%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : RNG095+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 : n009.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 08:45:39 AM UTC 2026 % Result : Theorem 15.86s 16.12s % Output : Proof 15.86s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : RNG095+1 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.18/0.34 % Computer : n009.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 14:06:44 EDT 2026 % 0.18/0.34 % CPUTime : % 0.27/0.50 %----Proving TF0_NAR, FOF, or CNF % 15.86/16.12 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 15.86/16.12 --- Run --no-e-matching --full-saturate-quant at 6... % 15.86/16.12 % SZS status Theorem % 15.86/16.12 % SZS output start Proof % 15.86/16.12 ( % 15.86/16.12 (declare-sort $$unsorted 0) % 15.86/16.12 (declare-const tptp.xx $$unsorted) % 15.86/16.12 (declare-const tptp.xy $$unsorted) % 15.86/16.12 (declare-const tptp.xI $$unsorted) % 15.86/16.12 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 15.86/16.12 (declare-const tptp.sz00 $$unsorted) % 15.86/16.12 (declare-const tptp.sz10 $$unsorted) % 15.86/16.12 (declare-const tptp.smndt0 (-> $$unsorted $$unsorted)) % 15.86/16.12 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 15.86/16.12 (declare-const tptp.sdtasasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 15.86/16.12 (declare-const tptp.aIdeal0 (-> $$unsorted Bool)) % 15.86/16.12 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 15.86/16.12 (declare-const tptp.xJ $$unsorted) % 15.86/16.12 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 15.86/16.12 (declare-const tptp.sdtpldt1 (-> $$unsorted $$unsorted $$unsorted)) % 15.86/16.12 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 15.86/16.12 (declare-const tptp.sdteqdtlpzmzozddtrp0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 15.86/16.12 (define @t1 () (@var "W0" $$unsorted)) % 15.86/16.12 (define @t2 () (tptp.aElement0 @t1)) % 15.86/16.12 (define @t3 () (@list @t1)) % 15.86/16.12 (define @t4 () (tptp.aElement0 tptp.sz10)) % 15.86/16.12 (define @t5 () (tptp.smndt0 @t1)) % 15.86/16.12 (define @t6 () (@var "W1" $$unsorted)) % 15.86/16.12 (define @t7 () (tptp.sdtpldt0 @t1 @t6)) % 15.86/16.12 (define @t8 () (tptp.aElement0 @t6)) % 15.86/16.12 (define @t9 () (and @t2 @t8)) % 15.86/16.12 (define @t10 () (@list @t1 @t6)) % 15.86/16.12 (define @t11 () (tptp.sdtasdt0 @t1 @t6)) % 15.86/16.12 (define @t12 () (@var "W2" $$unsorted)) % 15.86/16.12 (define @t13 () (tptp.sdtpldt0 @t6 @t12)) % 15.86/16.12 (define @t14 () (tptp.aElement0 @t12)) % 15.86/16.12 (define @t15 () (and @t2 @t8 @t14)) % 15.86/16.12 (define @t16 () (@list @t1 @t6 @t12)) % 15.86/16.12 (define @t17 () (tptp.sdtasdt0 @t6 @t1)) % 15.86/16.12 (define @t18 () (tptp.smndt0 tptp.sz10)) % 15.86/16.12 (define @t19 () (tptp.aSet0 @t1)) % 15.86/16.12 (define @t20 () (tptp.aElementOf0 @t6 @t1)) % 15.86/16.12 (define @t21 () (@list @t6)) % 15.86/16.12 (define @t22 () (tptp.aElementOf0 @t12 @t1)) % 15.86/16.12 (define @t23 () (tptp.aElementOf0 @t12 @t6)) % 15.86/16.12 (define @t24 () (@list @t12)) % 15.86/16.12 (define @t25 () (tptp.aSet0 @t6)) % 15.86/16.12 (define @t26 () (and @t19 @t25)) % 15.86/16.12 (define @t27 () (@var "W3" $$unsorted)) % 15.86/16.12 (define @t28 () (@var "W5" $$unsorted)) % 15.86/16.12 (define @t29 () (@var "W4" $$unsorted)) % 15.86/16.12 (define @t30 () (tptp.sdtpldt0 @t29 @t28)) % 15.86/16.12 (define @t31 () (tptp.aElementOf0 @t28 @t6)) % 15.86/16.12 (define @t32 () (tptp.aElementOf0 @t29 @t1)) % 15.86/16.12 (define @t33 () (and @t32 @t31 (= @t30 @t27))) % 15.86/16.12 (define @t34 () (@list @t29 @t28)) % 15.86/16.12 (define @t35 () (exists @t34 @t33)) % 15.86/16.12 (define @t36 () (tptp.aElementOf0 @t27 @t12)) % 15.86/16.12 (define @t37 () (= @t36 @t35)) % 15.86/16.12 (define @t38 () (@list @t27)) % 15.86/16.12 (define @t39 () (forall @t38 @t37)) % 15.86/16.12 (define @t40 () (tptp.aSet0 @t12)) % 15.86/16.12 (define @t41 () (and @t40 @t39)) % 15.86/16.12 (define @t42 () (tptp.sdtpldt1 @t1 @t6)) % 15.86/16.12 (define @t43 () (= @t12 @t42)) % 15.86/16.12 (define @t44 () (= @t43 @t41)) % 15.86/16.12 (define @t45 () (forall @t24 @t44)) % 15.86/16.12 (define @t46 () (=> @t26 @t45)) % 15.86/16.12 (define @t47 () (forall @t10 @t46)) % 15.86/16.12 (define @t48 () (tptp.sdtasasdt0 @t1 @t6)) % 15.86/16.12 (define @t49 () (tptp.aElementOf0 (tptp.sdtasdt0 @t12 @t6) @t1)) % 15.86/16.12 (define @t50 () (forall @t24 (=> @t14 @t49))) % 15.86/16.12 (define @t51 () (tptp.aElementOf0 @t13 @t1)) % 15.86/16.12 (define @t52 () (forall @t24 (=> @t22 @t51))) % 15.86/16.12 (define @t53 () (and @t52 @t50)) % 15.86/16.12 (define @t54 () (=> @t20 @t53)) % 15.86/16.12 (define @t55 () (forall @t21 @t54)) % 15.86/16.12 (define @t56 () (and @t19 @t55)) % 15.86/16.12 (define @t57 () (tptp.aIdeal0 @t1)) % 15.86/16.12 (define @t58 () (= @t57 @t56)) % 15.86/16.12 (define @t59 () (forall @t3 @t58)) % 15.86/16.12 (define @t60 () (and @t57 (tptp.aIdeal0 @t6))) % 15.86/16.12 (define @t61 () (tptp.aIdeal0 tptp.xJ)) % 15.86/16.12 (define @t62 () (tptp.aIdeal0 tptp.xI)) % 15.86/16.12 (define @t63 () (tptp.sdtpldt1 tptp.xI tptp.xJ)) % 15.86/16.12 (define @t64 () (tptp.aElementOf0 @t1 @t63)) % 15.86/16.12 (define @t65 () (forall @t3 (=> @t2 @t64))) % 15.86/16.12 (define @t66 () (tptp.aElementOf0 @t6 tptp.xJ)) % 15.86/16.12 (define @t67 () (tptp.aElementOf0 @t1 tptp.xI)) % 15.86/16.12 (define @t68 () (and @t67 @t66 (= @t7 tptp.sz10))) % 15.86/16.12 (define @t69 () (exists @t10 @t68)) % 15.86/16.12 (define @t70 () (not @t69)) % 15.86/16.12 (define @t71 () (@list tptp.sz10)) % 15.86/16.12 (define @t72 () (tptp.aElementOf0 tptp.sz10 @t63)) % 15.86/16.12 (define @t73 () (not @t4)) % 15.86/16.12 (define @t74 () (or @t73 @t72)) % 15.86/16.12 (define @t75 () (@list false false)) % 15.86/16.12 (define @t76 () (= tptp.sz10 @t7)) % 15.86/16.12 (define @t77 () (not @t76)) % 15.86/16.12 (define @t78 () (not @t66)) % 15.86/16.12 (define @t79 () (not @t67)) % 15.86/16.12 (define @t80 () (or @t79 @t78 @t77)) % 15.86/16.12 (define @t81 () (forall @t10 @t80)) % 15.86/16.12 (define @t82 () (and @t67 @t66 @t76)) % 15.86/16.12 (define @t83 () (forall @t10 (not @t82))) % 15.86/16.12 (define @t84 () (not @t83)) % 15.86/16.12 (define @t85 () (not (tptp.aElementOf0 @t28 tptp.xJ))) % 15.86/16.12 (define @t86 () (not (tptp.aElementOf0 @t29 tptp.xI))) % 15.86/16.12 (define @t87 () (forall @t34 (or @t86 @t85 (not (= tptp.sz10 @t30))))) % 15.86/16.12 (define @t88 () (@list false)) % 15.86/16.12 (define @t89 () (@var "BOUND_VARIABLE_7780" $$unsorted)) % 15.86/16.12 (define @t90 () (tptp.aElementOf0 @t27 @t89)) % 15.86/16.12 (define @t91 () (= @t27 @t30)) % 15.86/16.12 (define @t92 () (not @t91)) % 15.86/16.12 (define @t93 () (not @t31)) % 15.86/16.12 (define @t94 () (not @t32)) % 15.86/16.12 (define @t95 () (or @t94 @t93 @t92)) % 15.86/16.12 (define @t96 () (not (forall @t34 @t95))) % 15.86/16.12 (define @t97 () (forall @t38 (= @t90 @t96))) % 15.86/16.12 (define @t98 () (tptp.aSet0 @t89)) % 15.86/16.12 (define @t99 () (and @t98 @t97)) % 15.86/16.12 (define @t100 () (= (= @t89 @t42) @t99)) % 15.86/16.12 (define @t101 () (not @t25)) % 15.86/16.12 (define @t102 () (not @t19)) % 15.86/16.12 (define @t103 () (or @t102 @t101 @t100)) % 15.86/16.12 (define @t104 () (@list @t1 @t6 @t89)) % 15.86/16.12 (define @t105 () (forall @t104 @t103)) % 15.86/16.12 (define @t106 () (@list @t89)) % 15.86/16.12 (define @t107 () (forall @t106 @t103)) % 15.86/16.12 (define @t108 () (forall @t106 @t100)) % 15.86/16.12 (define @t109 () (@list @t12)) % 15.86/16.12 (define @t110 () (or @t102 @t101 @t108)) % 15.86/16.12 (define @t111 () (forall @t24 (= @t43 (and @t40 (forall @t38 (= @t36 @t96)))))) % 15.86/16.12 (define @t112 () (or @t102 @t101 @t111)) % 15.86/16.12 (define @t113 () (and @t32 @t31 @t91)) % 15.86/16.12 (define @t114 () (forall @t34 (not @t113))) % 15.86/16.12 (define @t115 () (not @t114)) % 15.86/16.12 (define @t116 () (forall @t38 (= (not (forall @t34 (or @t86 @t85 @t92))) (tptp.aElementOf0 @t27 @t63)))) % 15.86/16.12 (define @t117 () (and (tptp.aSet0 @t63) @t116)) % 15.86/16.12 (define @t118 () (= (= @t63 @t63) @t117)) % 15.86/16.12 (define @t119 () (tptp.aSet0 tptp.xJ)) % 15.86/16.12 (define @t120 () (not @t119)) % 15.86/16.12 (define @t121 () (tptp.aSet0 tptp.xI)) % 15.86/16.12 (define @t122 () (not @t121)) % 15.86/16.12 (define @t123 () (or @t122 @t120 @t118)) % 15.86/16.12 (define @t124 () (forall @t104 (or @t102 @t101 (= (= @t42 @t89) (and @t98 (forall @t38 (= @t96 @t90))))))) % 15.86/16.12 (define @t125 () (or @t122 @t120 @t117)) % 15.86/16.12 (define @t126 () (@var "BOUND_VARIABLE_7838" $$unsorted)) % 15.86/16.12 (define @t127 () (tptp.sdtasdt0 @t126 @t6)) % 15.86/16.12 (define @t128 () (not (tptp.aElement0 @t126))) % 15.86/16.12 (define @t129 () (or @t128 (tptp.aElementOf0 @t127 @t1))) % 15.86/16.12 (define @t130 () (@var "BOUND_VARIABLE_7831" $$unsorted)) % 15.86/16.12 (define @t131 () (tptp.sdtpldt0 @t6 @t130)) % 15.86/16.12 (define @t132 () (or (not (tptp.aElementOf0 @t130 @t1)) (tptp.aElementOf0 @t131 @t1))) % 15.86/16.12 (define @t133 () (and @t132 @t129)) % 15.86/16.12 (define @t134 () (not @t20)) % 15.86/16.12 (define @t135 () (or @t134 @t133)) % 15.86/16.12 (define @t136 () (@list @t6 @t130 @t126)) % 15.86/16.12 (define @t137 () (@list @t130 @t126)) % 15.86/16.12 (define @t138 () (forall @t137 @t135)) % 15.86/16.12 (define @t139 () (forall (@list @t126) @t129)) % 15.86/16.12 (define @t140 () (forall @t137 @t129)) % 15.86/16.12 (define @t141 () (forall (@list @t130) @t132)) % 15.86/16.12 (define @t142 () (forall @t137 @t132)) % 15.86/16.12 (define @t143 () (and @t142 @t140)) % 15.86/16.12 (define @t144 () (forall @t137 @t133)) % 15.86/16.12 (define @t145 () (or @t134 @t144)) % 15.86/16.12 (define @t146 () (and (forall @t24 (or (not @t22) @t51)) (forall @t24 (or (not @t14) @t49)))) % 15.86/16.12 (define @t147 () (and @t119 (forall @t136 (or @t78 (and (or (not (tptp.aElementOf0 @t130 tptp.xJ)) (tptp.aElementOf0 @t131 tptp.xJ)) (or @t128 (tptp.aElementOf0 @t127 tptp.xJ))))))) % 15.86/16.12 (define @t148 () (= @t61 @t147)) % 15.86/16.12 (define @t149 () (and @t121 (forall @t136 (or (not (tptp.aElementOf0 @t6 tptp.xI)) (and (or (not (tptp.aElementOf0 @t130 tptp.xI)) (tptp.aElementOf0 @t131 tptp.xI)) (or @t128 (tptp.aElementOf0 @t127 tptp.xI))))))) % 15.86/16.12 (define @t150 () (= @t62 @t149)) % 15.86/16.12 (define @t151 () (@list false false false)) % 15.86/16.12 (define @t152 () (not @t87)) % 15.86/16.12 (define @t153 () (= @t152 @t72)) % 15.86/16.12 (define @t154 () (= @t72 @t152)) % 15.86/16.12 (assume @p1 (forall @t3 (=> @t2 true))) % 15.86/16.12 (assume @p2 (tptp.aElement0 tptp.sz00)) % 15.86/16.12 (assume @p3 @t4) % 15.86/16.12 (assume @p4 (forall @t3 (=> @t2 (tptp.aElement0 @t5)))) % 15.86/16.12 (assume @p5 (forall @t10 (=> @t9 (tptp.aElement0 @t7)))) % 15.86/16.12 (assume @p6 (forall @t10 (=> @t9 (tptp.aElement0 @t11)))) % 15.86/16.12 (assume @p7 (forall @t10 (=> @t9 (= @t7 (tptp.sdtpldt0 @t6 @t1))))) % 15.86/16.12 (assume @p8 (forall @t16 (=> @t15 (= (tptp.sdtpldt0 @t7 @t12) (tptp.sdtpldt0 @t1 @t13))))) % 15.86/16.12 (assume @p9 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 tptp.sz00) @t1) (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1)))))) % 15.86/16.12 (assume @p10 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 @t5) tptp.sz00) (= tptp.sz00 (tptp.sdtpldt0 @t5 @t1)))))) % 15.86/16.12 (assume @p11 (forall @t10 (=> @t9 (= @t11 @t17)))) % 15.86/16.12 (assume @p12 (forall @t16 (=> @t15 (= (tptp.sdtasdt0 @t11 @t12) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t6 @t12)))))) % 15.86/16.12 (assume @p13 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 15.86/16.12 (assume @p14 (forall @t16 (=> @t15 (and (= (tptp.sdtasdt0 @t1 @t13) (tptp.sdtpldt0 @t11 (tptp.sdtasdt0 @t1 @t12))) (= (tptp.sdtasdt0 @t13 @t1) (tptp.sdtpldt0 @t17 (tptp.sdtasdt0 @t12 @t1))))))) % 15.86/16.12 (assume @p15 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t18 @t1) @t5) (= @t5 (tptp.sdtasdt0 @t1 @t18)))))) % 15.86/16.12 (assume @p16 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 15.86/16.12 (assume @p17 (forall @t10 (=> @t9 (=> (= @t11 tptp.sz00) (or (= @t1 tptp.sz00) (= @t6 tptp.sz00)))))) % 15.86/16.12 (assume @p18 (not (= tptp.sz10 tptp.sz00))) % 15.86/16.12 (assume @p19 (forall @t3 (=> @t19 true))) % 15.86/16.12 (assume @p20 (forall @t3 (=> @t19 (forall @t21 (=> @t20 @t8))))) % 15.86/16.12 (assume @p21 (forall @t10 (=> @t26 (=> (and (forall @t24 (=> @t22 @t23)) (forall @t24 (=> @t23 @t22))) (= @t1 @t6))))) % 15.86/16.12 (assume @p22 @t47) % 15.86/16.12 (assume @p23 (forall @t10 (=> @t26 (forall @t24 (= (= @t12 @t48) (and @t40 (forall @t38 (= @t36 (and (tptp.aElementOf0 @t27 @t1) (tptp.aElementOf0 @t27 @t6)))))))))) % 15.86/16.12 (assume @p24 @t59) % 15.86/16.12 (assume @p25 (forall @t10 (=> @t60 (tptp.aIdeal0 @t42)))) % 15.86/16.12 (assume @p26 (forall @t10 (=> @t60 (tptp.aIdeal0 @t48)))) % 15.86/16.12 (assume @p27 (forall @t16 (=> (and @t2 @t8 (tptp.aIdeal0 @t12)) (= (tptp.sdteqdtlpzmzozddtrp0 @t1 @t6 @t12) (tptp.aElementOf0 (tptp.sdtpldt0 @t1 (tptp.smndt0 @t6)) @t12))))) % 15.86/16.12 (assume @p28 (and @t62 @t61)) % 15.86/16.12 (assume @p29 @t65) % 15.86/16.12 (assume @p30 (and (tptp.aElement0 tptp.xx) (tptp.aElement0 tptp.xy))) % 15.86/16.12 (assume @p31 @t70) % 15.86/16.12 (assume @p32 true) % 15.86/16.12 (step @p33 :rule bool-impl-elim :args (@t2 @t64)) % 15.86/16.12 (step @p34 :rule cong :premises (@p33) :args (@t65)) % 15.86/16.12 (step @p35 :rule eq_resolve :premises (@p29 @p34)) % 15.86/16.12 (step @p36 :rule instantiate :premises (@p35) :args (@t71)) % 15.86/16.12 (step @p37 :rule cnf_or_pos :args (@t74)) % 15.86/16.12 (step @p38 :rule reordering :premises (@p37) :args ((or @t73 @t72 (not @t74)))) % 15.86/16.12 (step @p39 :rule chain_m_resolution :premises (@p38 @p3 @p36) :args (@t72 @t75 (@list @t4 @t74))) % 15.86/16.12 (step @p40 :rule bool-double-not-elim :args (@t81)) % 15.86/16.12 (step @p41 :rule aci_norm :args ((= (or @t79 (or @t78 @t77)) @t80))) % 15.86/16.12 (step @p42 :rule bool-and-de-morgan :args (@t66 @t76 true)) % 15.86/16.12 (step @p43 :rule refl :args (@t79)) % 15.86/16.12 (step @p44 :rule nary_cong :premises (@p43 @p42) :args ((or @t79 (not (and @t66 @t76))))) % 15.86/16.12 (step @p45 :rule bool-and-de-morgan :args (@t67 @t66 (and @t76))) % 15.86/16.12 (step @p46 :rule trans :premises (@p45 @p44)) % 15.86/16.12 (step @p47 :rule trans :premises (@p46 @p41)) % 15.86/16.12 (step @p48 :rule cong :premises (@p47) :args (@t83)) % 15.86/16.12 (step @p49 :rule cong :premises (@p48) :args (@t84)) % 15.86/16.12 (step @p50 :rule exists-elim :args ((= (exists @t10 @t82) @t84))) % 15.86/16.12 (step @p51 :rule trans :premises (@p50 @p49)) % 15.86/16.12 (step @p52 :rule eq-symm :args (@t7 tptp.sz10)) % 15.86/16.12 (step @p53 :rule refl :args (@t66)) % 15.86/16.12 (step @p54 :rule refl :args (@t67)) % 15.86/16.12 (step @p55 :rule nary_cong :premises (@p54 @p53 @p52) :args (@t68)) % 15.86/16.12 (step @p56 :rule cong :premises (@p55) :args (@t69)) % 15.86/16.12 (step @p57 :rule trans :premises (@p56 @p51)) % 15.86/16.12 (step @p58 :rule cong :premises (@p57) :args (@t70)) % 15.86/16.12 (step @p59 :rule trans :premises (@p58 @p40)) % 15.86/16.12 (step @p60 :rule eq_resolve :premises (@p31 @p59)) % 15.86/16.12 (step @p61 :rule alpha_equiv :args (@t81 (@list @t1 @t6) (@list @t29 @t28))) % 15.86/16.12 (step @p62 :rule equiv_elim1 :premises (@p61)) % 15.86/16.12 (step @p63 :rule chain_m_resolution :premises (@p62 @p60) :args (@t87 @t88 (@list @t81))) % 15.86/16.12 (step @p64 :rule eq-symm :args (@t90 @t96)) % 15.86/16.12 (step @p65 :rule cong :premises (@p64) :args (@t97)) % 15.86/16.12 (step @p66 :rule refl :args (@t98)) % 15.86/16.12 (step @p67 :rule nary_cong :premises (@p66 @p65) :args (@t99)) % 15.86/16.12 (step @p68 :rule eq-symm :args (@t89 @t42)) % 15.86/16.12 (step @p69 :rule cong :premises (@p68 @p67) :args (@t100)) % 15.86/16.12 (step @p70 :rule refl :args (@t101)) % 15.86/16.12 (step @p71 :rule refl :args (@t102)) % 15.86/16.12 (step @p72 :rule nary_cong :premises (@p71 @p70 @p69) :args (@t103)) % 15.86/16.12 (step @p73 :rule cong :premises (@p72) :args (@t105)) % 15.86/16.12 (step @p74 :rule quant-merge-prenex :args ((= (forall @t10 @t107) @t105))) % 15.86/16.12 (step @p75 :rule alpha_equiv :args (@t108 (@list @t89) @t109)) % 15.86/16.12 (step @p76 :rule refl :args (@t101)) % 15.86/16.12 (step @p77 :rule refl :args (@t102)) % 15.86/16.12 (step @p78 :rule nary_cong :premises (@p77 @p76 @p75) :args (@t110)) % 15.86/16.12 (step @p79 :rule quant-miniscope-or :args ((= @t107 @t110))) % 15.86/16.12 (step @p80 :rule trans :premises (@p79 @p78)) % 15.86/16.12 (step @p81 :rule symm :premises (@p80)) % 15.86/16.12 (step @p82 :rule cong :premises (@p81) :args ((forall @t10 @t112))) % 15.86/16.12 (step @p83 :rule trans :premises (@p82 @p74)) % 15.86/16.12 (step @p84 :rule trans :premises (@p83 @p73)) % 15.86/16.12 (step @p85 :rule aci_norm :args ((= (or (or @t102 @t101) @t111) @t112))) % 15.86/16.12 (step @p86 :rule refl :args (@t111)) % 15.86/16.12 (step @p87 :rule bool-and-de-morgan :args (@t19 @t25 true)) % 15.86/16.12 (step @p88 :rule nary_cong :premises (@p87 @p86) :args ((or (not @t26) @t111))) % 15.86/16.12 (step @p89 :rule trans :premises (@p88 @p85)) % 15.86/16.12 (step @p90 :rule bool-impl-elim :args (@t26 @t111)) % 15.86/16.12 (step @p91 :rule trans :premises (@p90 @p89)) % 15.86/16.12 (step @p92 :rule cong :premises (@p91) :args ((forall @t10 (=> @t26 @t111)))) % 15.86/16.12 (step @p93 :rule trans :premises (@p92 @p84)) % 15.86/16.12 (step @p94 :rule aci_norm :args ((= (or @t94 (or @t93 @t92)) @t95))) % 15.86/16.12 (step @p95 :rule bool-and-de-morgan :args (@t31 @t91 true)) % 15.86/16.12 (step @p96 :rule refl :args (@t94)) % 15.86/16.12 (step @p97 :rule nary_cong :premises (@p96 @p95) :args ((or @t94 (not (and @t31 @t91))))) % 15.86/16.12 (step @p98 :rule bool-and-de-morgan :args (@t32 @t31 (and @t91))) % 15.86/16.12 (step @p99 :rule trans :premises (@p98 @p97)) % 15.86/16.12 (step @p100 :rule trans :premises (@p99 @p94)) % 15.86/16.12 (step @p101 :rule cong :premises (@p100) :args (@t114)) % 15.86/16.12 (step @p102 :rule cong :premises (@p101) :args (@t115)) % 15.86/16.12 (step @p103 :rule exists-elim :args ((= (exists @t34 @t113) @t115))) % 15.86/16.12 (step @p104 :rule trans :premises (@p103 @p102)) % 15.86/16.12 (step @p105 :rule eq-symm :args (@t30 @t27)) % 15.86/16.12 (step @p106 :rule refl :args (@t31)) % 15.86/16.12 (step @p107 :rule refl :args (@t32)) % 15.86/16.12 (step @p108 :rule nary_cong :premises (@p107 @p106 @p105) :args (@t33)) % 15.86/16.12 (step @p109 :rule cong :premises (@p108) :args (@t35)) % 15.86/16.12 (step @p110 :rule trans :premises (@p109 @p104)) % 15.86/16.12 (step @p111 :rule refl :args (@t36)) % 15.86/16.12 (step @p112 :rule cong :premises (@p111 @p110) :args (@t37)) % 15.86/16.12 (step @p113 :rule cong :premises (@p112) :args (@t39)) % 15.86/16.12 (step @p114 :rule refl :args (@t40)) % 15.86/16.12 (step @p115 :rule nary_cong :premises (@p114 @p113) :args (@t41)) % 15.86/16.12 (step @p116 :rule refl :args (@t43)) % 15.86/16.12 (step @p117 :rule cong :premises (@p116 @p115) :args (@t44)) % 15.86/16.12 (step @p118 :rule cong :premises (@p117) :args (@t45)) % 15.86/16.12 (step @p119 :rule refl :args (@t26)) % 15.86/16.12 (step @p120 :rule cong :premises (@p119 @p118) :args (@t46)) % 15.86/16.12 (step @p121 :rule cong :premises (@p120) :args (@t47)) % 15.86/16.12 (step @p122 :rule trans :premises (@p121 @p93)) % 15.86/16.12 (step @p123 :rule eq_resolve :premises (@p22 @p122)) % 15.86/16.12 (step @p124 :rule bool-eq-true :args (@t117)) % 15.86/16.12 (step @p125 :rule eq-symm :args (true @t117)) % 15.86/16.12 (step @p126 :rule trans :premises (@p125 @p124)) % 15.86/16.12 (step @p127 :rule refl :args (@t117)) % 15.86/16.12 (step @p128 :rule eq-refl :args (@t63)) % 15.86/16.12 (step @p129 :rule cong :premises (@p128 @p127) :args (@t118)) % 15.86/16.12 (step @p130 :rule trans :premises (@p129 @p126)) % 15.86/16.12 (step @p131 :rule refl :args (@t120)) % 15.86/16.12 (step @p132 :rule refl :args (@t122)) % 15.86/16.12 (step @p133 :rule nary_cong :premises (@p132 @p131 @p130) :args (@t123)) % 15.86/16.12 (step @p134 :rule refl :args (@t124)) % 15.86/16.12 (step @p135 :rule cong :premises (@p134 @p133) :args ((=> @t124 @t123))) % 15.86/16.12 (assume-push @p213 @t124) % 15.86/16.12 (step @p137 :rule instantiate :premises (@p123) :args ((@list tptp.xI tptp.xJ @t63))) % 15.86/16.12 (step-pop @p214 :rule scope :premises (@p137)) % 15.86/16.12 (step @p138 :rule process_scope :premises (@p214) :args (@t123)) % 15.86/16.12 (step @p140 :rule eq_resolve :premises (@p138 @p135)) % 15.86/16.12 (step @p141 :rule implies_elim :premises (@p140)) % 15.86/16.12 (step @p142 :rule chain_m_resolution :premises (@p141 @p123) :args (@t125 @t88 (@list @t124))) % 15.86/16.12 (step @p143 :rule quant-merge-prenex :args ((= (forall @t21 @t138) (forall @t136 @t135)))) % 15.86/16.12 (step @p144 :rule alpha_equiv :args (@t139 (@list @t126) @t109)) % 15.86/16.12 (step @p145 :rule quant-unused-vars :args ((= @t140 @t139))) % 15.86/16.12 (step @p146 :rule trans :premises (@p145 @p144)) % 15.86/16.12 (step @p147 :rule alpha_equiv :args (@t141 (@list @t130) @t109)) % 15.86/16.12 (step @p148 :rule quant-unused-vars :args ((= @t142 @t141))) % 15.86/16.12 (step @p149 :rule trans :premises (@p148 @p147)) % 15.86/16.12 (step @p150 :rule nary_cong :premises (@p149 @p146) :args (@t143)) % 15.86/16.12 (step @p151 :rule quant-miniscope-and :args ((= @t144 @t143))) % 15.86/16.12 (step @p152 :rule trans :premises (@p151 @p150)) % 15.86/16.12 (step @p153 :rule refl :args (@t134)) % 15.86/16.12 (step @p154 :rule nary_cong :premises (@p153 @p152) :args (@t145)) % 15.86/16.12 (step @p155 :rule quant-miniscope-or :args ((= @t138 @t145))) % 15.86/16.12 (step @p156 :rule trans :premises (@p155 @p154)) % 15.86/16.12 (step @p157 :rule symm :premises (@p156)) % 15.86/16.12 (step @p158 :rule cong :premises (@p157) :args ((forall @t21 (or @t134 @t146)))) % 15.86/16.12 (step @p159 :rule trans :premises (@p158 @p143)) % 15.86/16.12 (step @p160 :rule bool-impl-elim :args (@t20 @t146)) % 15.86/16.12 (step @p161 :rule cong :premises (@p160) :args ((forall @t21 (=> @t20 @t146)))) % 15.86/16.12 (step @p162 :rule trans :premises (@p161 @p159)) % 15.86/16.12 (step @p163 :rule bool-impl-elim :args (@t14 @t49)) % 15.86/16.12 (step @p164 :rule cong :premises (@p163) :args (@t50)) % 15.86/16.12 (step @p165 :rule bool-impl-elim :args (@t22 @t51)) % 15.86/16.12 (step @p166 :rule cong :premises (@p165) :args (@t52)) % 15.86/16.12 (step @p167 :rule nary_cong :premises (@p166 @p164) :args (@t53)) % 15.86/16.12 (step @p168 :rule refl :args (@t20)) % 15.86/16.12 (step @p169 :rule cong :premises (@p168 @p167) :args (@t54)) % 15.86/16.12 (step @p170 :rule cong :premises (@p169) :args (@t55)) % 15.86/16.12 (step @p171 :rule trans :premises (@p170 @p162)) % 15.86/16.12 (step @p172 :rule refl :args (@t19)) % 15.86/16.12 (step @p173 :rule nary_cong :premises (@p172 @p171) :args (@t56)) % 15.86/16.12 (step @p174 :rule refl :args (@t57)) % 15.86/16.12 (step @p175 :rule cong :premises (@p174 @p173) :args (@t58)) % 15.86/16.12 (step @p176 :rule cong :premises (@p175) :args (@t59)) % 15.86/16.12 (step @p177 :rule eq_resolve :premises (@p24 @p176)) % 15.86/16.12 (step @p178 :rule instantiate :premises (@p177) :args ((@list tptp.xJ))) % 15.86/16.12 (step @p179 :rule and_elim :premises (@p28) :args (1)) % 15.86/16.12 (step @p180 :rule cnf_equiv_pos1 :args (@t148)) % 15.86/16.12 (step @p181 :rule reordering :premises (@p180) :args ((or (not @t61) @t147 (not @t148)))) % 15.86/16.12 (step @p182 :rule chain_m_resolution :premises (@p181 @p179 @p178) :args (@t147 @t75 (@list @t61 @t148))) % 15.86/16.12 (step @p183 :rule cnf_and_pos :args (@t147 0)) % 15.86/16.12 (step @p184 :rule reordering :premises (@p183) :args ((or @t119 (not @t147)))) % 15.86/16.12 (step @p185 :rule chain_m_resolution :premises (@p184 @p182) :args (@t119 @t88 (@list @t147))) % 15.86/16.12 (step @p186 :rule instantiate :premises (@p177) :args ((@list tptp.xI))) % 15.86/16.12 (step @p187 :rule and_elim :premises (@p28) :args (0)) % 15.86/16.12 (step @p188 :rule cnf_equiv_pos1 :args (@t150)) % 15.86/16.12 (step @p189 :rule reordering :premises (@p188) :args ((or (not @t62) @t149 (not @t150)))) % 15.86/16.12 (step @p190 :rule chain_m_resolution :premises (@p189 @p187 @p186) :args (@t149 @t75 (@list @t62 @t150))) % 15.86/16.12 (step @p191 :rule cnf_and_pos :args (@t149 0)) % 15.86/16.12 (step @p192 :rule reordering :premises (@p191) :args ((or @t121 (not @t149)))) % 15.86/16.12 (step @p193 :rule chain_m_resolution :premises (@p192 @p190) :args (@t121 @t88 (@list @t149))) % 15.86/16.12 (step @p194 :rule cnf_or_pos :args (@t125)) % 15.86/16.12 (step @p195 :rule reordering :premises (@p194) :args ((or @t122 @t120 @t117 (not @t125)))) % 15.86/16.12 (step @p196 :rule chain_m_resolution :premises (@p195 @p193 @p185 @p142) :args (@t117 @t151 (@list @t121 @t119 @t125))) % 15.86/16.12 (step @p197 :rule cnf_and_pos :args (@t117 1)) % 15.86/16.12 (step @p198 :rule reordering :premises (@p197) :args ((or @t116 (not @t117)))) % 15.86/16.12 (step @p199 :rule chain_m_resolution :premises (@p198 @p196) :args (@t116 @t88 (@list @t117))) % 15.86/16.12 (step @p200 :rule eq-symm :args (@t152 @t72)) % 15.86/16.12 (step @p201 :rule refl :args (@t116)) % 15.86/16.12 (step @p202 :rule cong :premises (@p201 @p200) :args ((=> @t116 @t153))) % 15.86/16.12 (assume-push @p215 @t116) % 15.86/16.12 (step @p204 :rule instantiate :premises (@p199) :args (@t71)) % 15.86/16.12 (step-pop @p216 :rule scope :premises (@p204)) % 15.86/16.12 (step @p205 :rule process_scope :premises (@p216) :args (@t153)) % 15.86/16.12 (step @p207 :rule eq_resolve :premises (@p205 @p202)) % 15.86/16.12 (step @p208 :rule implies_elim :premises (@p207)) % 15.86/16.12 (step @p209 :rule chain_m_resolution :premises (@p208 @p199) :args (@t154 @t88 (@list @t116))) % 15.86/16.12 (step @p210 :rule cnf_equiv_pos1 :args (@t154)) % 15.86/16.12 (step @p211 :rule reordering :premises (@p210) :args ((or (not @t72) @t152 (not @t154)))) % 15.86/16.12 (step @p212 false :rule chain_m_resolution :premises (@p211 @p209 @p63 @p39) :args (false @t151 (@list @t154 @t87 @t72))) % 15.86/16.12 ) % 15.86/16.12 % SZS output end Proof % 15.86/16.12 % cvc5 exiting %------------------------------------------------------------------------------