%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : RNG086+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 : n021.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 08:45:37 AM UTC 2026 % Result : Theorem 2.41s 2.67s % Output : Proof 2.41s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : RNG086+1 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n021.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 14:07:50 EDT 2026 % 0.17/0.34 % CPUTime : % 0.30/0.50 %----Proving TF0_NAR, FOF, or CNF % 2.41/2.67 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 2.41/2.67 % SZS status Theorem % 2.41/2.67 % SZS output start Proof % 2.41/2.67 ( % 2.41/2.67 (declare-sort $$unsorted 0) % 2.41/2.67 (declare-const tptp.xx $$unsorted) % 2.41/2.67 (declare-const tptp.xy $$unsorted) % 2.41/2.67 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 2.41/2.67 (declare-const tptp.sz00 $$unsorted) % 2.41/2.67 (declare-const tptp.xI $$unsorted) % 2.41/2.67 (declare-const tptp.sz10 $$unsorted) % 2.41/2.67 (declare-const tptp.smndt0 (-> $$unsorted $$unsorted)) % 2.41/2.67 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 2.41/2.67 (declare-const tptp.aIdeal0 (-> $$unsorted Bool)) % 2.41/2.67 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 2.41/2.67 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 2.41/2.67 (declare-const tptp.xz $$unsorted) % 2.41/2.67 (declare-const tptp.sdtpldt1 (-> $$unsorted $$unsorted $$unsorted)) % 2.41/2.67 (declare-const tptp.sdtasasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 2.41/2.67 (declare-const tptp.xJ $$unsorted) % 2.41/2.67 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 2.41/2.67 (define @t1 () (@var "W0" $$unsorted)) % 2.41/2.67 (define @t2 () (tptp.aElement0 @t1)) % 2.41/2.67 (define @t3 () (@list @t1)) % 2.41/2.67 (define @t4 () (tptp.smndt0 @t1)) % 2.41/2.67 (define @t5 () (@var "W1" $$unsorted)) % 2.41/2.67 (define @t6 () (tptp.sdtpldt0 @t1 @t5)) % 2.41/2.67 (define @t7 () (tptp.aElement0 @t5)) % 2.41/2.67 (define @t8 () (and @t2 @t7)) % 2.41/2.67 (define @t9 () (@list @t1 @t5)) % 2.41/2.67 (define @t10 () (tptp.sdtasdt0 @t1 @t5)) % 2.41/2.67 (define @t11 () (@var "W2" $$unsorted)) % 2.41/2.67 (define @t12 () (tptp.sdtpldt0 @t5 @t11)) % 2.41/2.67 (define @t13 () (tptp.aElement0 @t11)) % 2.41/2.67 (define @t14 () (and @t2 @t7 @t13)) % 2.41/2.67 (define @t15 () (@list @t1 @t5 @t11)) % 2.41/2.67 (define @t16 () (tptp.sdtasdt0 @t5 @t1)) % 2.41/2.67 (define @t17 () (tptp.smndt0 tptp.sz10)) % 2.41/2.67 (define @t18 () (tptp.aSet0 @t1)) % 2.41/2.67 (define @t19 () (tptp.aElementOf0 @t5 @t1)) % 2.41/2.67 (define @t20 () (@list @t5)) % 2.41/2.67 (define @t21 () (tptp.aElementOf0 @t11 @t1)) % 2.41/2.67 (define @t22 () (tptp.aElementOf0 @t11 @t5)) % 2.41/2.67 (define @t23 () (@list @t11)) % 2.41/2.67 (define @t24 () (tptp.aSet0 @t5)) % 2.41/2.67 (define @t25 () (and @t18 @t24)) % 2.41/2.67 (define @t26 () (@var "W3" $$unsorted)) % 2.41/2.67 (define @t27 () (@var "W5" $$unsorted)) % 2.41/2.67 (define @t28 () (@var "W4" $$unsorted)) % 2.41/2.67 (define @t29 () (tptp.sdtpldt0 @t28 @t27)) % 2.41/2.67 (define @t30 () (tptp.aElementOf0 @t27 @t5)) % 2.41/2.67 (define @t31 () (tptp.aElementOf0 @t28 @t1)) % 2.41/2.67 (define @t32 () (and @t31 @t30 (= @t29 @t26))) % 2.41/2.67 (define @t33 () (@list @t28 @t27)) % 2.41/2.67 (define @t34 () (exists @t33 @t32)) % 2.41/2.67 (define @t35 () (tptp.aElementOf0 @t26 @t11)) % 2.41/2.67 (define @t36 () (= @t35 @t34)) % 2.41/2.67 (define @t37 () (@list @t26)) % 2.41/2.67 (define @t38 () (forall @t37 @t36)) % 2.41/2.67 (define @t39 () (tptp.aSet0 @t11)) % 2.41/2.67 (define @t40 () (and @t39 @t38)) % 2.41/2.67 (define @t41 () (tptp.sdtpldt1 @t1 @t5)) % 2.41/2.67 (define @t42 () (= @t11 @t41)) % 2.41/2.67 (define @t43 () (= @t42 @t40)) % 2.41/2.67 (define @t44 () (forall @t23 @t43)) % 2.41/2.67 (define @t45 () (=> @t25 @t44)) % 2.41/2.67 (define @t46 () (forall @t9 @t45)) % 2.41/2.67 (define @t47 () (tptp.aElementOf0 (tptp.sdtasdt0 @t11 @t5) @t1)) % 2.41/2.67 (define @t48 () (forall @t23 (=> @t13 @t47))) % 2.41/2.67 (define @t49 () (tptp.aElementOf0 @t12 @t1)) % 2.41/2.67 (define @t50 () (forall @t23 (=> @t21 @t49))) % 2.41/2.67 (define @t51 () (and @t50 @t48)) % 2.41/2.67 (define @t52 () (=> @t19 @t51)) % 2.41/2.67 (define @t53 () (forall @t20 @t52)) % 2.41/2.67 (define @t54 () (and @t18 @t53)) % 2.41/2.67 (define @t55 () (tptp.aIdeal0 @t1)) % 2.41/2.67 (define @t56 () (= @t55 @t54)) % 2.41/2.67 (define @t57 () (forall @t3 @t56)) % 2.41/2.67 (define @t58 () (tptp.aIdeal0 tptp.xJ)) % 2.41/2.67 (define @t59 () (tptp.aIdeal0 tptp.xI)) % 2.41/2.67 (define @t60 () (tptp.sdtpldt1 tptp.xI tptp.xJ)) % 2.41/2.67 (define @t61 () (tptp.aElementOf0 tptp.xx @t60)) % 2.41/2.67 (define @t62 () (tptp.aElementOf0 @t5 tptp.xJ)) % 2.41/2.67 (define @t63 () (tptp.aElementOf0 @t1 tptp.xI)) % 2.41/2.67 (define @t64 () (and @t63 @t62 (= tptp.xx @t6))) % 2.41/2.67 (define @t65 () (exists @t9 @t64)) % 2.41/2.67 (define @t66 () (not @t65)) % 2.41/2.67 (define @t67 () (= @t6 tptp.xx)) % 2.41/2.67 (define @t68 () (not @t67)) % 2.41/2.67 (define @t69 () (not @t62)) % 2.41/2.67 (define @t70 () (not @t63)) % 2.41/2.67 (define @t71 () (or @t70 @t69 @t68)) % 2.41/2.67 (define @t72 () (forall @t9 @t71)) % 2.41/2.67 (define @t73 () (and @t63 @t62 @t67)) % 2.41/2.67 (define @t74 () (forall @t9 (not @t73))) % 2.41/2.67 (define @t75 () (not @t74)) % 2.41/2.67 (define @t76 () (not (tptp.aElementOf0 @t27 tptp.xJ))) % 2.41/2.67 (define @t77 () (not (tptp.aElementOf0 @t28 tptp.xI))) % 2.41/2.67 (define @t78 () (forall @t33 (or @t77 @t76 (not (= @t29 tptp.xx))))) % 2.41/2.67 (define @t79 () (@list false)) % 2.41/2.67 (define @t80 () (@var "BOUND_VARIABLE_7760" $$unsorted)) % 2.41/2.67 (define @t81 () (tptp.aElementOf0 @t26 @t80)) % 2.41/2.67 (define @t82 () (= @t26 @t29)) % 2.41/2.67 (define @t83 () (not @t82)) % 2.41/2.67 (define @t84 () (not @t30)) % 2.41/2.67 (define @t85 () (not @t31)) % 2.41/2.67 (define @t86 () (or @t85 @t84 @t83)) % 2.41/2.67 (define @t87 () (not (forall @t33 @t86))) % 2.41/2.67 (define @t88 () (forall @t37 (= @t81 @t87))) % 2.41/2.67 (define @t89 () (tptp.aSet0 @t80)) % 2.41/2.67 (define @t90 () (and @t89 @t88)) % 2.41/2.67 (define @t91 () (= (= @t80 @t41) @t90)) % 2.41/2.67 (define @t92 () (not @t24)) % 2.41/2.67 (define @t93 () (not @t18)) % 2.41/2.67 (define @t94 () (or @t93 @t92 @t91)) % 2.41/2.67 (define @t95 () (@list @t1 @t5 @t80)) % 2.41/2.67 (define @t96 () (forall @t95 @t94)) % 2.41/2.67 (define @t97 () (@list @t80)) % 2.41/2.67 (define @t98 () (forall @t97 @t94)) % 2.41/2.67 (define @t99 () (forall @t97 @t91)) % 2.41/2.67 (define @t100 () (@list @t11)) % 2.41/2.67 (define @t101 () (or @t93 @t92 @t99)) % 2.41/2.67 (define @t102 () (forall @t23 (= @t42 (and @t39 (forall @t37 (= @t35 @t87)))))) % 2.41/2.67 (define @t103 () (or @t93 @t92 @t102)) % 2.41/2.67 (define @t104 () (and @t31 @t30 @t82)) % 2.41/2.67 (define @t105 () (forall @t33 (not @t104))) % 2.41/2.67 (define @t106 () (not @t105)) % 2.41/2.67 (define @t107 () (not (forall @t33 (or @t77 @t76 @t83)))) % 2.41/2.67 (define @t108 () (tptp.aElementOf0 @t26 @t60)) % 2.41/2.67 (define @t109 () (forall @t37 (= @t108 @t107))) % 2.41/2.67 (define @t110 () (tptp.aSet0 @t60)) % 2.41/2.67 (define @t111 () (and @t110 @t109)) % 2.41/2.67 (define @t112 () (forall @t37 (= @t107 @t108))) % 2.41/2.67 (define @t113 () (and @t110 @t112)) % 2.41/2.67 (define @t114 () (= (= @t60 @t60) @t113)) % 2.41/2.67 (define @t115 () (tptp.aSet0 tptp.xJ)) % 2.41/2.67 (define @t116 () (not @t115)) % 2.41/2.67 (define @t117 () (tptp.aSet0 tptp.xI)) % 2.41/2.67 (define @t118 () (not @t117)) % 2.41/2.67 (define @t119 () (or @t118 @t116 @t114)) % 2.41/2.67 (define @t120 () (forall @t95 (or @t93 @t92 (= (= @t41 @t80) (and @t89 (forall @t37 (= @t87 @t81))))))) % 2.41/2.67 (define @t121 () (or @t118 @t116 @t111)) % 2.41/2.67 (define @t122 () (@var "BOUND_VARIABLE_7818" $$unsorted)) % 2.41/2.67 (define @t123 () (tptp.sdtasdt0 @t122 @t5)) % 2.41/2.67 (define @t124 () (not (tptp.aElement0 @t122))) % 2.41/2.67 (define @t125 () (or @t124 (tptp.aElementOf0 @t123 @t1))) % 2.41/2.67 (define @t126 () (@var "BOUND_VARIABLE_7811" $$unsorted)) % 2.41/2.67 (define @t127 () (tptp.sdtpldt0 @t5 @t126)) % 2.41/2.67 (define @t128 () (or (not (tptp.aElementOf0 @t126 @t1)) (tptp.aElementOf0 @t127 @t1))) % 2.41/2.67 (define @t129 () (and @t128 @t125)) % 2.41/2.67 (define @t130 () (not @t19)) % 2.41/2.67 (define @t131 () (or @t130 @t129)) % 2.41/2.67 (define @t132 () (@list @t5 @t126 @t122)) % 2.41/2.67 (define @t133 () (@list @t126 @t122)) % 2.41/2.67 (define @t134 () (forall @t133 @t131)) % 2.41/2.67 (define @t135 () (forall (@list @t122) @t125)) % 2.41/2.67 (define @t136 () (forall @t133 @t125)) % 2.41/2.67 (define @t137 () (forall (@list @t126) @t128)) % 2.41/2.67 (define @t138 () (forall @t133 @t128)) % 2.41/2.67 (define @t139 () (and @t138 @t136)) % 2.41/2.67 (define @t140 () (forall @t133 @t129)) % 2.41/2.67 (define @t141 () (or @t130 @t140)) % 2.41/2.67 (define @t142 () (and (forall @t23 (or (not @t21) @t49)) (forall @t23 (or (not @t13) @t47)))) % 2.41/2.67 (define @t143 () (and @t115 (forall @t132 (or @t69 (and (or (not (tptp.aElementOf0 @t126 tptp.xJ)) (tptp.aElementOf0 @t127 tptp.xJ)) (or @t124 (tptp.aElementOf0 @t123 tptp.xJ))))))) % 2.41/2.67 (define @t144 () (= @t58 @t143)) % 2.41/2.67 (define @t145 () (@list false false)) % 2.41/2.67 (define @t146 () (and @t117 (forall @t132 (or (not (tptp.aElementOf0 @t5 tptp.xI)) (and (or (not (tptp.aElementOf0 @t126 tptp.xI)) (tptp.aElementOf0 @t127 tptp.xI)) (or @t124 (tptp.aElementOf0 @t123 tptp.xI))))))) % 2.41/2.67 (define @t147 () (= @t59 @t146)) % 2.41/2.67 (define @t148 () (@list false false false)) % 2.41/2.67 (define @t149 () (not (= tptp.xx @t29))) % 2.41/2.67 (define @t150 () (or @t77 @t76 @t149)) % 2.41/2.67 (define @t151 () (forall @t33 @t150)) % 2.41/2.67 (define @t152 () (not @t151)) % 2.41/2.67 (define @t153 () (= @t61 @t152)) % 2.41/2.67 (define @t154 () (not @t78)) % 2.41/2.67 (define @t155 () (= @t61 @t154)) % 2.41/2.67 (assume @p1 (forall @t3 (=> @t2 true))) % 2.41/2.67 (assume @p2 (tptp.aElement0 tptp.sz00)) % 2.41/2.67 (assume @p3 (tptp.aElement0 tptp.sz10)) % 2.41/2.67 (assume @p4 (forall @t3 (=> @t2 (tptp.aElement0 @t4)))) % 2.41/2.67 (assume @p5 (forall @t9 (=> @t8 (tptp.aElement0 @t6)))) % 2.41/2.67 (assume @p6 (forall @t9 (=> @t8 (tptp.aElement0 @t10)))) % 2.41/2.67 (assume @p7 (forall @t9 (=> @t8 (= @t6 (tptp.sdtpldt0 @t5 @t1))))) % 2.41/2.67 (assume @p8 (forall @t15 (=> @t14 (= (tptp.sdtpldt0 @t6 @t11) (tptp.sdtpldt0 @t1 @t12))))) % 2.41/2.67 (assume @p9 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 tptp.sz00) @t1) (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1)))))) % 2.41/2.67 (assume @p10 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 @t4) tptp.sz00) (= tptp.sz00 (tptp.sdtpldt0 @t4 @t1)))))) % 2.41/2.67 (assume @p11 (forall @t9 (=> @t8 (= @t10 @t16)))) % 2.41/2.67 (assume @p12 (forall @t15 (=> @t14 (= (tptp.sdtasdt0 @t10 @t11) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t5 @t11)))))) % 2.41/2.67 (assume @p13 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 2.41/2.67 (assume @p14 (forall @t15 (=> @t14 (and (= (tptp.sdtasdt0 @t1 @t12) (tptp.sdtpldt0 @t10 (tptp.sdtasdt0 @t1 @t11))) (= (tptp.sdtasdt0 @t12 @t1) (tptp.sdtpldt0 @t16 (tptp.sdtasdt0 @t11 @t1))))))) % 2.41/2.67 (assume @p15 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t17 @t1) @t4) (= @t4 (tptp.sdtasdt0 @t1 @t17)))))) % 2.41/2.67 (assume @p16 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 2.41/2.67 (assume @p17 (forall @t9 (=> @t8 (=> (= @t10 tptp.sz00) (or (= @t1 tptp.sz00) (= @t5 tptp.sz00)))))) % 2.41/2.67 (assume @p18 (not (= tptp.sz10 tptp.sz00))) % 2.41/2.67 (assume @p19 (forall @t3 (=> @t18 true))) % 2.41/2.67 (assume @p20 (forall @t3 (=> @t18 (forall @t20 (=> @t19 @t7))))) % 2.41/2.67 (assume @p21 (forall @t9 (=> @t25 (=> (and (forall @t23 (=> @t21 @t22)) (forall @t23 (=> @t22 @t21))) (= @t1 @t5))))) % 2.41/2.67 (assume @p22 @t46) % 2.41/2.67 (assume @p23 (forall @t9 (=> @t25 (forall @t23 (= (= @t11 (tptp.sdtasasdt0 @t1 @t5)) (and @t39 (forall @t37 (= @t35 (and (tptp.aElementOf0 @t26 @t1) (tptp.aElementOf0 @t26 @t5)))))))))) % 2.41/2.67 (assume @p24 @t57) % 2.41/2.67 (assume @p25 (and @t59 @t58)) % 2.41/2.67 (assume @p26 (and @t61 (tptp.aElementOf0 tptp.xy @t60) (tptp.aElement0 tptp.xz))) % 2.41/2.67 (assume @p27 @t66) % 2.41/2.67 (assume @p28 true) % 2.41/2.67 (step @p29 :rule and_elim :premises (@p26) :args (0)) % 2.41/2.67 (step @p30 :rule bool-double-not-elim :args (@t72)) % 2.41/2.67 (step @p31 :rule aci_norm :args ((= (or @t70 (or @t69 @t68)) @t71))) % 2.41/2.67 (step @p32 :rule bool-and-de-morgan :args (@t62 @t67 true)) % 2.41/2.67 (step @p33 :rule refl :args (@t70)) % 2.41/2.67 (step @p34 :rule nary_cong :premises (@p33 @p32) :args ((or @t70 (not (and @t62 @t67))))) % 2.41/2.67 (step @p35 :rule bool-and-de-morgan :args (@t63 @t62 (and @t67))) % 2.41/2.67 (step @p36 :rule trans :premises (@p35 @p34)) % 2.41/2.67 (step @p37 :rule trans :premises (@p36 @p31)) % 2.41/2.67 (step @p38 :rule cong :premises (@p37) :args (@t74)) % 2.41/2.67 (step @p39 :rule cong :premises (@p38) :args (@t75)) % 2.41/2.67 (step @p40 :rule exists-elim :args ((= (exists @t9 @t73) @t75))) % 2.41/2.67 (step @p41 :rule trans :premises (@p40 @p39)) % 2.41/2.67 (step @p42 :rule eq-symm :args (tptp.xx @t6)) % 2.41/2.67 (step @p43 :rule refl :args (@t62)) % 2.41/2.67 (step @p44 :rule refl :args (@t63)) % 2.41/2.67 (step @p45 :rule nary_cong :premises (@p44 @p43 @p42) :args (@t64)) % 2.41/2.67 (step @p46 :rule cong :premises (@p45) :args (@t65)) % 2.41/2.67 (step @p47 :rule trans :premises (@p46 @p41)) % 2.41/2.67 (step @p48 :rule cong :premises (@p47) :args (@t66)) % 2.41/2.67 (step @p49 :rule trans :premises (@p48 @p30)) % 2.41/2.67 (step @p50 :rule eq_resolve :premises (@p27 @p49)) % 2.41/2.67 (step @p51 :rule alpha_equiv :args (@t72 (@list @t1 @t5) (@list @t28 @t27))) % 2.41/2.67 (step @p52 :rule equiv_elim1 :premises (@p51)) % 2.41/2.67 (step @p53 :rule chain_m_resolution :premises (@p52 @p50) :args (@t78 @t79 (@list @t72))) % 2.41/2.67 (step @p54 :rule eq-symm :args (@t81 @t87)) % 2.41/2.67 (step @p55 :rule cong :premises (@p54) :args (@t88)) % 2.41/2.67 (step @p56 :rule refl :args (@t89)) % 2.41/2.67 (step @p57 :rule nary_cong :premises (@p56 @p55) :args (@t90)) % 2.41/2.67 (step @p58 :rule eq-symm :args (@t80 @t41)) % 2.41/2.67 (step @p59 :rule cong :premises (@p58 @p57) :args (@t91)) % 2.41/2.67 (step @p60 :rule refl :args (@t92)) % 2.41/2.67 (step @p61 :rule refl :args (@t93)) % 2.41/2.67 (step @p62 :rule nary_cong :premises (@p61 @p60 @p59) :args (@t94)) % 2.41/2.67 (step @p63 :rule cong :premises (@p62) :args (@t96)) % 2.41/2.67 (step @p64 :rule quant-merge-prenex :args ((= (forall @t9 @t98) @t96))) % 2.41/2.67 (step @p65 :rule alpha_equiv :args (@t99 (@list @t80) @t100)) % 2.41/2.67 (step @p66 :rule refl :args (@t92)) % 2.41/2.67 (step @p67 :rule refl :args (@t93)) % 2.41/2.67 (step @p68 :rule nary_cong :premises (@p67 @p66 @p65) :args (@t101)) % 2.41/2.67 (step @p69 :rule quant-miniscope-or :args ((= @t98 @t101))) % 2.41/2.67 (step @p70 :rule trans :premises (@p69 @p68)) % 2.41/2.67 (step @p71 :rule symm :premises (@p70)) % 2.41/2.67 (step @p72 :rule cong :premises (@p71) :args ((forall @t9 @t103))) % 2.41/2.67 (step @p73 :rule trans :premises (@p72 @p64)) % 2.41/2.67 (step @p74 :rule trans :premises (@p73 @p63)) % 2.41/2.67 (step @p75 :rule aci_norm :args ((= (or (or @t93 @t92) @t102) @t103))) % 2.41/2.67 (step @p76 :rule refl :args (@t102)) % 2.41/2.67 (step @p77 :rule bool-and-de-morgan :args (@t18 @t24 true)) % 2.41/2.67 (step @p78 :rule nary_cong :premises (@p77 @p76) :args ((or (not @t25) @t102))) % 2.41/2.67 (step @p79 :rule trans :premises (@p78 @p75)) % 2.41/2.67 (step @p80 :rule bool-impl-elim :args (@t25 @t102)) % 2.41/2.67 (step @p81 :rule trans :premises (@p80 @p79)) % 2.41/2.67 (step @p82 :rule cong :premises (@p81) :args ((forall @t9 (=> @t25 @t102)))) % 2.41/2.67 (step @p83 :rule trans :premises (@p82 @p74)) % 2.41/2.67 (step @p84 :rule aci_norm :args ((= (or @t85 (or @t84 @t83)) @t86))) % 2.41/2.67 (step @p85 :rule bool-and-de-morgan :args (@t30 @t82 true)) % 2.41/2.67 (step @p86 :rule refl :args (@t85)) % 2.41/2.67 (step @p87 :rule nary_cong :premises (@p86 @p85) :args ((or @t85 (not (and @t30 @t82))))) % 2.41/2.67 (step @p88 :rule bool-and-de-morgan :args (@t31 @t30 (and @t82))) % 2.41/2.67 (step @p89 :rule trans :premises (@p88 @p87)) % 2.41/2.67 (step @p90 :rule trans :premises (@p89 @p84)) % 2.41/2.67 (step @p91 :rule cong :premises (@p90) :args (@t105)) % 2.41/2.67 (step @p92 :rule cong :premises (@p91) :args (@t106)) % 2.41/2.67 (step @p93 :rule exists-elim :args ((= (exists @t33 @t104) @t106))) % 2.41/2.67 (step @p94 :rule trans :premises (@p93 @p92)) % 2.41/2.67 (step @p95 :rule eq-symm :args (@t29 @t26)) % 2.41/2.67 (step @p96 :rule refl :args (@t30)) % 2.41/2.67 (step @p97 :rule refl :args (@t31)) % 2.41/2.67 (step @p98 :rule nary_cong :premises (@p97 @p96 @p95) :args (@t32)) % 2.41/2.67 (step @p99 :rule cong :premises (@p98) :args (@t34)) % 2.41/2.67 (step @p100 :rule trans :premises (@p99 @p94)) % 2.41/2.67 (step @p101 :rule refl :args (@t35)) % 2.41/2.67 (step @p102 :rule cong :premises (@p101 @p100) :args (@t36)) % 2.41/2.67 (step @p103 :rule cong :premises (@p102) :args (@t38)) % 2.41/2.67 (step @p104 :rule refl :args (@t39)) % 2.41/2.67 (step @p105 :rule nary_cong :premises (@p104 @p103) :args (@t40)) % 2.41/2.67 (step @p106 :rule refl :args (@t42)) % 2.41/2.67 (step @p107 :rule cong :premises (@p106 @p105) :args (@t43)) % 2.41/2.67 (step @p108 :rule cong :premises (@p107) :args (@t44)) % 2.41/2.67 (step @p109 :rule refl :args (@t25)) % 2.41/2.67 (step @p110 :rule cong :premises (@p109 @p108) :args (@t45)) % 2.41/2.67 (step @p111 :rule cong :premises (@p110) :args (@t46)) % 2.41/2.67 (step @p112 :rule trans :premises (@p111 @p83)) % 2.41/2.67 (step @p113 :rule eq_resolve :premises (@p22 @p112)) % 2.41/2.67 (step @p114 :rule bool-eq-true :args (@t111)) % 2.41/2.67 (step @p115 :rule eq-symm :args (true @t111)) % 2.41/2.67 (step @p116 :rule trans :premises (@p115 @p114)) % 2.41/2.67 (step @p117 :rule eq-symm :args (@t107 @t108)) % 2.41/2.67 (step @p118 :rule cong :premises (@p117) :args (@t112)) % 2.41/2.67 (step @p119 :rule refl :args (@t110)) % 2.41/2.67 (step @p120 :rule nary_cong :premises (@p119 @p118) :args (@t113)) % 2.41/2.67 (step @p121 :rule eq-refl :args (@t60)) % 2.41/2.67 (step @p122 :rule cong :premises (@p121 @p120) :args (@t114)) % 2.41/2.67 (step @p123 :rule trans :premises (@p122 @p116)) % 2.41/2.67 (step @p124 :rule refl :args (@t116)) % 2.41/2.67 (step @p125 :rule refl :args (@t118)) % 2.41/2.67 (step @p126 :rule nary_cong :premises (@p125 @p124 @p123) :args (@t119)) % 2.41/2.67 (step @p127 :rule refl :args (@t120)) % 2.41/2.67 (step @p128 :rule cong :premises (@p127 @p126) :args ((=> @t120 @t119))) % 2.41/2.67 (assume-push @p214 @t120) % 2.41/2.67 (step @p130 :rule instantiate :premises (@p113) :args ((@list tptp.xI tptp.xJ @t60))) % 2.41/2.67 (step-pop @p215 :rule scope :premises (@p130)) % 2.41/2.67 (step @p131 :rule process_scope :premises (@p215) :args (@t119)) % 2.41/2.67 (step @p133 :rule eq_resolve :premises (@p131 @p128)) % 2.41/2.67 (step @p134 :rule implies_elim :premises (@p133)) % 2.41/2.67 (step @p135 :rule chain_m_resolution :premises (@p134 @p113) :args (@t121 @t79 (@list @t120))) % 2.41/2.67 (step @p136 :rule quant-merge-prenex :args ((= (forall @t20 @t134) (forall @t132 @t131)))) % 2.41/2.67 (step @p137 :rule alpha_equiv :args (@t135 (@list @t122) @t100)) % 2.41/2.67 (step @p138 :rule quant-unused-vars :args ((= @t136 @t135))) % 2.41/2.67 (step @p139 :rule trans :premises (@p138 @p137)) % 2.41/2.67 (step @p140 :rule alpha_equiv :args (@t137 (@list @t126) @t100)) % 2.41/2.67 (step @p141 :rule quant-unused-vars :args ((= @t138 @t137))) % 2.41/2.67 (step @p142 :rule trans :premises (@p141 @p140)) % 2.41/2.67 (step @p143 :rule nary_cong :premises (@p142 @p139) :args (@t139)) % 2.41/2.67 (step @p144 :rule quant-miniscope-and :args ((= @t140 @t139))) % 2.41/2.67 (step @p145 :rule trans :premises (@p144 @p143)) % 2.41/2.67 (step @p146 :rule refl :args (@t130)) % 2.41/2.67 (step @p147 :rule nary_cong :premises (@p146 @p145) :args (@t141)) % 2.41/2.67 (step @p148 :rule quant-miniscope-or :args ((= @t134 @t141))) % 2.41/2.67 (step @p149 :rule trans :premises (@p148 @p147)) % 2.41/2.67 (step @p150 :rule symm :premises (@p149)) % 2.41/2.67 (step @p151 :rule cong :premises (@p150) :args ((forall @t20 (or @t130 @t142)))) % 2.41/2.67 (step @p152 :rule trans :premises (@p151 @p136)) % 2.41/2.67 (step @p153 :rule bool-impl-elim :args (@t19 @t142)) % 2.41/2.69 (step @p154 :rule cong :premises (@p153) :args ((forall @t20 (=> @t19 @t142)))) % 2.41/2.69 (step @p155 :rule trans :premises (@p154 @p152)) % 2.41/2.69 (step @p156 :rule bool-impl-elim :args (@t13 @t47)) % 2.41/2.69 (step @p157 :rule cong :premises (@p156) :args (@t48)) % 2.41/2.69 (step @p158 :rule bool-impl-elim :args (@t21 @t49)) % 2.41/2.69 (step @p159 :rule cong :premises (@p158) :args (@t50)) % 2.41/2.69 (step @p160 :rule nary_cong :premises (@p159 @p157) :args (@t51)) % 2.41/2.69 (step @p161 :rule refl :args (@t19)) % 2.41/2.69 (step @p162 :rule cong :premises (@p161 @p160) :args (@t52)) % 2.41/2.69 (step @p163 :rule cong :premises (@p162) :args (@t53)) % 2.41/2.69 (step @p164 :rule trans :premises (@p163 @p155)) % 2.41/2.69 (step @p165 :rule refl :args (@t18)) % 2.41/2.69 (step @p166 :rule nary_cong :premises (@p165 @p164) :args (@t54)) % 2.41/2.69 (step @p167 :rule refl :args (@t55)) % 2.41/2.69 (step @p168 :rule cong :premises (@p167 @p166) :args (@t56)) % 2.41/2.69 (step @p169 :rule cong :premises (@p168) :args (@t57)) % 2.41/2.69 (step @p170 :rule eq_resolve :premises (@p24 @p169)) % 2.41/2.69 (step @p171 :rule instantiate :premises (@p170) :args ((@list tptp.xJ))) % 2.41/2.69 (step @p172 :rule and_elim :premises (@p25) :args (1)) % 2.41/2.69 (step @p173 :rule cnf_equiv_pos1 :args (@t144)) % 2.41/2.69 (step @p174 :rule reordering :premises (@p173) :args ((or (not @t58) @t143 (not @t144)))) % 2.41/2.69 (step @p175 :rule chain_m_resolution :premises (@p174 @p172 @p171) :args (@t143 @t145 (@list @t58 @t144))) % 2.41/2.69 (step @p176 :rule cnf_and_pos :args (@t143 0)) % 2.41/2.69 (step @p177 :rule reordering :premises (@p176) :args ((or @t115 (not @t143)))) % 2.41/2.69 (step @p178 :rule chain_m_resolution :premises (@p177 @p175) :args (@t115 @t79 (@list @t143))) % 2.41/2.69 (step @p179 :rule instantiate :premises (@p170) :args ((@list tptp.xI))) % 2.41/2.69 (step @p180 :rule and_elim :premises (@p25) :args (0)) % 2.41/2.69 (step @p181 :rule cnf_equiv_pos1 :args (@t147)) % 2.41/2.69 (step @p182 :rule reordering :premises (@p181) :args ((or (not @t59) @t146 (not @t147)))) % 2.41/2.69 (step @p183 :rule chain_m_resolution :premises (@p182 @p180 @p179) :args (@t146 @t145 (@list @t59 @t147))) % 2.41/2.69 (step @p184 :rule cnf_and_pos :args (@t146 0)) % 2.41/2.69 (step @p185 :rule reordering :premises (@p184) :args ((or @t117 (not @t146)))) % 2.41/2.69 (step @p186 :rule chain_m_resolution :premises (@p185 @p183) :args (@t117 @t79 (@list @t146))) % 2.41/2.69 (step @p187 :rule cnf_or_pos :args (@t121)) % 2.41/2.69 (step @p188 :rule reordering :premises (@p187) :args ((or @t118 @t116 @t111 (not @t121)))) % 2.41/2.69 (step @p189 :rule chain_m_resolution :premises (@p188 @p186 @p178 @p135) :args (@t111 @t148 (@list @t117 @t115 @t121))) % 2.41/2.69 (step @p190 :rule cnf_and_pos :args (@t111 1)) % 2.41/2.69 (step @p191 :rule reordering :premises (@p190) :args ((or @t109 (not @t111)))) % 2.41/2.69 (step @p192 :rule chain_m_resolution :premises (@p191 @p189) :args (@t109 @t79 (@list @t111))) % 2.41/2.69 (step @p193 :rule eq-symm :args (tptp.xx @t29)) % 2.41/2.69 (step @p194 :rule cong :premises (@p193) :args (@t149)) % 2.41/2.69 (step @p195 :rule refl :args (@t76)) % 2.41/2.69 (step @p196 :rule refl :args (@t77)) % 2.41/2.69 (step @p197 :rule nary_cong :premises (@p196 @p195 @p194) :args (@t150)) % 2.41/2.69 (step @p198 :rule cong :premises (@p197) :args (@t151)) % 2.41/2.69 (step @p199 :rule cong :premises (@p198) :args (@t152)) % 2.41/2.69 (step @p200 :rule refl :args (@t61)) % 2.41/2.69 (step @p201 :rule cong :premises (@p200 @p199) :args (@t153)) % 2.41/2.69 (step @p202 :rule refl :args (@t109)) % 2.41/2.69 (step @p203 :rule cong :premises (@p202 @p201) :args ((=> @t109 @t153))) % 2.41/2.69 (assume-push @p216 @t109) % 2.41/2.69 (step @p205 :rule instantiate :premises (@p192) :args ((@list tptp.xx))) % 2.41/2.69 (step-pop @p217 :rule scope :premises (@p205)) % 2.41/2.69 (step @p206 :rule process_scope :premises (@p217) :args (@t153)) % 2.41/2.69 (step @p208 :rule eq_resolve :premises (@p206 @p203)) % 2.41/2.69 (step @p209 :rule implies_elim :premises (@p208)) % 2.41/2.69 (step @p210 :rule chain_m_resolution :premises (@p209 @p192) :args (@t155 @t79 (@list @t109))) % 2.41/2.69 (step @p211 :rule cnf_equiv_pos1 :args (@t155)) % 2.41/2.69 (step @p212 :rule reordering :premises (@p211) :args ((or (not @t61) @t154 (not @t155)))) % 2.41/2.69 (step @p213 false :rule chain_m_resolution :premises (@p212 @p210 @p53 @p29) :args (false @t148 (@list @t155 @t78 @t61))) % 2.41/2.69 ) % 2.41/2.69 % SZS output end Proof % 2.41/2.69 % cvc5 exiting %------------------------------------------------------------------------------