%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : RNG098+1 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n006.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 08:45:40 AM UTC 2026 % Result : Theorem 1.73s 2.02s % Output : Proof 0.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : RNG098+1 : TPTP v9.2.1. Released v4.0.0. % 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.18/0.34 % Computer : n006.cluster.edu % 0.18/0.34 % Model : x86_64 x86_64 % 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.34 % Memory : 8042.1875MB % 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.34 % CPULimit : 300 % 0.18/0.34 % WCLimit : 300 % 0.18/0.34 % DateTime : Tue Jun 2 14:07:04 EDT 2026 % 0.18/0.35 % CPUTime : % 0.29/0.50 %----Proving TF0_NAR, FOF, or CNF % 1.73/2.02 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 1.73/2.02 % SZS status Theorem % 1.73/2.02 % SZS output start Proof % 1.73/2.02 ( % 1.73/2.02 (declare-sort $$unsorted 0) % 1.73/2.02 (declare-const tptp.xw $$unsorted) % 1.73/2.02 (declare-const tptp.xa $$unsorted) % 1.73/2.02 (declare-const tptp.xb $$unsorted) % 1.73/2.02 (declare-const tptp.xx $$unsorted) % 1.73/2.02 (declare-const tptp.xy $$unsorted) % 1.73/2.02 (declare-const tptp.xI $$unsorted) % 1.73/2.02 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 1.73/2.02 (declare-const tptp.sz00 $$unsorted) % 1.73/2.02 (declare-const tptp.sz10 $$unsorted) % 1.73/2.02 (declare-const tptp.smndt0 (-> $$unsorted $$unsorted)) % 1.73/2.02 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 1.73/2.02 (declare-const tptp.sdtasasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 1.73/2.02 (declare-const tptp.aIdeal0 (-> $$unsorted Bool)) % 1.73/2.02 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 1.73/2.02 (declare-const tptp.xJ $$unsorted) % 1.73/2.02 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 1.73/2.02 (declare-const tptp.sdtpldt1 (-> $$unsorted $$unsorted $$unsorted)) % 1.73/2.02 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 1.73/2.02 (declare-const tptp.sdteqdtlpzmzozddtrp0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 1.73/2.02 (define @t1 () (@var "W0" $$unsorted)) % 1.73/2.02 (define @t2 () (tptp.aElement0 @t1)) % 1.73/2.02 (define @t3 () (@list @t1)) % 1.73/2.02 (define @t4 () (tptp.aElement0 tptp.sz10)) % 1.73/2.02 (define @t5 () (tptp.smndt0 @t1)) % 1.73/2.02 (define @t6 () (tptp.aElement0 @t5)) % 1.73/2.02 (define @t7 () (forall @t3 (=> @t2 @t6))) % 1.73/2.02 (define @t8 () (@var "W1" $$unsorted)) % 1.73/2.02 (define @t9 () (tptp.sdtpldt0 @t1 @t8)) % 1.73/2.02 (define @t10 () (tptp.aElement0 @t8)) % 1.73/2.02 (define @t11 () (and @t2 @t10)) % 1.73/2.02 (define @t12 () (@list @t1 @t8)) % 1.73/2.02 (define @t13 () (tptp.sdtasdt0 @t1 @t8)) % 1.73/2.02 (define @t14 () (@var "W2" $$unsorted)) % 1.73/2.02 (define @t15 () (tptp.sdtpldt0 @t8 @t14)) % 1.73/2.02 (define @t16 () (tptp.aElement0 @t14)) % 1.73/2.02 (define @t17 () (and @t2 @t10 @t16)) % 1.73/2.02 (define @t18 () (@list @t1 @t8 @t14)) % 1.73/2.02 (define @t19 () (tptp.sdtasdt0 @t8 @t1)) % 1.73/2.02 (define @t20 () (and (= (tptp.sdtasdt0 @t1 @t15) (tptp.sdtpldt0 @t13 (tptp.sdtasdt0 @t1 @t14))) (= (tptp.sdtasdt0 @t15 @t1) (tptp.sdtpldt0 @t19 (tptp.sdtasdt0 @t14 @t1))))) % 1.73/2.02 (define @t21 () (forall @t18 (=> @t17 @t20))) % 1.73/2.02 (define @t22 () (tptp.smndt0 tptp.sz10)) % 1.73/2.02 (define @t23 () (= @t5 (tptp.sdtasdt0 @t1 @t22))) % 1.73/2.02 (define @t24 () (tptp.sdtasdt0 @t22 @t1)) % 1.73/2.02 (define @t25 () (and (= @t24 @t5) @t23)) % 1.73/2.02 (define @t26 () (=> @t2 @t25)) % 1.73/2.02 (define @t27 () (forall @t3 @t26)) % 1.73/2.02 (define @t28 () (tptp.aSet0 @t1)) % 1.73/2.02 (define @t29 () (tptp.aElementOf0 @t8 @t1)) % 1.73/2.02 (define @t30 () (@list @t8)) % 1.73/2.02 (define @t31 () (forall @t30 (=> @t29 @t10))) % 1.73/2.02 (define @t32 () (=> @t28 @t31)) % 1.73/2.02 (define @t33 () (forall @t3 @t32)) % 1.73/2.02 (define @t34 () (tptp.aElementOf0 @t14 @t1)) % 1.73/2.02 (define @t35 () (tptp.aElementOf0 @t14 @t8)) % 1.73/2.02 (define @t36 () (@list @t14)) % 1.73/2.02 (define @t37 () (and @t28 (tptp.aSet0 @t8))) % 1.73/2.02 (define @t38 () (@var "W3" $$unsorted)) % 1.73/2.02 (define @t39 () (@var "W5" $$unsorted)) % 1.73/2.02 (define @t40 () (@var "W4" $$unsorted)) % 1.73/2.02 (define @t41 () (tptp.aElementOf0 @t38 @t14)) % 1.73/2.02 (define @t42 () (@list @t38)) % 1.73/2.02 (define @t43 () (tptp.aSet0 @t14)) % 1.73/2.02 (define @t44 () (tptp.sdtpldt1 @t1 @t8)) % 1.73/2.02 (define @t45 () (tptp.sdtasasdt0 @t1 @t8)) % 1.73/2.02 (define @t46 () (tptp.aElementOf0 (tptp.sdtasdt0 @t14 @t8) @t1)) % 1.73/2.02 (define @t47 () (forall @t36 (=> @t16 @t46))) % 1.73/2.02 (define @t48 () (tptp.aElementOf0 @t15 @t1)) % 1.73/2.02 (define @t49 () (forall @t36 (=> @t34 @t48))) % 1.73/2.02 (define @t50 () (and @t49 @t47)) % 1.73/2.02 (define @t51 () (=> @t29 @t50)) % 1.73/2.02 (define @t52 () (forall @t30 @t51)) % 1.73/2.02 (define @t53 () (and @t28 @t52)) % 1.73/2.02 (define @t54 () (tptp.aIdeal0 @t1)) % 1.73/2.02 (define @t55 () (= @t54 @t53)) % 1.73/2.02 (define @t56 () (forall @t3 @t55)) % 1.73/2.02 (define @t57 () (and @t54 (tptp.aIdeal0 @t8))) % 1.73/2.02 (define @t58 () (tptp.aIdeal0 tptp.xJ)) % 1.73/2.02 (define @t59 () (tptp.aIdeal0 tptp.xI)) % 1.73/2.02 (define @t60 () (tptp.aElement0 tptp.xy)) % 1.73/2.02 (define @t61 () (tptp.aElement0 tptp.xx)) % 1.73/2.02 (define @t62 () (tptp.sdtpldt0 tptp.xa tptp.xb)) % 1.73/2.02 (define @t63 () (tptp.aElementOf0 tptp.xb tptp.xJ)) % 1.73/2.02 (define @t64 () (tptp.aElementOf0 tptp.xa tptp.xI)) % 1.73/2.02 (define @t65 () (tptp.sdtasdt0 tptp.xx tptp.xb)) % 1.73/2.02 (define @t66 () (tptp.sdtasdt0 tptp.xy tptp.xa)) % 1.73/2.02 (define @t67 () (tptp.smndt0 tptp.xx)) % 1.73/2.02 (define @t68 () (tptp.sdtpldt0 @t65 @t67)) % 1.73/2.02 (define @t69 () (tptp.sdtpldt0 @t66 @t68)) % 1.73/2.02 (define @t70 () (tptp.sdtpldt0 tptp.xw @t67)) % 1.73/2.02 (define @t71 () (tptp.sdtpldt0 tptp.xb @t22)) % 1.73/2.02 (define @t72 () (tptp.sdtasdt0 tptp.xx @t71)) % 1.73/2.02 (define @t73 () (@var "BOUND_VARIABLE_7855" $$unsorted)) % 1.73/2.02 (define @t74 () (tptp.sdtasdt0 @t73 @t8)) % 1.73/2.02 (define @t75 () (not (tptp.aElement0 @t73))) % 1.73/2.02 (define @t76 () (or @t75 (tptp.aElementOf0 @t74 @t1))) % 1.73/2.02 (define @t77 () (@var "BOUND_VARIABLE_7848" $$unsorted)) % 1.73/2.02 (define @t78 () (tptp.sdtpldt0 @t8 @t77)) % 1.73/2.02 (define @t79 () (or (not (tptp.aElementOf0 @t77 @t1)) (tptp.aElementOf0 @t78 @t1))) % 1.73/2.02 (define @t80 () (and @t79 @t76)) % 1.73/2.02 (define @t81 () (not @t29)) % 1.73/2.02 (define @t82 () (or @t81 @t80)) % 1.73/2.02 (define @t83 () (@list @t8 @t77 @t73)) % 1.73/2.02 (define @t84 () (@list @t77 @t73)) % 1.73/2.02 (define @t85 () (forall @t84 @t82)) % 1.73/2.02 (define @t86 () (forall (@list @t73) @t76)) % 1.73/2.02 (define @t87 () (@list @t14)) % 1.73/2.02 (define @t88 () (forall @t84 @t76)) % 1.73/2.02 (define @t89 () (forall (@list @t77) @t79)) % 1.73/2.02 (define @t90 () (forall @t84 @t79)) % 1.73/2.02 (define @t91 () (and @t90 @t88)) % 1.73/2.02 (define @t92 () (forall @t84 @t80)) % 1.73/2.02 (define @t93 () (or @t81 @t92)) % 1.73/2.02 (define @t94 () (not @t16)) % 1.73/2.02 (define @t95 () (and (forall @t36 (or (not @t34) @t48)) (forall @t36 (or @t94 @t46)))) % 1.73/2.02 (define @t96 () (forall @t83 (or (not (tptp.aElementOf0 @t8 tptp.xI)) (and (or (not (tptp.aElementOf0 @t77 tptp.xI)) (tptp.aElementOf0 @t78 tptp.xI)) (or @t75 (tptp.aElementOf0 @t74 tptp.xI)))))) % 1.73/2.02 (define @t97 () (and (tptp.aSet0 tptp.xI) @t96)) % 1.73/2.02 (define @t98 () (= @t59 @t97)) % 1.73/2.02 (define @t99 () (@list false false)) % 1.73/2.02 (define @t100 () (@list false)) % 1.73/2.02 (define @t101 () (tptp.aElementOf0 @t69 tptp.xI)) % 1.73/2.02 (define @t102 () (not @t10)) % 1.73/2.02 (define @t103 () (not @t2)) % 1.73/2.02 (define @t104 () (or @t103 @t102 @t94)) % 1.73/2.02 (define @t105 () (tptp.aElement0 @t22)) % 1.73/2.02 (define @t106 () (not @t4)) % 1.73/2.02 (define @t107 () (or @t106 @t105)) % 1.73/2.02 (define @t108 () (@var "BOUND_VARIABLE_7743" $$unsorted)) % 1.73/2.02 (define @t109 () (tptp.aElement0 @t108)) % 1.73/2.02 (define @t110 () (not (tptp.aElementOf0 @t108 @t1))) % 1.73/2.02 (define @t111 () (not @t28)) % 1.73/2.02 (define @t112 () (or @t110 @t109)) % 1.73/2.02 (define @t113 () (or @t111 @t112)) % 1.73/2.02 (define @t114 () (forall (@list @t1 @t108) @t113)) % 1.73/2.02 (define @t115 () (@list @t108)) % 1.73/2.02 (define @t116 () (forall @t115 @t113)) % 1.73/2.02 (define @t117 () (forall @t115 @t112)) % 1.73/2.02 (define @t118 () (or @t111 @t117)) % 1.73/2.02 (define @t119 () (forall @t30 (or @t81 @t10))) % 1.73/2.02 (define @t120 () (tptp.aSet0 tptp.xJ)) % 1.73/2.02 (define @t121 () (and @t120 (forall @t83 (or (not (tptp.aElementOf0 @t8 tptp.xJ)) (and (or (not (tptp.aElementOf0 @t77 tptp.xJ)) (tptp.aElementOf0 @t78 tptp.xJ)) (or @t75 (tptp.aElementOf0 @t74 tptp.xJ))))))) % 1.73/2.02 (define @t122 () (= @t58 @t121)) % 1.73/2.02 (define @t123 () (tptp.aElement0 tptp.xb)) % 1.73/2.02 (define @t124 () (not @t63)) % 1.73/2.02 (define @t125 () (not @t120)) % 1.73/2.02 (define @t126 () (or @t125 @t124 @t123)) % 1.73/2.02 (define @t127 () (tptp.sdtasdt0 @t22 tptp.xx)) % 1.73/2.02 (define @t128 () (tptp.sdtasdt0 tptp.xx @t22)) % 1.73/2.02 (define @t129 () (= @t72 (tptp.sdtpldt0 @t65 @t128))) % 1.73/2.02 (define @t130 () (and @t129 (= (tptp.sdtasdt0 @t71 tptp.xx) (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xb tptp.xx) @t127)))) % 1.73/2.02 (define @t131 () (not @t105)) % 1.73/2.02 (define @t132 () (not @t123)) % 1.73/2.02 (define @t133 () (not @t61)) % 1.73/2.02 (define @t134 () (or @t133 @t132 @t131 @t130)) % 1.73/2.02 (define @t135 () (and (= @t5 @t24) @t23)) % 1.73/2.02 (define @t136 () (= @t67 @t128)) % 1.73/2.02 (define @t137 () (and (= @t67 @t127) @t136)) % 1.73/2.02 (define @t138 () (or @t133 @t137)) % 1.73/2.02 (define @t139 () (tptp.aElementOf0 @t68 tptp.xI)) % 1.73/2.02 (define @t140 () (not @t139)) % 1.73/2.02 (define @t141 () (or @t140 @t101)) % 1.73/2.02 (define @t142 () (not @t141)) % 1.73/2.02 (define @t143 () (@list false true)) % 1.73/2.02 (define @t144 () (not @t60)) % 1.73/2.02 (define @t145 () (and @t141 (or @t144 (tptp.aElementOf0 (tptp.sdtasdt0 tptp.xy @t66) tptp.xI)))) % 1.73/2.02 (define @t146 () (not @t145)) % 1.73/2.02 (define @t147 () (@list true)) % 1.73/2.02 (define @t148 () (tptp.aElementOf0 @t66 tptp.xI)) % 1.73/2.02 (define @t149 () (not @t148)) % 1.73/2.02 (define @t150 () (or @t149 @t145)) % 1.73/2.02 (define @t151 () (or @t144 @t148)) % 1.73/2.02 (define @t152 () (not @t151)) % 1.73/2.02 (define @t153 () (and (or (not (tptp.aElementOf0 tptp.xb tptp.xI)) (tptp.aElementOf0 @t62 tptp.xI)) @t151)) % 1.73/2.02 (define @t154 () (not @t153)) % 1.73/2.02 (define @t155 () (not @t64)) % 1.73/2.02 (define @t156 () (or @t155 @t153)) % 1.73/2.02 (assume @p1 (forall @t3 (=> @t2 true))) % 1.73/2.02 (assume @p2 (tptp.aElement0 tptp.sz00)) % 1.73/2.02 (assume @p3 @t4) % 1.73/2.02 (assume @p4 @t7) % 1.73/2.02 (assume @p5 (forall @t12 (=> @t11 (tptp.aElement0 @t9)))) % 1.73/2.02 (assume @p6 (forall @t12 (=> @t11 (tptp.aElement0 @t13)))) % 1.73/2.02 (assume @p7 (forall @t12 (=> @t11 (= @t9 (tptp.sdtpldt0 @t8 @t1))))) % 1.73/2.02 (assume @p8 (forall @t18 (=> @t17 (= (tptp.sdtpldt0 @t9 @t14) (tptp.sdtpldt0 @t1 @t15))))) % 1.73/2.02 (assume @p9 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 tptp.sz00) @t1) (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1)))))) % 1.73/2.02 (assume @p10 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 @t5) tptp.sz00) (= tptp.sz00 (tptp.sdtpldt0 @t5 @t1)))))) % 1.73/2.02 (assume @p11 (forall @t12 (=> @t11 (= @t13 @t19)))) % 1.73/2.02 (assume @p12 (forall @t18 (=> @t17 (= (tptp.sdtasdt0 @t13 @t14) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t8 @t14)))))) % 1.73/2.02 (assume @p13 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 1.73/2.02 (assume @p14 @t21) % 1.73/2.02 (assume @p15 @t27) % 1.73/2.02 (assume @p16 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 1.73/2.02 (assume @p17 (forall @t12 (=> @t11 (=> (= @t13 tptp.sz00) (or (= @t1 tptp.sz00) (= @t8 tptp.sz00)))))) % 1.73/2.02 (assume @p18 (not (= tptp.sz10 tptp.sz00))) % 1.73/2.02 (assume @p19 (forall @t3 (=> @t28 true))) % 1.73/2.02 (assume @p20 @t33) % 1.73/2.02 (assume @p21 (forall @t12 (=> @t37 (=> (and (forall @t36 (=> @t34 @t35)) (forall @t36 (=> @t35 @t34))) (= @t1 @t8))))) % 1.73/2.02 (assume @p22 (forall @t12 (=> @t37 (forall @t36 (= (= @t14 @t44) (and @t43 (forall @t42 (= @t41 (exists (@list @t40 @t39) (and (tptp.aElementOf0 @t40 @t1) (tptp.aElementOf0 @t39 @t8) (= (tptp.sdtpldt0 @t40 @t39) @t38))))))))))) % 1.73/2.02 (assume @p23 (forall @t12 (=> @t37 (forall @t36 (= (= @t14 @t45) (and @t43 (forall @t42 (= @t41 (and (tptp.aElementOf0 @t38 @t1) (tptp.aElementOf0 @t38 @t8)))))))))) % 1.73/2.02 (assume @p24 @t56) % 1.73/2.02 (assume @p25 (forall @t12 (=> @t57 (tptp.aIdeal0 @t44)))) % 1.73/2.02 (assume @p26 (forall @t12 (=> @t57 (tptp.aIdeal0 @t45)))) % 1.73/2.02 (assume @p27 (forall @t18 (=> (and @t2 @t10 (tptp.aIdeal0 @t14)) (= (tptp.sdteqdtlpzmzozddtrp0 @t1 @t8 @t14) (tptp.aElementOf0 (tptp.sdtpldt0 @t1 (tptp.smndt0 @t8)) @t14))))) % 1.73/2.02 (assume @p28 (and @t59 @t58)) % 1.73/2.02 (assume @p29 (forall @t3 (=> @t2 (tptp.aElementOf0 @t1 (tptp.sdtpldt1 tptp.xI tptp.xJ))))) % 1.73/2.02 (assume @p30 (and @t61 @t60)) % 1.73/2.02 (assume @p31 (and @t64 @t63 (= @t62 tptp.sz10))) % 1.73/2.02 (assume @p32 (= tptp.xw (tptp.sdtpldt0 @t66 @t65))) % 1.73/2.02 (assume @p33 (= @t70 @t69)) % 1.73/2.02 (assume @p34 (tptp.aElementOf0 @t72 tptp.xI)) % 1.73/2.02 (assume @p35 (not (tptp.aElementOf0 @t70 tptp.xI))) % 1.73/2.02 (assume @p36 true) % 1.73/2.02 (step @p37 :rule and_elim :premises (@p31) :args (0)) % 1.73/2.02 (step @p38 :rule quant-merge-prenex :args ((= (forall @t30 @t85) (forall @t83 @t82)))) % 1.73/2.02 (step @p39 :rule alpha_equiv :args (@t86 (@list @t73) @t87)) % 1.73/2.02 (step @p40 :rule quant-unused-vars :args ((= @t88 @t86))) % 1.73/2.02 (step @p41 :rule trans :premises (@p40 @p39)) % 1.73/2.02 (step @p42 :rule alpha_equiv :args (@t89 (@list @t77) @t87)) % 1.73/2.02 (step @p43 :rule quant-unused-vars :args ((= @t90 @t89))) % 1.73/2.02 (step @p44 :rule trans :premises (@p43 @p42)) % 1.73/2.02 (step @p45 :rule nary_cong :premises (@p44 @p41) :args (@t91)) % 1.73/2.02 (step @p46 :rule quant-miniscope-and :args ((= @t92 @t91))) % 1.73/2.02 (step @p47 :rule trans :premises (@p46 @p45)) % 1.73/2.02 (step @p48 :rule refl :args (@t81)) % 1.73/2.02 (step @p49 :rule nary_cong :premises (@p48 @p47) :args (@t93)) % 1.73/2.02 (step @p50 :rule quant-miniscope-or :args ((= @t85 @t93))) % 1.73/2.02 (step @p51 :rule trans :premises (@p50 @p49)) % 1.73/2.02 (step @p52 :rule symm :premises (@p51)) % 1.73/2.02 (step @p53 :rule cong :premises (@p52) :args ((forall @t30 (or @t81 @t95)))) % 1.73/2.02 (step @p54 :rule trans :premises (@p53 @p38)) % 1.73/2.02 (step @p55 :rule bool-impl-elim :args (@t29 @t95)) % 1.73/2.02 (step @p56 :rule cong :premises (@p55) :args ((forall @t30 (=> @t29 @t95)))) % 1.73/2.02 (step @p57 :rule trans :premises (@p56 @p54)) % 1.73/2.02 (step @p58 :rule bool-impl-elim :args (@t16 @t46)) % 1.73/2.02 (step @p59 :rule cong :premises (@p58) :args (@t47)) % 1.73/2.02 (step @p60 :rule bool-impl-elim :args (@t34 @t48)) % 1.73/2.02 (step @p61 :rule cong :premises (@p60) :args (@t49)) % 1.73/2.02 (step @p62 :rule nary_cong :premises (@p61 @p59) :args (@t50)) % 1.73/2.02 (step @p63 :rule refl :args (@t29)) % 1.73/2.02 (step @p64 :rule cong :premises (@p63 @p62) :args (@t51)) % 1.73/2.02 (step @p65 :rule cong :premises (@p64) :args (@t52)) % 1.73/2.02 (step @p66 :rule trans :premises (@p65 @p57)) % 1.73/2.02 (step @p67 :rule refl :args (@t28)) % 1.73/2.02 (step @p68 :rule nary_cong :premises (@p67 @p66) :args (@t53)) % 1.73/2.02 (step @p69 :rule refl :args (@t54)) % 1.73/2.02 (step @p70 :rule cong :premises (@p69 @p68) :args (@t55)) % 1.73/2.02 (step @p71 :rule cong :premises (@p70) :args (@t56)) % 1.73/2.02 (step @p72 :rule eq_resolve :premises (@p24 @p71)) % 1.73/2.02 (step @p73 :rule instantiate :premises (@p72) :args ((@list tptp.xI))) % 1.73/2.02 (step @p74 :rule and_elim :premises (@p28) :args (0)) % 1.73/2.02 (step @p75 :rule cnf_equiv_pos1 :args (@t98)) % 1.73/2.02 (step @p76 :rule reordering :premises (@p75) :args ((or (not @t59) @t97 (not @t98)))) % 1.73/2.02 (step @p77 :rule chain_m_resolution :premises (@p76 @p74 @p73) :args (@t97 @t99 (@list @t59 @t98))) % 1.73/2.02 (step @p78 :rule cnf_and_pos :args (@t97 1)) % 1.73/2.02 (step @p79 :rule reordering :premises (@p78) :args ((or @t96 (not @t97)))) % 1.73/2.02 (step @p80 :rule chain_m_resolution :premises (@p79 @p77) :args (@t96 @t100 (@list @t97))) % 1.73/2.02 (step @p81 :rule instantiate :premises (@p80) :args ((@list tptp.xa tptp.xb tptp.xy))) % 1.73/2.02 (step @p82 :rule instantiate :premises (@p80) :args ((@list @t66 @t68 tptp.xy))) % 1.73/2.02 (step @p83 :rule false_intro :premises (@p35)) % 1.73/2.02 (step @p84 :rule refl :args (tptp.xI)) % 1.73/2.02 (step @p85 :rule symm :premises (@p33)) % 1.73/2.02 (step @p86 :rule cong :premises (@p85 @p84) :args (@t101)) % 1.73/2.02 (step @p87 :rule trans :premises (@p86 @p83)) % 1.73/2.02 (step @p88 :rule false_elim :premises (@p87)) % 1.73/2.02 (step @p89 :rule true_intro :premises (@p34)) % 1.73/2.02 (step @p90 :rule aci_norm :args ((= (or @t104 @t20) (or @t103 @t102 @t94 @t20)))) % 1.73/2.02 (step @p91 :rule refl :args (@t20)) % 1.73/2.02 (step @p92 :rule aci_norm :args ((= (or @t103 (or @t102 @t94)) @t104))) % 1.73/2.02 (step @p93 :rule bool-and-de-morgan :args (@t10 @t16 true)) % 1.73/2.02 (step @p94 :rule refl :args (@t103)) % 1.73/2.02 (step @p95 :rule nary_cong :premises (@p94 @p93) :args ((or @t103 (not (and @t10 @t16))))) % 1.73/2.02 (step @p96 :rule bool-and-de-morgan :args (@t2 @t10 (and @t16))) % 1.73/2.02 (step @p97 :rule trans :premises (@p96 @p95)) % 1.73/2.02 (step @p98 :rule trans :premises (@p97 @p92)) % 1.73/2.02 (step @p99 :rule nary_cong :premises (@p98 @p91) :args ((or (not @t17) @t20))) % 1.73/2.02 (step @p100 :rule trans :premises (@p99 @p90)) % 1.73/2.02 (step @p101 :rule bool-impl-elim :args (@t17 @t20)) % 1.73/2.02 (step @p102 :rule trans :premises (@p101 @p100)) % 1.73/2.02 (step @p103 :rule cong :premises (@p102) :args (@t21)) % 1.73/2.02 (step @p104 :rule eq_resolve :premises (@p14 @p103)) % 1.73/2.02 (step @p105 :rule instantiate :premises (@p104) :args ((@list tptp.xx tptp.xb @t22))) % 1.73/2.02 (step @p106 :rule bool-impl-elim :args (@t2 @t6)) % 1.73/2.02 (step @p107 :rule cong :premises (@p106) :args (@t7)) % 1.73/2.02 (step @p108 :rule eq_resolve :premises (@p4 @p107)) % 1.73/2.02 (step @p109 :rule instantiate :premises (@p108) :args ((@list tptp.sz10))) % 1.73/2.02 (step @p110 :rule cnf_or_pos :args (@t107)) % 1.73/2.02 (step @p111 :rule reordering :premises (@p110) :args ((or @t106 @t105 (not @t107)))) % 1.73/2.02 (step @p112 :rule chain_m_resolution :premises (@p111 @p3 @p109) :args (@t105 @t99 (@list @t4 @t107))) % 1.73/2.02 (step @p113 :rule aci_norm :args ((= @t113 (or @t111 @t110 @t109)))) % 1.73/2.02 (step @p114 :rule cong :premises (@p113) :args (@t114)) % 1.73/2.02 (step @p115 :rule quant-merge-prenex :args ((= (forall @t3 @t116) @t114))) % 1.73/2.02 (step @p116 :rule alpha_equiv :args (@t117 (@list @t108) (@list @t8))) % 1.73/2.02 (step @p117 :rule refl :args (@t111)) % 1.73/2.02 (step @p118 :rule nary_cong :premises (@p117 @p116) :args (@t118)) % 1.73/2.02 (step @p119 :rule quant-miniscope-or :args ((= @t116 @t118))) % 1.73/2.02 (step @p120 :rule trans :premises (@p119 @p118)) % 1.73/2.02 (step @p121 :rule symm :premises (@p120)) % 1.73/2.02 (step @p122 :rule cong :premises (@p121) :args ((forall @t3 (or @t111 @t119)))) % 1.73/2.02 (step @p123 :rule trans :premises (@p122 @p115)) % 1.73/2.02 (step @p124 :rule trans :premises (@p123 @p114)) % 1.73/2.02 (step @p125 :rule bool-impl-elim :args (@t28 @t119)) % 1.73/2.02 (step @p126 :rule cong :premises (@p125) :args ((forall @t3 (=> @t28 @t119)))) % 1.73/2.02 (step @p127 :rule trans :premises (@p126 @p124)) % 1.73/2.02 (step @p128 :rule bool-impl-elim :args (@t29 @t10)) % 1.73/2.02 (step @p129 :rule cong :premises (@p128) :args (@t31)) % 1.73/2.02 (step @p130 :rule cong :premises (@p67 @p129) :args (@t32)) % 1.73/2.02 (step @p131 :rule cong :premises (@p130) :args (@t33)) % 1.73/2.02 (step @p132 :rule trans :premises (@p131 @p127)) % 1.73/2.02 (step @p133 :rule eq_resolve :premises (@p20 @p132)) % 1.73/2.02 (step @p134 :rule instantiate :premises (@p133) :args ((@list tptp.xJ tptp.xb))) % 1.73/2.02 (step @p135 :rule instantiate :premises (@p72) :args ((@list tptp.xJ))) % 1.73/2.02 (step @p136 :rule and_elim :premises (@p28) :args (1)) % 1.73/2.02 (step @p137 :rule cnf_equiv_pos1 :args (@t122)) % 1.73/2.02 (step @p138 :rule reordering :premises (@p137) :args ((or (not @t58) @t121 (not @t122)))) % 1.73/2.02 (step @p139 :rule chain_m_resolution :premises (@p138 @p136 @p135) :args (@t121 @t99 (@list @t58 @t122))) % 1.73/2.02 (step @p140 :rule cnf_and_pos :args (@t121 0)) % 1.73/2.02 (step @p141 :rule reordering :premises (@p140) :args ((or @t120 (not @t121)))) % 1.73/2.02 (step @p142 :rule chain_m_resolution :premises (@p141 @p139) :args (@t120 @t100 (@list @t121))) % 1.73/2.02 (step @p143 :rule and_elim :premises (@p31) :args (1)) % 1.73/2.02 (step @p144 :rule cnf_or_pos :args (@t126)) % 1.73/2.02 (step @p145 :rule reordering :premises (@p144) :args ((or @t124 @t123 @t125 (not @t126)))) % 1.73/2.02 (step @p146 :rule chain_m_resolution :premises (@p145 @p143 @p142 @p134) :args (@t123 (@list false false false) (@list @t63 @t120 @t126))) % 1.73/2.02 (step @p147 :rule and_elim :premises (@p30) :args (0)) % 1.73/2.02 (step @p148 :rule cnf_or_pos :args (@t134)) % 1.73/2.02 (step @p149 :rule reordering :premises (@p148) :args ((or @t133 @t132 @t131 @t130 (not @t134)))) % 1.73/2.02 (step @p150 :rule chain_m_resolution :premises (@p149 @p147 @p146 @p112 @p105) :args (@t130 (@list false false false false) (@list @t61 @t123 @t105 @t134))) % 1.73/2.02 (step @p151 :rule cnf_and_pos :args (@t130 0)) % 1.73/2.02 (step @p152 :rule reordering :premises (@p151) :args ((or @t129 (not @t130)))) % 1.73/2.02 (step @p153 :rule chain_m_resolution :premises (@p152 @p150) :args (@t129 @t100 (@list @t130))) % 1.73/2.02 (step @p154 :rule symm :premises (@p153)) % 1.73/2.02 (step @p155 :rule bool-impl-elim :args (@t2 @t135)) % 1.73/2.02 (step @p156 :rule cong :premises (@p155) :args ((forall @t3 (=> @t2 @t135)))) % 1.73/2.02 (step @p157 :rule refl :args (@t23)) % 1.73/2.02 (step @p158 :rule eq-symm :args (@t24 @t5)) % 1.73/2.02 (step @p159 :rule nary_cong :premises (@p158 @p157) :args (@t25)) % 1.73/2.02 (step @p160 :rule refl :args (@t2)) % 1.73/2.02 (step @p161 :rule cong :premises (@p160 @p159) :args (@t26)) % 1.73/2.02 (step @p162 :rule cong :premises (@p161) :args (@t27)) % 1.73/2.02 (step @p163 :rule trans :premises (@p162 @p156)) % 1.73/2.02 (step @p164 :rule eq_resolve :premises (@p15 @p163)) % 1.73/2.02 (step @p165 :rule instantiate :premises (@p164) :args ((@list tptp.xx))) % 1.73/2.02 (step @p166 :rule cnf_or_pos :args (@t138)) % 1.73/2.02 (step @p167 :rule reordering :premises (@p166) :args ((or @t133 @t137 (not @t138)))) % 1.73/2.02 (step @p168 :rule chain_m_resolution :premises (@p167 @p147 @p165) :args (@t137 @t99 (@list @t61 @t138))) % 1.73/2.02 (step @p169 :rule cnf_and_pos :args (@t137 1)) % 1.73/2.02 (step @p170 :rule reordering :premises (@p169) :args ((or @t136 (not @t137)))) % 1.73/2.02 (step @p171 :rule chain_m_resolution :premises (@p170 @p168) :args (@t136 @t100 (@list @t137))) % 1.73/2.02 (step @p172 :rule refl :args (@t65)) % 1.73/2.02 (step @p173 :rule cong :premises (@p172 @p171) :args (@t68)) % 1.73/2.02 (step @p174 :rule trans :premises (@p173 @p154)) % 1.73/2.02 (step @p175 :rule cong :premises (@p174 @p84) :args (@t139)) % 1.73/2.02 (step @p176 :rule trans :premises (@p175 @p89)) % 1.73/2.02 (step @p177 :rule true_elim :premises (@p176)) % 1.73/2.02 (step @p178 :rule cnf_or_pos :args (@t141)) % 1.73/2.02 (step @p179 :rule reordering :premises (@p178) :args ((or @t140 @t101 @t142))) % 1.73/2.02 (step @p180 :rule chain_m_resolution :premises (@p179 @p177 @p88) :args (@t142 @t143 (@list @t139 @t101))) % 1.73/2.02 (step @p181 :rule cnf_and_pos :args (@t145 0)) % 1.73/2.02 (step @p182 :rule reordering :premises (@p181) :args ((or @t141 @t146))) % 1.73/2.02 (step @p183 :rule chain_m_resolution :premises (@p182 @p180) :args (@t146 @t147 (@list @t141))) % 1.73/2.02 (step @p184 :rule cnf_or_pos :args (@t150)) % 1.73/2.02 (step @p185 :rule reordering :premises (@p184) :args ((or @t149 @t145 (not @t150)))) % 1.73/2.02 (step @p186 :rule chain_m_resolution :premises (@p185 @p183 @p82) :args (@t149 (@list true false) (@list @t145 @t150))) % 1.73/2.02 (step @p187 :rule and_elim :premises (@p30) :args (1)) % 1.73/2.02 (step @p188 :rule cnf_or_pos :args (@t151)) % 1.73/2.02 (step @p189 :rule reordering :premises (@p188) :args ((or @t144 @t148 @t152))) % 1.73/2.02 (step @p190 :rule chain_m_resolution :premises (@p189 @p187 @p186) :args (@t152 @t143 (@list @t60 @t148))) % 1.73/2.02 (step @p191 :rule cnf_and_pos :args (@t153 1)) % 1.73/2.02 (step @p192 :rule reordering :premises (@p191) :args ((or @t151 @t154))) % 1.73/2.02 (step @p193 :rule chain_m_resolution :premises (@p192 @p190) :args (@t154 @t147 (@list @t151))) % 1.73/2.02 (step @p194 :rule cnf_or_pos :args (@t156)) % 1.73/2.02 (step @p195 :rule reordering :premises (@p194) :args ((or @t155 @t153 (not @t156)))) % 1.73/2.02 (step @p196 false :rule chain_m_resolution :premises (@p195 @p193 @p81 @p37) :args (false (@list true false false) (@list @t153 @t156 @t64))) % 0.35/2.03 ) % 0.35/2.03 % SZS output end Proof % 0.35/2.03 % cvc5 exiting %------------------------------------------------------------------------------