (forall @t30 (=> (and @t2 @t50) (=> (and @t9 (tptp.sdtlseqdt0 @t5 @t59)) (exists @t17 (and (tptp.aSubsetOf0 @t14 @t1) (= (tptp.sbrdtbr0 @t14) @t5))))))) % 16.42/16.65 (assume @p47 @t69) % 16.42/16.65 (assume @p48 (forall @t3 (=> (and @t66 @t9 @t13) (forall @t8 (= (= @t5 (tptp.szmzazxdt0 @t1)) (and @t7 (forall @t17 (=> @t15 (tptp.sdtlseqdt0 @t14 @t5))))))))) % 16.42/16.65 (assume @p49 (and @t73 @t72 (not @t71) (not @t70))) % 16.42/16.65 (assume @p50 (and @t77 @t75)) % 16.42/16.65 (assume @p51 (not @t78)) % 16.42/16.65 (assume @p52 true) % 16.42/16.65 (step @p53 :rule eq-symm :args (@t80 @t82)) % 16.42/16.65 (step @p54 :rule refl :args (@t82)) % 16.42/16.65 (step @p55 :rule eq-symm :args (@t79 @t62)) % 16.42/16.65 (step @p56 :rule cong :premises (@p55 @p54) :args (@t83)) % 16.42/16.65 (step @p57 :rule trans :premises (@p56 @p53)) % 16.42/16.65 (step @p58 :rule refl :args (@t10)) % 16.42/16.65 (step @p59 :rule refl :args (@t84)) % 16.42/16.65 (step @p60 :rule nary_cong :premises (@p59 @p58 @p57) :args (@t85)) % 16.42/16.65 (step @p61 :rule cong :premises (@p60) :args (@t87)) % 16.42/16.65 (step @p62 :rule quant-merge-prenex :args ((= (forall @t3 @t89) @t87))) % 16.42/16.65 (step @p63 :rule alpha_equiv :args (@t90 (@list @t79) @t91)) % 16.42/16.65 (step @p64 :rule refl :args (@t10)) % 16.42/16.65 (step @p65 :rule refl :args (@t84)) % 16.42/16.65 (step @p66 :rule nary_cong :premises (@p65 @p64 @p63) :args (@t92)) % 16.42/16.65 (step @p67 :rule quant-miniscope-or :args ((= @t89 @t92))) % 16.42/16.65 (step @p68 :rule trans :premises (@p67 @p66)) % 16.42/16.65 (step @p69 :rule symm :premises (@p68)) % 16.42/16.65 (step @p70 :rule cong :premises (@p69) :args ((forall @t3 @t94))) % 16.42/16.65 (step @p71 :rule trans :premises (@p70 @p62)) % 16.42/16.65 (step @p72 :rule trans :premises (@p71 @p61)) % 16.42/16.65 (step @p73 :rule aci_norm :args ((= (or (or @t84 @t10) @t93) @t94))) % 16.42/16.65 (step @p74 :rule refl :args (@t93)) % 16.42/16.65 (step @p75 :rule bool-double-not-elim :args (@t10)) % 16.42/16.65 (step @p76 :rule nary_cong :premises (@p65 @p75) :args ((or @t84 (not @t13)))) % 16.42/16.65 (step @p77 :rule bool-and-de-morgan :args (@t66 @t13 true)) % 16.42/16.65 (step @p78 :rule trans :premises (@p77 @p76)) % 16.42/16.65 (step @p79 :rule nary_cong :premises (@p78 @p74) :args ((or (not @t67) @t93))) % 16.42/16.65 (step @p80 :rule trans :premises (@p79 @p73)) % 16.42/16.65 (step @p81 :rule bool-impl-elim :args (@t67 @t93)) % 16.42/16.65 (step @p82 :rule trans :premises (@p81 @p80)) % 16.42/16.65 (step @p83 :rule cong :premises (@p82) :args ((forall @t3 (=> @t67 @t93)))) % 16.42/16.65 (step @p84 :rule trans :premises (@p83 @p72)) % 16.42/16.65 (step @p85 :rule bool-impl-elim :args (@t15 @t57)) % 16.42/16.65 (step @p86 :rule cong :premises (@p85) :args (@t60)) % 16.42/16.65 (step @p87 :rule refl :args (@t7)) % 16.42/16.65 (step @p88 :rule nary_cong :premises (@p87 @p86) :args (@t61)) % 16.42/16.65 (step @p89 :rule refl :args (@t63)) % 16.42/16.65 (step @p90 :rule cong :premises (@p89 @p88) :args (@t64)) % 16.42/16.65 (step @p91 :rule cong :premises (@p90) :args (@t65)) % 16.42/16.65 (step @p92 :rule refl :args (@t67)) % 16.42/16.65 (step @p93 :rule cong :premises (@p92 @p91) :args (@t68)) % 16.42/16.65 (step @p94 :rule cong :premises (@p93) :args (@t69)) % 16.42/16.65 (step @p95 :rule trans :premises (@p94 @p84)) % 16.42/16.65 (step @p96 :rule eq_resolve :premises (@p47 @p95)) % 16.42/16.65 (step @p97 :rule bool-eq-true :args (@t96)) % 16.42/16.65 (step @p98 :rule eq-symm :args (true @t96)) % 16.42/16.65 (step @p99 :rule trans :premises (@p98 @p97)) % 16.42/16.65 (step @p100 :rule refl :args (@t96)) % 16.42/16.65 (step @p101 :rule eq-refl :args (@t74)) % 16.42/16.65 (step @p102 :rule cong :premises (@p101 @p100) :args ((= @t97 @t96))) % 16.42/16.65 (step @p103 :rule trans :premises (@p102 @p99)) % 16.42/16.65 (step @p104 :rule eq-symm :args (@t96 @t97)) % 16.42/16.65 (step @p105 :rule trans :premises (@p104 @p103)) % 16.42/16.65 (step @p106 :rule eq-symm :args (tptp.xT tptp.slcrc0)) % 16.42/16.65 (step @p107 :rule refl :args (@t98)) % 16.42/16.65 (step @p108 :rule nary_cong :premises (@p107 @p106 @p105) :args (@t99)) % 16.42/16.65 (step @p109 :rule refl :args (@t100)) % 16.42/16.65 (step @p110 :rule cong :premises (@p109 @p108) :args ((=> @t100 @t99))) % 16.42/16.65 (assume-push @p232 @t100) % 16.42/16.65 (step @p112 :rule instantiate :premises (@p96) :args ((@list tptp.xT @t74))) % 16.42/16.65 (step-pop @p233 :rule scope :premises (@p112)) % 16.42/16.65 (step @p113 :rule process_scope :premises (@p233) :args (@t99)) % 16.42/16.65 (step @p115 :rule eq_resolve :premises (@p113 @p110)) % 16.42/16.65 (step @p116 :rule implies_elim :premises (@p115)) % 16.42/16.65 (step @p117 :rule chain_m_resolution :premises (@p116 @p96) :args (@t102 @t103 @t104)) % 16.42/16.65 (step @p118 :rule and_elim :premises (@p49) :args (1)) % 16.42/16.65 (step @p119 :rule and_elim :premises (@p49) :args (3)) % 16.42/16.65 (step @p120 :rule symm :premises (@p119)) % 16.42/16.65 (step @p121 :rule cnf_or_pos :args (@t102)) % 16.42/16.65 (step @p122 :rule reordering :premises (@p121) :args ((or @t101 @t98 @t96 (not @t102)))) % 16.42/16.65 (step @p123 :rule chain_m_resolution :premises (@p122 @p120 @p118 @p117) :args (@t96 @t105 (@list @t101 @t72 @t102))) % 16.42/16.65 (step @p124 :rule cnf_and_pos :args (@t96 1)) % 16.42/16.65 (step @p125 :rule reordering :premises (@p124) :args ((or @t95 (not @t96)))) % 16.42/16.65 (step @p126 :rule chain_m_resolution :premises (@p125 @p123) :args (@t95 @t103 (@list @t96))) % 16.42/16.65 (step @p127 :rule aci_norm :args ((= (or (or @t109 @t108) @t110) (or @t109 @t108 @t107 @t106 @t28)))) % 16.42/16.65 (step @p128 :rule aci_norm :args ((= (or (or @t107 @t106) @t28) @t110))) % 16.42/16.65 (step @p129 :rule refl :args (@t28)) % 16.42/16.65 (step @p130 :rule bool-and-de-morgan :args (@t52 @t53 true)) % 16.42/16.65 (step @p131 :rule nary_cong :premises (@p130 @p129) :args ((or (not @t54) @t28))) % 16.42/16.65 (step @p132 :rule trans :premises (@p131 @p128)) % 16.42/16.65 (step @p133 :rule bool-impl-elim :args (@t54 @t28)) % 16.42/16.65 (step @p134 :rule trans :premises (@p133 @p132)) % 16.42/16.65 (step @p135 :rule bool-and-de-morgan :args (@t48 @t50 true)) % 16.42/16.65 (step @p136 :rule nary_cong :premises (@p135 @p134) :args ((or (not @t51) @t55))) % 16.42/16.65 (step @p137 :rule trans :premises (@p136 @p127)) % 16.42/16.65 (step @p138 :rule bool-impl-elim :args (@t51 @t55)) % 16.42/16.65 (step @p139 :rule trans :premises (@p138 @p137)) % 16.42/16.65 (step @p140 :rule cong :premises (@p139) :args (@t56)) % 16.42/16.65 (step @p141 :rule eq_resolve :premises (@p35 @p140)) % 16.42/16.65 (step @p142 :rule instantiate :premises (@p141) :args ((@list @t76 @t74))) % 16.42/16.65 (step @p143 :rule bool-eq-true :args (@t114)) % 16.42/16.65 (step @p144 :rule eq-refl :args (@t76)) % 16.42/16.65 (step @p145 :rule refl :args (@t114)) % 16.42/16.65 (step @p146 :rule cong :premises (@p145 @p144) :args (@t115)) % 16.42/16.65 (step @p147 :rule trans :premises (@p146 @p143)) % 16.42/16.65 (step @p148 :rule eq-symm :args (tptp.xS tptp.slcrc0)) % 16.42/16.65 (step @p149 :rule refl :args (@t116)) % 16.42/16.65 (step @p150 :rule nary_cong :premises (@p149 @p148 @p147) :args (@t117)) % 16.42/16.65 (step @p151 :rule cong :premises (@p109 @p150) :args ((=> @t100 @t117))) % 16.42/16.65 (assume-push @p234 @t100) % 16.42/16.65 (step @p153 :rule instantiate :premises (@p96) :args ((@list tptp.xS @t76))) % 16.42/16.65 (step-pop @p235 :rule scope :premises (@p153)) % 16.42/16.65 (step @p154 :rule process_scope :premises (@p235) :args (@t117)) % 16.42/16.65 (step @p156 :rule eq_resolve :premises (@p154 @p151)) % 16.42/16.65 (step @p157 :rule implies_elim :premises (@p156)) % 16.42/16.65 (step @p158 :rule chain_m_resolution :premises (@p157 @p96) :args (@t119 @t103 @t104)) % 16.42/16.65 (step @p159 :rule and_elim :premises (@p49) :args (0)) % 16.42/16.65 (step @p160 :rule and_elim :premises (@p49) :args (2)) % 16.42/16.65 (step @p161 :rule symm :premises (@p160)) % 16.42/16.65 (step @p162 :rule cnf_or_pos :args (@t119)) % 16.42/16.65 (step @p163 :rule reordering :premises (@p162) :args ((or @t118 @t116 @t114 (not @t119)))) % 16.42/16.65 (step @p164 :rule chain_m_resolution :premises (@p163 @p161 @p159 @p158) :args (@t114 @t105 (@list @t118 @t73 @t119))) % 16.42/16.65 (step @p165 :rule cnf_and_pos :args (@t114 1)) % 16.42/16.65 (step @p166 :rule reordering :premises (@p165) :args ((or @t112 @t120))) % 16.42/16.65 (step @p167 :rule chain_m_resolution :premises (@p166 @p164) :args (@t112 @t103 @t121)) % 16.42/16.65 (step @p168 :rule instantiate :premises (@p167) :args (@t122)) % 16.42/16.65 (step @p169 :rule and_elim :premises (@p50) :args (1)) % 16.42/16.65 (step @p170 :rule cnf_or_pos :args (@t125)) % 16.42/16.65 (step @p171 :rule reordering :premises (@p170) :args ((or @t124 @t123 (not @t125)))) % 16.42/16.65 (step @p172 :rule chain_m_resolution :premises (@p171 @p169 @p168) :args (@t123 @t126 (@list @t75 @t125))) % 16.42/16.65 (step @p173 :rule quant-merge-prenex :args ((= (forall @t3 @t132) (forall (@list @t1 @t127) @t130)))) % 16.42/16.65 (step @p174 :rule alpha_equiv :args (@t133 (@list @t127) @t91)) % 16.42/16.65 (step @p175 :rule refl :args (@t129)) % 16.42/16.65 (step @p176 :rule nary_cong :premises (@p175 @p174) :args (@t134)) % 16.42/16.65 (step @p177 :rule quant-miniscope-or :args ((= @t132 @t134))) % 16.42/16.65 (step @p178 :rule trans :premises (@p177 @p176)) % 16.42/16.65 (step @p179 :rule symm :premises (@p178)) % 16.42/16.65 (step @p180 :rule cong :premises (@p179) :args ((forall @t3 (or @t129 @t135)))) % 16.42/16.65 (step @p181 :rule trans :premises (@p180 @p173)) % 16.42/16.65 (step @p182 :rule bool-impl-elim :args (@t2 @t135)) % 16.42/16.65 (step @p183 :rule cong :premises (@p182) :args ((forall @t3 (=> @t2 @t135)))) % 16.42/16.65 (step @p184 :rule trans :premises (@p183 @p181)) % 16.42/16.65 (step @p185 :rule bool-impl-elim :args (@t16 @t15)) % 16.42/16.65 (step @p186 :rule cong :premises (@p185) :args (@t18)) % 16.42/16.65 (step @p187 :rule refl :args (@t19)) % 16.42/16.65 (step @p188 :rule nary_cong :premises (@p187 @p186) :args (@t20)) % 16.42/16.65 (step @p189 :rule refl :args (@t21)) % 16.42/16.65 (step @p190 :rule cong :premises (@p189 @p188) :args (@t22)) % 16.42/16.65 (step @p191 :rule cong :premises (@p190) :args (@t23)) % 16.42/16.65 (step @p192 :rule refl :args (@t2)) % 16.42/16.65 (step @p193 :rule cong :premises (@p192 @p191) :args (@t24)) % 16.42/16.65 (step @p194 :rule cong :premises (@p193) :args (@t25)) % 16.42/16.65 (step @p195 :rule trans :premises (@p194 @p184)) % 16.42/16.65 (step @p196 :rule eq_resolve :premises (@p10 @p195)) % 16.42/16.65 (step @p197 :rule instantiate :premises (@p196) :args ((@list tptp.szNzAzT0 tptp.xS))) % 16.42/16.65 (step @p198 :rule and_elim :premises (@p23) :args (0)) % 16.42/16.65 (step @p199 :rule cnf_or_pos :args (@t140)) % 16.42/16.65 (step @p200 :rule reordering :premises (@p199) :args ((or @t139 @t138 (not @t140)))) % 16.42/16.65 (step @p201 :rule chain_m_resolution :premises (@p200 @p198 @p197) :args (@t138 @t126 (@list @t46 @t140))) % 16.42/16.65 (step @p202 :rule cnf_equiv_pos1 :args (@t138)) % 16.42/16.65 (step @p203 :rule reordering :premises (@p202) :args ((or @t116 @t137 (not @t138)))) % 16.42/16.65 (step @p204 :rule chain_m_resolution :premises (@p203 @p159 @p201) :args (@t137 @t126 (@list @t73 @t138))) % 16.42/16.65 (step @p205 :rule cnf_and_pos :args (@t137 1)) % 16.42/16.65 (step @p206 :rule reordering :premises (@p205) :args ((or @t136 (not @t137)))) % 16.42/16.65 (step @p207 :rule chain_m_resolution :premises (@p206 @p204) :args (@t136 @t103 (@list @t137))) % 16.42/16.65 (step @p208 :rule instantiate :premises (@p207) :args (@t122)) % 16.42/16.65 (step @p209 :rule cnf_or_pos :args (@t142)) % 16.42/16.65 (step @p210 :rule reordering :premises (@p209) :args ((or @t124 @t141 (not @t142)))) % 16.42/16.65 (step @p211 :rule chain_m_resolution :premises (@p210 @p169 @p208) :args (@t141 @t126 (@list @t75 @t142))) % 16.42/16.65 (step @p212 :rule instantiate :premises (@p207) :args (@t143)) % 16.42/16.65 (step @p213 :rule cnf_and_pos :args (@t114 0)) % 16.42/16.65 (step @p214 :rule reordering :premises (@p213) :args ((or @t113 @t120))) % 16.42/16.65 (step @p215 :rule chain_m_resolution :premises (@p214 @p164) :args (@t113 @t103 @t121)) % 16.42/16.65 (step @p216 :rule cnf_or_pos :args (@t146)) % 16.42/16.65 (step @p217 :rule reordering :premises (@p216) :args ((or @t144 @t145 (not @t146)))) % 16.42/16.65 (step @p218 :rule chain_m_resolution :premises (@p217 @p215 @p212) :args (@t144 @t126 (@list @t113 @t146))) % 16.42/16.65 (step @p219 :rule cnf_or_pos :args (@t152)) % 16.42/16.65 (step @p220 :rule reordering :premises (@p219) :args ((or @t78 @t151 @t150 @t148 @t149 (not @t152)))) % 16.42/16.65 (step @p221 :rule chain_m_resolution :premises (@p220 @p51 @p218 @p211 @p172 @p142) :args (@t148 (@list true false false false false) (@list @t78 @t144 @t141 @t123 @t152))) % 16.42/16.65 (step @p222 :rule and_elim :premises (@p50) :args (0)) % 16.42/16.65 (step @p223 :rule cnf_or_pos :args (@t154)) % 16.42/16.65 (step @p224 :rule reordering :premises (@p223) :args ((or @t153 @t147 @t155))) % 16.42/16.65 (step @p225 :rule chain_m_resolution :premises (@p224 @p222 @p221) :args (@t155 (@list false true) (@list @t77 @t147))) % 16.42/16.65 (assume-push @p236 @t95) % 16.42/16.65 (step @p227 :rule instantiate :premises (@p126) :args (@t143)) % 16.42/16.65 (step-pop @p237 :rule scope :premises (@p227)) % 16.42/16.65 (step @p228 :rule process_scope :premises (@p237) :args (@t154)) % 16.42/16.65 (step @p230 :rule implies_elim :premises (@p228)) % 16.42/16.65 (step @p231 false :rule chain_m_resolution :premises (@p230 @p225 @p126) :args (false (@list true false) (@list @t154 @t95))) % 16.42/16.65 ) % 16.42/16.65 % SZS output end Proof % 16.42/16.65 % cvc5 exiting %------------------------------------------------------------------------------