%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : RNG098+2 : 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 : n023.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 3.33s 3.50s % Output : Proof 3.33s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : RNG098+2 : 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 % 0.16/0.34 % Computer : n023.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 14:07:58 EDT 2026 % 0.16/0.34 % CPUTime : % 0.29/0.49 %----Proving TF0_NAR, FOF, or CNF % 3.33/3.50 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 3.33/3.50 % SZS status Theorem % 3.33/3.50 % SZS output start Proof % 3.33/3.50 ( % 3.33/3.50 (declare-sort $$unsorted 0) % 3.33/3.50 (declare-const tptp.xa $$unsorted) % 3.33/3.50 (declare-const tptp.xb $$unsorted) % 3.33/3.50 (declare-const tptp.xx $$unsorted) % 3.33/3.50 (declare-const tptp.xI $$unsorted) % 3.33/3.50 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 3.33/3.50 (declare-const tptp.sz00 $$unsorted) % 3.33/3.50 (declare-const tptp.sz10 $$unsorted) % 3.33/3.50 (declare-const tptp.smndt0 (-> $$unsorted $$unsorted)) % 3.33/3.50 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 3.33/3.50 (declare-const tptp.xy $$unsorted) % 3.33/3.50 (declare-const tptp.sdtasasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 3.33/3.50 (declare-const tptp.aIdeal0 (-> $$unsorted Bool)) % 3.33/3.50 (declare-const tptp.xw $$unsorted) % 3.33/3.50 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 3.33/3.50 (declare-const tptp.xJ $$unsorted) % 3.33/3.50 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 3.33/3.50 (declare-const tptp.sdtpldt1 (-> $$unsorted $$unsorted $$unsorted)) % 3.33/3.50 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 3.33/3.50 (declare-const tptp.sdteqdtlpzmzozddtrp0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 3.33/3.50 (define @t1 () (@var "W0" $$unsorted)) % 3.33/3.50 (define @t2 () (tptp.aElement0 @t1)) % 3.33/3.50 (define @t3 () (@list @t1)) % 3.33/3.50 (define @t4 () (tptp.aElement0 tptp.sz10)) % 3.33/3.50 (define @t5 () (tptp.smndt0 @t1)) % 3.33/3.50 (define @t6 () (tptp.aElement0 @t5)) % 3.33/3.50 (define @t7 () (forall @t3 (=> @t2 @t6))) % 3.33/3.50 (define @t8 () (@var "W1" $$unsorted)) % 3.33/3.50 (define @t9 () (tptp.sdtpldt0 @t1 @t8)) % 3.33/3.50 (define @t10 () (tptp.aElement0 @t8)) % 3.33/3.50 (define @t11 () (and @t2 @t10)) % 3.33/3.50 (define @t12 () (@list @t1 @t8)) % 3.33/3.50 (define @t13 () (tptp.sdtasdt0 @t1 @t8)) % 3.33/3.50 (define @t14 () (@var "W2" $$unsorted)) % 3.33/3.50 (define @t15 () (tptp.sdtpldt0 @t8 @t14)) % 3.33/3.50 (define @t16 () (tptp.aElement0 @t14)) % 3.33/3.50 (define @t17 () (and @t2 @t10 @t16)) % 3.33/3.50 (define @t18 () (@list @t1 @t8 @t14)) % 3.33/3.50 (define @t19 () (tptp.sdtasdt0 @t8 @t1)) % 3.33/3.50 (define @t20 () (and (= (tptp.sdtasdt0 @t1 @t15) (tptp.sdtpldt0 @t13 (tptp.sdtasdt0 @t1 @t14))) (= (tptp.sdtasdt0 @t15 @t1) (tptp.sdtpldt0 @t19 (tptp.sdtasdt0 @t14 @t1))))) % 3.33/3.50 (define @t21 () (forall @t18 (=> @t17 @t20))) % 3.33/3.50 (define @t22 () (tptp.smndt0 tptp.sz10)) % 3.33/3.50 (define @t23 () (= @t5 (tptp.sdtasdt0 @t1 @t22))) % 3.33/3.50 (define @t24 () (tptp.sdtasdt0 @t22 @t1)) % 3.33/3.50 (define @t25 () (and (= @t24 @t5) @t23)) % 3.33/3.50 (define @t26 () (=> @t2 @t25)) % 3.33/3.50 (define @t27 () (forall @t3 @t26)) % 3.33/3.50 (define @t28 () (tptp.aSet0 @t1)) % 3.33/3.50 (define @t29 () (tptp.aElementOf0 @t8 @t1)) % 3.33/3.50 (define @t30 () (@list @t8)) % 3.33/3.50 (define @t31 () (forall @t30 (=> @t29 @t10))) % 3.33/3.50 (define @t32 () (=> @t28 @t31)) % 3.33/3.50 (define @t33 () (forall @t3 @t32)) % 3.33/3.50 (define @t34 () (tptp.aElementOf0 @t14 @t1)) % 3.33/3.50 (define @t35 () (tptp.aElementOf0 @t14 @t8)) % 3.33/3.50 (define @t36 () (@list @t14)) % 3.33/3.50 (define @t37 () (and @t28 (tptp.aSet0 @t8))) % 3.33/3.50 (define @t38 () (@var "W3" $$unsorted)) % 3.33/3.50 (define @t39 () (@var "W5" $$unsorted)) % 3.33/3.50 (define @t40 () (@var "W4" $$unsorted)) % 3.33/3.50 (define @t41 () (tptp.aElementOf0 @t38 @t14)) % 3.33/3.50 (define @t42 () (@list @t38)) % 3.33/3.50 (define @t43 () (tptp.aSet0 @t14)) % 3.33/3.50 (define @t44 () (tptp.sdtpldt1 @t1 @t8)) % 3.33/3.50 (define @t45 () (tptp.sdtasasdt0 @t1 @t8)) % 3.33/3.50 (define @t46 () (tptp.aIdeal0 @t1)) % 3.33/3.50 (define @t47 () (and @t46 (tptp.aIdeal0 @t8))) % 3.33/3.50 (define @t48 () (tptp.aSet0 tptp.xJ)) % 3.33/3.50 (define @t49 () (tptp.aElementOf0 @t19 tptp.xI)) % 3.33/3.50 (define @t50 () (forall @t30 (=> @t10 @t49))) % 3.33/3.50 (define @t51 () (tptp.aElementOf0 @t9 tptp.xI)) % 3.33/3.50 (define @t52 () (tptp.aElementOf0 @t8 tptp.xI)) % 3.33/3.50 (define @t53 () (forall @t30 (=> @t52 @t51))) % 3.33/3.50 (define @t54 () (and @t53 @t50)) % 3.33/3.50 (define @t55 () (tptp.aElementOf0 @t1 tptp.xI)) % 3.33/3.50 (define @t56 () (=> @t55 @t54)) % 3.33/3.50 (define @t57 () (forall @t3 @t56)) % 3.33/3.50 (define @t58 () (tptp.aElement0 tptp.xy)) % 3.33/3.50 (define @t59 () (tptp.aElement0 tptp.xx)) % 3.33/3.50 (define @t60 () (tptp.sdtpldt0 tptp.xa tptp.xb)) % 3.33/3.50 (define @t61 () (tptp.aElementOf0 tptp.xb tptp.xJ)) % 3.33/3.50 (define @t62 () (tptp.aElementOf0 tptp.xa tptp.xI)) % 3.33/3.50 (define @t63 () (tptp.sdtasdt0 tptp.xx tptp.xb)) % 3.33/3.50 (define @t64 () (tptp.sdtasdt0 tptp.xy tptp.xa)) % 3.33/3.50 (define @t65 () (tptp.smndt0 tptp.xx)) % 3.33/3.50 (define @t66 () (tptp.sdtpldt0 @t63 @t65)) % 3.33/3.50 (define @t67 () (tptp.sdtpldt0 @t64 @t66)) % 3.33/3.50 (define @t68 () (tptp.sdtpldt0 tptp.xw @t65)) % 3.33/3.50 (define @t69 () (tptp.sdtpldt0 tptp.xb @t22)) % 3.33/3.50 (define @t70 () (tptp.sdtasdt0 tptp.xx @t69)) % 3.33/3.50 (define @t71 () (@var "BOUND_VARIABLE_7937" $$unsorted)) % 3.33/3.50 (define @t72 () (or (not (tptp.aElement0 @t71)) (tptp.aElementOf0 (tptp.sdtasdt0 @t71 @t1) tptp.xI))) % 3.33/3.50 (define @t73 () (@var "BOUND_VARIABLE_7930" $$unsorted)) % 3.33/3.50 (define @t74 () (or (not (tptp.aElementOf0 @t73 tptp.xI)) (tptp.aElementOf0 (tptp.sdtpldt0 @t1 @t73) tptp.xI))) % 3.33/3.50 (define @t75 () (and @t74 @t72)) % 3.33/3.50 (define @t76 () (not @t55)) % 3.33/3.50 (define @t77 () (or @t76 @t75)) % 3.33/3.50 (define @t78 () (@list @t73 @t71)) % 3.33/3.50 (define @t79 () (forall @t78 @t77)) % 3.33/3.50 (define @t80 () (forall (@list @t71) @t72)) % 3.33/3.50 (define @t81 () (@list @t8)) % 3.33/3.50 (define @t82 () (forall @t78 @t72)) % 3.33/3.50 (define @t83 () (forall (@list @t73) @t74)) % 3.33/3.50 (define @t84 () (forall @t78 @t74)) % 3.33/3.50 (define @t85 () (and @t84 @t82)) % 3.33/3.50 (define @t86 () (forall @t78 @t75)) % 3.33/3.50 (define @t87 () (or @t76 @t86)) % 3.33/3.50 (define @t88 () (not @t10)) % 3.33/3.50 (define @t89 () (and (forall @t30 (or (not @t52) @t51)) (forall @t30 (or @t88 @t49)))) % 3.33/3.50 (define @t90 () (tptp.aElementOf0 @t67 tptp.xI)) % 3.33/3.50 (define @t91 () (not @t16)) % 3.33/3.50 (define @t92 () (not @t2)) % 3.33/3.50 (define @t93 () (or @t92 @t88 @t91)) % 3.33/3.50 (define @t94 () (tptp.aElement0 @t22)) % 3.33/3.50 (define @t95 () (not @t4)) % 3.33/3.50 (define @t96 () (or @t95 @t94)) % 3.33/3.50 (define @t97 () (@list false false)) % 3.33/3.50 (define @t98 () (@var "BOUND_VARIABLE_7776" $$unsorted)) % 3.33/3.50 (define @t99 () (tptp.aElement0 @t98)) % 3.33/3.50 (define @t100 () (not (tptp.aElementOf0 @t98 @t1))) % 3.33/3.50 (define @t101 () (not @t28)) % 3.33/3.50 (define @t102 () (or @t100 @t99)) % 3.33/3.50 (define @t103 () (or @t101 @t102)) % 3.33/3.50 (define @t104 () (forall (@list @t1 @t98) @t103)) % 3.33/3.50 (define @t105 () (@list @t98)) % 3.33/3.50 (define @t106 () (forall @t105 @t103)) % 3.33/3.50 (define @t107 () (forall @t105 @t102)) % 3.33/3.50 (define @t108 () (or @t101 @t107)) % 3.33/3.50 (define @t109 () (forall @t30 (or (not @t29) @t10))) % 3.33/3.50 (define @t110 () (tptp.aElement0 tptp.xb)) % 3.33/3.50 (define @t111 () (not @t61)) % 3.33/3.50 (define @t112 () (not @t48)) % 3.33/3.50 (define @t113 () (or @t112 @t111 @t110)) % 3.33/3.50 (define @t114 () (tptp.sdtasdt0 @t22 tptp.xx)) % 3.33/3.50 (define @t115 () (tptp.sdtasdt0 tptp.xx @t22)) % 3.33/3.50 (define @t116 () (= @t70 (tptp.sdtpldt0 @t63 @t115))) % 3.33/3.50 (define @t117 () (and @t116 (= (tptp.sdtasdt0 @t69 tptp.xx) (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xb tptp.xx) @t114)))) % 3.33/3.50 (define @t118 () (not @t94)) % 3.33/3.50 (define @t119 () (not @t110)) % 3.33/3.50 (define @t120 () (not @t59)) % 3.33/3.50 (define @t121 () (or @t120 @t119 @t118 @t117)) % 3.33/3.50 (define @t122 () (@list false)) % 3.33/3.50 (define @t123 () (and (= @t5 @t24) @t23)) % 3.33/3.50 (define @t124 () (= @t65 @t115)) % 3.33/3.50 (define @t125 () (and (= @t65 @t114) @t124)) % 3.33/3.50 (define @t126 () (or @t120 @t125)) % 3.33/3.50 (define @t127 () (tptp.aElementOf0 @t66 tptp.xI)) % 3.33/3.50 (define @t128 () (not @t127)) % 3.33/3.50 (define @t129 () (or @t128 @t90)) % 3.33/3.50 (define @t130 () (not @t129)) % 3.33/3.50 (define @t131 () (@list false true)) % 3.33/3.50 (define @t132 () (not @t58)) % 3.33/3.50 (define @t133 () (and @t129 (or @t132 (tptp.aElementOf0 (tptp.sdtasdt0 tptp.xy @t64) tptp.xI)))) % 3.33/3.50 (define @t134 () (not @t133)) % 3.33/3.50 (define @t135 () (@list true)) % 3.33/3.50 (define @t136 () (tptp.aElementOf0 @t64 tptp.xI)) % 3.33/3.50 (define @t137 () (not @t136)) % 3.33/3.50 (define @t138 () (or @t137 @t133)) % 3.33/3.50 (define @t139 () (or @t132 @t136)) % 3.33/3.50 (define @t140 () (not @t139)) % 3.33/3.50 (define @t141 () (and (or (not (tptp.aElementOf0 tptp.xb tptp.xI)) (tptp.aElementOf0 @t60 tptp.xI)) @t139)) % 3.33/3.50 (define @t142 () (not @t141)) % 3.33/3.50 (define @t143 () (not @t62)) % 3.33/3.50 (define @t144 () (or @t143 @t141)) % 3.33/3.50 (assume @p1 (forall @t3 (=> @t2 true))) % 3.33/3.50 (assume @p2 (tptp.aElement0 tptp.sz00)) % 3.33/3.50 (assume @p3 @t4) % 3.33/3.50 (assume @p4 @t7) % 3.33/3.50 (assume @p5 (forall @t12 (=> @t11 (tptp.aElement0 @t9)))) % 3.33/3.50 (assume @p6 (forall @t12 (=> @t11 (tptp.aElement0 @t13)))) % 3.33/3.50 (assume @p7 (forall @t12 (=> @t11 (= @t9 (tptp.sdtpldt0 @t8 @t1))))) % 3.33/3.50 (assume @p8 (forall @t18 (=> @t17 (= (tptp.sdtpldt0 @t9 @t14) (tptp.sdtpldt0 @t1 @t15))))) % 3.33/3.50 (assume @p9 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 tptp.sz00) @t1) (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1)))))) % 3.33/3.50 (assume @p10 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 @t5) tptp.sz00) (= tptp.sz00 (tptp.sdtpldt0 @t5 @t1)))))) % 3.33/3.50 (assume @p11 (forall @t12 (=> @t11 (= @t13 @t19)))) % 3.33/3.50 (assume @p12 (forall @t18 (=> @t17 (= (tptp.sdtasdt0 @t13 @t14) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t8 @t14)))))) % 3.33/3.50 (assume @p13 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 3.33/3.50 (assume @p14 @t21) % 3.33/3.50 (assume @p15 @t27) % 3.33/3.50 (assume @p16 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 3.33/3.50 (assume @p17 (forall @t12 (=> @t11 (=> (= @t13 tptp.sz00) (or (= @t1 tptp.sz00) (= @t8 tptp.sz00)))))) % 3.33/3.50 (assume @p18 (not (= tptp.sz10 tptp.sz00))) % 3.33/3.50 (assume @p19 (forall @t3 (=> @t28 true))) % 3.33/3.50 (assume @p20 @t33) % 3.33/3.50 (assume @p21 (forall @t12 (=> @t37 (=> (and (forall @t36 (=> @t34 @t35)) (forall @t36 (=> @t35 @t34))) (= @t1 @t8))))) % 3.33/3.50 (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))))))))))) % 3.33/3.50 (assume @p23 (forall @t12 (=> @t37 (forall @t36 (= (= @t14 @t45) (and @t43 (forall @t42 (= @t41 (and (tptp.aElementOf0 @t38 @t1) (tptp.aElementOf0 @t38 @t8)))))))))) % 3.33/3.50 (assume @p24 (forall @t3 (= @t46 (and @t28 (forall @t30 (=> @t29 (and (forall @t36 (=> @t34 (tptp.aElementOf0 @t15 @t1))) (forall @t36 (=> @t16 (tptp.aElementOf0 (tptp.sdtasdt0 @t14 @t8) @t1)))))))))) % 3.33/3.50 (assume @p25 (forall @t12 (=> @t47 (tptp.aIdeal0 @t44)))) % 3.33/3.50 (assume @p26 (forall @t12 (=> @t47 (tptp.aIdeal0 @t45)))) % 3.33/3.50 (assume @p27 (forall @t18 (=> (and @t2 @t10 (tptp.aIdeal0 @t14)) (= (tptp.sdteqdtlpzmzozddtrp0 @t1 @t8 @t14) (tptp.aElementOf0 (tptp.sdtpldt0 @t1 (tptp.smndt0 @t8)) @t14))))) % 3.33/3.50 (assume @p28 (and (tptp.aSet0 tptp.xI) @t57 (tptp.aIdeal0 tptp.xI) @t48 (forall @t3 (=> (tptp.aElementOf0 @t1 tptp.xJ) (and (forall @t30 (=> (tptp.aElementOf0 @t8 tptp.xJ) (tptp.aElementOf0 @t9 tptp.xJ))) (forall @t30 (=> @t10 (tptp.aElementOf0 @t19 tptp.xJ)))))) (tptp.aIdeal0 tptp.xJ))) % 3.33/3.50 (assume @p29 (forall @t3 (=> @t2 (and (exists (@list @t8 @t14) (and @t52 (tptp.aElementOf0 @t14 tptp.xJ) (= @t15 @t1))) (tptp.aElementOf0 @t1 (tptp.sdtpldt1 tptp.xI tptp.xJ)))))) % 3.33/3.50 (assume @p30 (and @t59 @t58)) % 3.33/3.50 (assume @p31 (and @t62 @t61 (= @t60 tptp.sz10))) % 3.33/3.50 (assume @p32 (= tptp.xw (tptp.sdtpldt0 @t64 @t63))) % 3.33/3.50 (assume @p33 (= @t68 @t67)) % 3.33/3.50 (assume @p34 (tptp.aElementOf0 @t70 tptp.xI)) % 3.33/3.50 (assume @p35 (not (tptp.aElementOf0 @t68 tptp.xI))) % 3.33/3.50 (assume @p36 true) % 3.33/3.50 (step @p37 :rule and_elim :premises (@p31) :args (0)) % 3.33/3.50 (step @p38 :rule quant-merge-prenex :args ((= (forall @t3 @t79) (forall (@list @t1 @t73 @t71) @t77)))) % 3.33/3.50 (step @p39 :rule alpha_equiv :args (@t80 (@list @t71) @t81)) % 3.33/3.50 (step @p40 :rule quant-unused-vars :args ((= @t82 @t80))) % 3.33/3.50 (step @p41 :rule trans :premises (@p40 @p39)) % 3.33/3.50 (step @p42 :rule alpha_equiv :args (@t83 (@list @t73) @t81)) % 3.33/3.50 (step @p43 :rule quant-unused-vars :args ((= @t84 @t83))) % 3.33/3.50 (step @p44 :rule trans :premises (@p43 @p42)) % 3.33/3.50 (step @p45 :rule nary_cong :premises (@p44 @p41) :args (@t85)) % 3.33/3.50 (step @p46 :rule quant-miniscope-and :args ((= @t86 @t85))) % 3.33/3.50 (step @p47 :rule trans :premises (@p46 @p45)) % 3.33/3.50 (step @p48 :rule refl :args (@t76)) % 3.33/3.50 (step @p49 :rule nary_cong :premises (@p48 @p47) :args (@t87)) % 3.33/3.50 (step @p50 :rule quant-miniscope-or :args ((= @t79 @t87))) % 3.33/3.50 (step @p51 :rule trans :premises (@p50 @p49)) % 3.33/3.50 (step @p52 :rule symm :premises (@p51)) % 3.33/3.50 (step @p53 :rule cong :premises (@p52) :args ((forall @t3 (or @t76 @t89)))) % 3.33/3.50 (step @p54 :rule trans :premises (@p53 @p38)) % 3.33/3.50 (step @p55 :rule bool-impl-elim :args (@t55 @t89)) % 3.33/3.50 (step @p56 :rule cong :premises (@p55) :args ((forall @t3 (=> @t55 @t89)))) % 3.33/3.50 (step @p57 :rule trans :premises (@p56 @p54)) % 3.33/3.50 (step @p58 :rule bool-impl-elim :args (@t10 @t49)) % 3.33/3.50 (step @p59 :rule cong :premises (@p58) :args (@t50)) % 3.33/3.50 (step @p60 :rule bool-impl-elim :args (@t52 @t51)) % 3.33/3.50 (step @p61 :rule cong :premises (@p60) :args (@t53)) % 3.33/3.50 (step @p62 :rule nary_cong :premises (@p61 @p59) :args (@t54)) % 3.33/3.50 (step @p63 :rule refl :args (@t55)) % 3.33/3.50 (step @p64 :rule cong :premises (@p63 @p62) :args (@t56)) % 3.33/3.50 (step @p65 :rule cong :premises (@p64) :args (@t57)) % 3.33/3.50 (step @p66 :rule trans :premises (@p65 @p57)) % 3.33/3.50 (step @p67 :rule and_elim :premises (@p28) :args (1)) % 3.33/3.50 (step @p68 :rule eq_resolve :premises (@p67 @p66)) % 3.33/3.50 (step @p69 :rule instantiate :premises (@p68) :args ((@list tptp.xa tptp.xb tptp.xy))) % 3.33/3.50 (step @p70 :rule instantiate :premises (@p68) :args ((@list @t64 @t66 tptp.xy))) % 3.33/3.50 (step @p71 :rule false_intro :premises (@p35)) % 3.33/3.50 (step @p72 :rule refl :args (tptp.xI)) % 3.33/3.50 (step @p73 :rule symm :premises (@p33)) % 3.33/3.50 (step @p74 :rule cong :premises (@p73 @p72) :args (@t90)) % 3.33/3.50 (step @p75 :rule trans :premises (@p74 @p71)) % 3.33/3.50 (step @p76 :rule false_elim :premises (@p75)) % 3.33/3.50 (step @p77 :rule true_intro :premises (@p34)) % 3.33/3.50 (step @p78 :rule aci_norm :args ((= (or @t93 @t20) (or @t92 @t88 @t91 @t20)))) % 3.33/3.50 (step @p79 :rule refl :args (@t20)) % 3.33/3.50 (step @p80 :rule aci_norm :args ((= (or @t92 (or @t88 @t91)) @t93))) % 3.33/3.50 (step @p81 :rule bool-and-de-morgan :args (@t10 @t16 true)) % 3.33/3.50 (step @p82 :rule refl :args (@t92)) % 3.33/3.50 (step @p83 :rule nary_cong :premises (@p82 @p81) :args ((or @t92 (not (and @t10 @t16))))) % 3.33/3.50 (step @p84 :rule bool-and-de-morgan :args (@t2 @t10 (and @t16))) % 3.33/3.50 (step @p85 :rule trans :premises (@p84 @p83)) % 3.33/3.50 (step @p86 :rule trans :premises (@p85 @p80)) % 3.33/3.50 (step @p87 :rule nary_cong :premises (@p86 @p79) :args ((or (not @t17) @t20))) % 3.33/3.50 (step @p88 :rule trans :premises (@p87 @p78)) % 3.33/3.50 (step @p89 :rule bool-impl-elim :args (@t17 @t20)) % 3.33/3.50 (step @p90 :rule trans :premises (@p89 @p88)) % 3.33/3.50 (step @p91 :rule cong :premises (@p90) :args (@t21)) % 3.33/3.50 (step @p92 :rule eq_resolve :premises (@p14 @p91)) % 3.33/3.50 (step @p93 :rule instantiate :premises (@p92) :args ((@list tptp.xx tptp.xb @t22))) % 3.33/3.50 (step @p94 :rule bool-impl-elim :args (@t2 @t6)) % 3.33/3.50 (step @p95 :rule cong :premises (@p94) :args (@t7)) % 3.33/3.50 (step @p96 :rule eq_resolve :premises (@p4 @p95)) % 3.33/3.50 (step @p97 :rule instantiate :premises (@p96) :args ((@list tptp.sz10))) % 3.33/3.50 (step @p98 :rule cnf_or_pos :args (@t96)) % 3.33/3.50 (step @p99 :rule reordering :premises (@p98) :args ((or @t95 @t94 (not @t96)))) % 3.33/3.50 (step @p100 :rule chain_m_resolution :premises (@p99 @p3 @p97) :args (@t94 @t97 (@list @t4 @t96))) % 3.33/3.50 (step @p101 :rule aci_norm :args ((= @t103 (or @t101 @t100 @t99)))) % 3.33/3.50 (step @p102 :rule cong :premises (@p101) :args (@t104)) % 3.33/3.50 (step @p103 :rule quant-merge-prenex :args ((= (forall @t3 @t106) @t104))) % 3.33/3.50 (step @p104 :rule alpha_equiv :args (@t107 (@list @t98) @t81)) % 3.33/3.50 (step @p105 :rule refl :args (@t101)) % 3.33/3.50 (step @p106 :rule nary_cong :premises (@p105 @p104) :args (@t108)) % 3.33/3.50 (step @p107 :rule quant-miniscope-or :args ((= @t106 @t108))) % 3.33/3.50 (step @p108 :rule trans :premises (@p107 @p106)) % 3.33/3.50 (step @p109 :rule symm :premises (@p108)) % 3.33/3.50 (step @p110 :rule cong :premises (@p109) :args ((forall @t3 (or @t101 @t109)))) % 3.33/3.50 (step @p111 :rule trans :premises (@p110 @p103)) % 3.33/3.50 (step @p112 :rule trans :premises (@p111 @p102)) % 3.33/3.50 (step @p113 :rule bool-impl-elim :args (@t28 @t109)) % 3.33/3.50 (step @p114 :rule cong :premises (@p113) :args ((forall @t3 (=> @t28 @t109)))) % 3.33/3.50 (step @p115 :rule trans :premises (@p114 @p112)) % 3.33/3.50 (step @p116 :rule bool-impl-elim :args (@t29 @t10)) % 3.33/3.50 (step @p117 :rule cong :premises (@p116) :args (@t31)) % 3.33/3.50 (step @p118 :rule refl :args (@t28)) % 3.33/3.50 (step @p119 :rule cong :premises (@p118 @p117) :args (@t32)) % 3.33/3.50 (step @p120 :rule cong :premises (@p119) :args (@t33)) % 3.33/3.50 (step @p121 :rule trans :premises (@p120 @p115)) % 3.33/3.50 (step @p122 :rule eq_resolve :premises (@p20 @p121)) % 3.33/3.50 (step @p123 :rule instantiate :premises (@p122) :args ((@list tptp.xJ tptp.xb))) % 3.33/3.50 (step @p124 :rule and_elim :premises (@p31) :args (1)) % 3.33/3.50 (step @p125 :rule and_elim :premises (@p28) :args (3)) % 3.33/3.50 (step @p126 :rule cnf_or_pos :args (@t113)) % 3.33/3.50 (step @p127 :rule reordering :premises (@p126) :args ((or @t112 @t111 @t110 (not @t113)))) % 3.33/3.50 (step @p128 :rule chain_m_resolution :premises (@p127 @p125 @p124 @p123) :args (@t110 (@list false false false) (@list @t48 @t61 @t113))) % 3.33/3.50 (step @p129 :rule and_elim :premises (@p30) :args (0)) % 3.33/3.50 (step @p130 :rule cnf_or_pos :args (@t121)) % 3.33/3.50 (step @p131 :rule reordering :premises (@p130) :args ((or @t120 @t119 @t118 @t117 (not @t121)))) % 3.33/3.50 (step @p132 :rule chain_m_resolution :premises (@p131 @p129 @p128 @p100 @p93) :args (@t117 (@list false false false false) (@list @t59 @t110 @t94 @t121))) % 3.33/3.50 (step @p133 :rule cnf_and_pos :args (@t117 0)) % 3.33/3.50 (step @p134 :rule reordering :premises (@p133) :args ((or @t116 (not @t117)))) % 3.33/3.50 (step @p135 :rule chain_m_resolution :premises (@p134 @p132) :args (@t116 @t122 (@list @t117))) % 3.33/3.50 (step @p136 :rule symm :premises (@p135)) % 3.33/3.50 (step @p137 :rule bool-impl-elim :args (@t2 @t123)) % 3.33/3.50 (step @p138 :rule cong :premises (@p137) :args ((forall @t3 (=> @t2 @t123)))) % 3.33/3.50 (step @p139 :rule refl :args (@t23)) % 3.33/3.52 (step @p140 :rule eq-symm :args (@t24 @t5)) % 3.33/3.52 (step @p141 :rule nary_cong :premises (@p140 @p139) :args (@t25)) % 3.33/3.52 (step @p142 :rule refl :args (@t2)) % 3.33/3.52 (step @p143 :rule cong :premises (@p142 @p141) :args (@t26)) % 3.33/3.52 (step @p144 :rule cong :premises (@p143) :args (@t27)) % 3.33/3.52 (step @p145 :rule trans :premises (@p144 @p138)) % 3.33/3.52 (step @p146 :rule eq_resolve :premises (@p15 @p145)) % 3.33/3.52 (step @p147 :rule instantiate :premises (@p146) :args ((@list tptp.xx))) % 3.33/3.52 (step @p148 :rule cnf_or_pos :args (@t126)) % 3.33/3.52 (step @p149 :rule reordering :premises (@p148) :args ((or @t120 @t125 (not @t126)))) % 3.33/3.52 (step @p150 :rule chain_m_resolution :premises (@p149 @p129 @p147) :args (@t125 @t97 (@list @t59 @t126))) % 3.33/3.52 (step @p151 :rule cnf_and_pos :args (@t125 1)) % 3.33/3.52 (step @p152 :rule reordering :premises (@p151) :args ((or @t124 (not @t125)))) % 3.33/3.52 (step @p153 :rule chain_m_resolution :premises (@p152 @p150) :args (@t124 @t122 (@list @t125))) % 3.33/3.52 (step @p154 :rule refl :args (@t63)) % 3.33/3.52 (step @p155 :rule cong :premises (@p154 @p153) :args (@t66)) % 3.33/3.52 (step @p156 :rule trans :premises (@p155 @p136)) % 3.33/3.52 (step @p157 :rule cong :premises (@p156 @p72) :args (@t127)) % 3.33/3.52 (step @p158 :rule trans :premises (@p157 @p77)) % 3.33/3.52 (step @p159 :rule true_elim :premises (@p158)) % 3.33/3.52 (step @p160 :rule cnf_or_pos :args (@t129)) % 3.33/3.52 (step @p161 :rule reordering :premises (@p160) :args ((or @t128 @t90 @t130))) % 3.33/3.52 (step @p162 :rule chain_m_resolution :premises (@p161 @p159 @p76) :args (@t130 @t131 (@list @t127 @t90))) % 3.33/3.52 (step @p163 :rule cnf_and_pos :args (@t133 0)) % 3.33/3.52 (step @p164 :rule reordering :premises (@p163) :args ((or @t129 @t134))) % 3.33/3.52 (step @p165 :rule chain_m_resolution :premises (@p164 @p162) :args (@t134 @t135 (@list @t129))) % 3.33/3.52 (step @p166 :rule cnf_or_pos :args (@t138)) % 3.33/3.52 (step @p167 :rule reordering :premises (@p166) :args ((or @t137 @t133 (not @t138)))) % 3.33/3.52 (step @p168 :rule chain_m_resolution :premises (@p167 @p165 @p70) :args (@t137 (@list true false) (@list @t133 @t138))) % 3.33/3.52 (step @p169 :rule and_elim :premises (@p30) :args (1)) % 3.33/3.52 (step @p170 :rule cnf_or_pos :args (@t139)) % 3.33/3.52 (step @p171 :rule reordering :premises (@p170) :args ((or @t132 @t136 @t140))) % 3.33/3.52 (step @p172 :rule chain_m_resolution :premises (@p171 @p169 @p168) :args (@t140 @t131 (@list @t58 @t136))) % 3.33/3.52 (step @p173 :rule cnf_and_pos :args (@t141 1)) % 3.33/3.52 (step @p174 :rule reordering :premises (@p173) :args ((or @t139 @t142))) % 3.33/3.52 (step @p175 :rule chain_m_resolution :premises (@p174 @p172) :args (@t142 @t135 (@list @t139))) % 3.33/3.52 (step @p176 :rule cnf_or_pos :args (@t144)) % 3.33/3.52 (step @p177 :rule reordering :premises (@p176) :args ((or @t143 @t141 (not @t144)))) % 3.33/3.52 (step @p178 false :rule chain_m_resolution :premises (@p177 @p175 @p69 @p37) :args (false (@list true false false) (@list @t141 @t144 @t62))) % 3.33/3.52 ) % 3.33/3.52 % SZS output end Proof % 3.33/3.52 % cvc5 exiting %------------------------------------------------------------------------------