%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : RNG112+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 : n020.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 08:45:43 AM UTC 2026 % Result : Theorem 0.37s 0.61s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : RNG112+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 % 0.16/0.34 % Computer : n020.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 14:08:10 EDT 2026 % 0.16/0.34 % CPUTime : % 0.28/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.37/0.61 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.37/0.61 % SZS status Theorem % 0.37/0.61 % SZS output start Proof % 0.37/0.61 ( % 0.37/0.61 (declare-sort $$unsorted 0) % 0.37/0.61 (declare-const tptp.xc $$unsorted) % 0.37/0.61 (declare-const tptp.xa $$unsorted) % 0.37/0.61 (declare-const tptp.xI $$unsorted) % 0.37/0.61 (declare-const tptp.slsdtgt0 (-> $$unsorted $$unsorted)) % 0.37/0.61 (declare-const tptp.aDivisorOf0 (-> $$unsorted $$unsorted Bool)) % 0.37/0.61 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 0.37/0.61 (declare-const tptp.sbrdtbr0 (-> $$unsorted $$unsorted)) % 0.37/0.61 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 0.37/0.61 (declare-const tptp.sz00 $$unsorted) % 0.37/0.61 (declare-const tptp.sz10 $$unsorted) % 0.37/0.61 (declare-const tptp.aGcdOfAnd0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.37/0.61 (declare-const tptp.smndt0 (-> $$unsorted $$unsorted)) % 0.37/0.61 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.61 (declare-const tptp.sdtasasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.61 (declare-const tptp.aIdeal0 (-> $$unsorted Bool)) % 0.37/0.61 (declare-const tptp.misRelativelyPrime0 (-> $$unsorted $$unsorted Bool)) % 0.37/0.61 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.61 (declare-const tptp.doDivides0 (-> $$unsorted $$unsorted Bool)) % 0.37/0.61 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 0.37/0.61 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 0.37/0.61 (declare-const tptp.sdteqdtlpzmzozddtrp0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.37/0.61 (declare-const tptp.xb $$unsorted) % 0.37/0.61 (declare-const tptp.sdtpldt1 (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.61 (declare-const tptp.aNaturalNumber0 (-> $$unsorted Bool)) % 0.37/0.61 (define @t1 () (@var "W0" $$unsorted)) % 0.37/0.61 (define @t2 () (tptp.aElement0 @t1)) % 0.37/0.61 (define @t3 () (@list @t1)) % 0.37/0.61 (define @t4 () (tptp.smndt0 @t1)) % 0.37/0.61 (define @t5 () (@var "W1" $$unsorted)) % 0.37/0.61 (define @t6 () (tptp.sdtpldt0 @t1 @t5)) % 0.37/0.61 (define @t7 () (tptp.aElement0 @t5)) % 0.37/0.61 (define @t8 () (and @t2 @t7)) % 0.37/0.61 (define @t9 () (@list @t1 @t5)) % 0.37/0.61 (define @t10 () (tptp.sdtasdt0 @t1 @t5)) % 0.37/0.61 (define @t11 () (@var "W2" $$unsorted)) % 0.37/0.61 (define @t12 () (tptp.sdtpldt0 @t5 @t11)) % 0.37/0.61 (define @t13 () (tptp.aElement0 @t11)) % 0.37/0.61 (define @t14 () (and @t2 @t7 @t13)) % 0.37/0.61 (define @t15 () (@list @t1 @t5 @t11)) % 0.37/0.61 (define @t16 () (tptp.sdtasdt0 @t5 @t1)) % 0.37/0.61 (define @t17 () (tptp.sdtasdt0 @t1 @t11)) % 0.37/0.61 (define @t18 () (tptp.smndt0 tptp.sz10)) % 0.37/0.61 (define @t19 () (= @t5 tptp.sz00)) % 0.37/0.61 (define @t20 () (= @t1 tptp.sz00)) % 0.37/0.61 (define @t21 () (tptp.aSet0 @t1)) % 0.37/0.61 (define @t22 () (tptp.aElementOf0 @t5 @t1)) % 0.37/0.61 (define @t23 () (@list @t5)) % 0.37/0.61 (define @t24 () (tptp.aElementOf0 @t11 @t1)) % 0.37/0.61 (define @t25 () (tptp.aElementOf0 @t11 @t5)) % 0.37/0.61 (define @t26 () (@list @t11)) % 0.37/0.61 (define @t27 () (tptp.aSet0 @t5)) % 0.37/0.61 (define @t28 () (and @t21 @t27)) % 0.37/0.61 (define @t29 () (@var "W3" $$unsorted)) % 0.37/0.61 (define @t30 () (@var "W5" $$unsorted)) % 0.37/0.61 (define @t31 () (@var "W4" $$unsorted)) % 0.37/0.61 (define @t32 () (tptp.aElementOf0 @t29 @t11)) % 0.37/0.61 (define @t33 () (@list @t29)) % 0.37/0.61 (define @t34 () (tptp.aSet0 @t11)) % 0.37/0.61 (define @t35 () (tptp.sdtpldt1 @t1 @t5)) % 0.37/0.61 (define @t36 () (tptp.sdtasasdt0 @t1 @t5)) % 0.37/0.61 (define @t37 () (tptp.sdtasdt0 @t11 @t5)) % 0.37/0.61 (define @t38 () (tptp.aIdeal0 @t1)) % 0.37/0.61 (define @t39 () (and @t38 (tptp.aIdeal0 @t5))) % 0.37/0.61 (define @t40 () (tptp.aElement0 @t29)) % 0.37/0.61 (define @t41 () (@list @t11 @t29)) % 0.37/0.61 (define @t42 () (tptp.aNaturalNumber0 @t1)) % 0.37/0.61 (define @t43 () (tptp.sbrdtbr0 @t1)) % 0.37/0.61 (define @t44 () (not @t20)) % 0.37/0.61 (define @t45 () (tptp.sbrdtbr0 @t5)) % 0.37/0.61 (define @t46 () (not @t19)) % 0.37/0.61 (define @t47 () (tptp.slsdtgt0 @t1)) % 0.37/0.61 (define @t48 () (tptp.slsdtgt0 tptp.xb)) % 0.37/0.61 (define @t49 () (tptp.slsdtgt0 tptp.xa)) % 0.37/0.61 (define @t50 () (tptp.sdtpldt1 @t49 @t48)) % 0.37/0.61 (define @t51 () (tptp.aElementOf0 @t1 @t50)) % 0.37/0.61 (define @t52 () (and @t51 @t44)) % 0.37/0.61 (define @t53 () (exists @t3 @t52)) % 0.37/0.61 (define @t54 () (not (tptp.iLess0 (tptp.sbrdtbr0 @t11) @t45))) % 0.37/0.61 (define @t55 () (not (= @t11 tptp.sz00))) % 0.37/0.61 (define @t56 () (tptp.aElementOf0 @t11 tptp.xI)) % 0.37/0.61 (define @t57 () (and @t56 @t55)) % 0.37/0.61 (define @t58 () (=> @t57 @t54)) % 0.37/0.61 (define @t59 () (forall @t26 @t58)) % 0.37/0.61 (define @t60 () (tptp.aElementOf0 @t5 tptp.xI)) % 0.37/0.61 (define @t61 () (and @t60 @t46 @t59)) % 0.37/0.61 (define @t62 () (exists @t23 @t61)) % 0.37/0.61 (define @t63 () (tptp.aElementOf0 @t1 tptp.xI)) % 0.37/0.61 (define @t64 () (and @t63 @t44)) % 0.37/0.61 (define @t65 () (=> @t64 @t62)) % 0.37/0.61 (define @t66 () (forall @t3 @t65)) % 0.37/0.61 (define @t67 () (not (tptp.iLess0 @t45 @t43))) % 0.37/0.61 (define @t68 () (and @t60 @t46)) % 0.37/0.61 (define @t69 () (=> @t68 @t67)) % 0.37/0.61 (define @t70 () (forall @t23 @t69)) % 0.37/0.61 (define @t71 () (and @t63 @t44 @t70)) % 0.37/0.61 (define @t72 () (exists @t3 @t71)) % 0.37/0.61 (define @t73 () (not @t72)) % 0.37/0.61 (define @t74 () (= tptp.sz00 @t5)) % 0.37/0.61 (define @t75 () (not @t60)) % 0.37/0.61 (define @t76 () (or @t75 @t74 @t67)) % 0.37/0.61 (define @t77 () (forall @t23 @t76)) % 0.37/0.61 (define @t78 () (not @t77)) % 0.37/0.61 (define @t79 () (not @t63)) % 0.37/0.61 (define @t80 () (forall @t3 (or @t79 @t20 @t78))) % 0.37/0.61 (define @t81 () (not @t44)) % 0.37/0.61 (define @t82 () (or @t79 @t81 @t78)) % 0.37/0.61 (define @t83 () (and @t63 @t44 @t77)) % 0.37/0.61 (define @t84 () (forall @t3 (not @t83))) % 0.37/0.61 (define @t85 () (not @t84)) % 0.37/0.61 (define @t86 () (not @t74)) % 0.37/0.61 (define @t87 () (not @t86)) % 0.37/0.61 (define @t88 () (and @t60 @t86)) % 0.37/0.61 (define @t89 () (or @t79 (= tptp.sz00 @t1) @t78)) % 0.37/0.61 (define @t90 () (@var "BOUND_VARIABLE_8671" $$unsorted)) % 0.37/0.61 (define @t91 () (@var "BOUND_VARIABLE_8672" $$unsorted)) % 0.37/0.61 (define @t92 () (@list @t90 @t91)) % 0.37/0.61 (define @t93 () (= tptp.sz00 @t11)) % 0.37/0.61 (define @t94 () (not @t56)) % 0.37/0.61 (define @t95 () (or @t94 @t93 @t54)) % 0.37/0.61 (define @t96 () (forall @t26 @t95)) % 0.37/0.61 (define @t97 () (not @t96)) % 0.37/0.61 (define @t98 () (forall @t23 (or @t75 @t74 @t97))) % 0.37/0.61 (define @t99 () (@list false)) % 0.37/0.61 (define @t100 () (or @t79 @t20)) % 0.37/0.61 (define @t101 () (forall @t3 @t100)) % 0.37/0.61 (define @t102 () (not @t98)) % 0.37/0.61 (define @t103 () (or @t102 @t100)) % 0.37/0.61 (define @t104 () (or @t79 @t20 @t102)) % 0.37/0.61 (define @t105 () (or @t75 @t87 @t97)) % 0.37/0.61 (define @t106 () (and @t60 @t86 @t96)) % 0.37/0.61 (define @t107 () (forall @t23 (not @t106))) % 0.37/0.61 (define @t108 () (not @t107)) % 0.37/0.61 (define @t109 () (not @t93)) % 0.37/0.61 (define @t110 () (and @t56 @t109)) % 0.37/0.61 (define @t111 () (not @t51)) % 0.37/0.61 (define @t112 () (forall @t3 (or @t111 @t20))) % 0.37/0.61 (define @t113 () (@quantifiers_skolemize @t112 0)) % 0.37/0.61 (define @t114 () (not (tptp.aElementOf0 @t113 tptp.xI))) % 0.37/0.61 (define @t115 () (= @t113 tptp.sz00)) % 0.37/0.61 (define @t116 () (or @t114 @t115)) % 0.37/0.61 (define @t117 () (= tptp.sz00 @t113)) % 0.37/0.61 (define @t118 () (or @t114 @t117)) % 0.37/0.61 (define @t119 () (forall @t3 (not @t52))) % 0.37/0.61 (define @t120 () (not @t119)) % 0.37/0.61 (define @t121 () (tptp.aElementOf0 @t113 @t50)) % 0.37/0.61 (define @t122 () (not @t121)) % 0.37/0.61 (define @t123 () (or @t122 @t117)) % 0.37/0.61 (define @t124 () (not @t123)) % 0.37/0.61 (define @t125 () (not @t112)) % 0.37/0.61 (define @t126 () (or @t122 @t115)) % 0.37/0.61 (define @t127 () (not @t126)) % 0.37/0.61 (define @t128 () (@list true)) % 0.37/0.61 (define @t129 () (@list @t123)) % 0.37/0.61 (assume @p1 (forall @t3 (=> @t2 true))) % 0.37/0.61 (assume @p2 (tptp.aElement0 tptp.sz00)) % 0.37/0.61 (assume @p3 (tptp.aElement0 tptp.sz10)) % 0.37/0.61 (assume @p4 (forall @t3 (=> @t2 (tptp.aElement0 @t4)))) % 0.37/0.61 (assume @p5 (forall @t9 (=> @t8 (tptp.aElement0 @t6)))) % 0.37/0.61 (assume @p6 (forall @t9 (=> @t8 (tptp.aElement0 @t10)))) % 0.37/0.61 (assume @p7 (forall @t9 (=> @t8 (= @t6 (tptp.sdtpldt0 @t5 @t1))))) % 0.37/0.61 (assume @p8 (forall @t15 (=> @t14 (= (tptp.sdtpldt0 @t6 @t11) (tptp.sdtpldt0 @t1 @t12))))) % 0.37/0.61 (assume @p9 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 tptp.sz00) @t1) (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1)))))) % 0.37/0.61 (assume @p10 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 @t4) tptp.sz00) (= tptp.sz00 (tptp.sdtpldt0 @t4 @t1)))))) % 0.37/0.61 (assume @p11 (forall @t9 (=> @t8 (= @t10 @t16)))) % 0.37/0.61 (assume @p12 (forall @t15 (=> @t14 (= (tptp.sdtasdt0 @t10 @t11) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t5 @t11)))))) % 0.37/0.61 (assume @p13 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 0.37/0.61 (assume @p14 (forall @t15 (=> @t14 (and (= (tptp.sdtasdt0 @t1 @t12) (tptp.sdtpldt0 @t10 @t17)) (= (tptp.sdtasdt0 @t12 @t1) (tptp.sdtpldt0 @t16 (tptp.sdtasdt0 @t11 @t1))))))) % 0.37/0.61 (assume @p15 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t18 @t1) @t4) (= @t4 (tptp.sdtasdt0 @t1 @t18)))))) % 0.37/0.61 (assume @p16 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 0.37/0.61 (assume @p17 (forall @t9 (=> @t8 (=> (= @t10 tptp.sz00) (or @t20 @t19))))) % 0.37/0.61 (assume @p18 (not (= tptp.sz10 tptp.sz00))) % 0.37/0.61 (assume @p19 (forall @t3 (=> @t21 true))) % 0.37/0.61 (assume @p20 (forall @t3 (=> @t21 (forall @t23 (=> @t22 @t7))))) % 0.37/0.61 (assume @p21 (forall @t9 (=> @t28 (=> (and (forall @t26 (=> @t24 @t25)) (forall @t26 (=> @t25 @t24))) (= @t1 @t5))))) % 0.37/0.61 (assume @p22 (forall @t9 (=> @t28 (forall @t26 (= (= @t11 @t35) (and @t34 (forall @t33 (= @t32 (exists (@list @t31 @t30) (and (tptp.aElementOf0 @t31 @t1) (tptp.aElementOf0 @t30 @t5) (= (tptp.sdtpldt0 @t31 @t30) @t29))))))))))) % 0.37/0.61 (assume @p23 (forall @t9 (=> @t28 (forall @t26 (= (= @t11 @t36) (and @t34 (forall @t33 (= @t32 (and (tptp.aElementOf0 @t29 @t1) (tptp.aElementOf0 @t29 @t5)))))))))) % 0.37/0.61 (assume @p24 (forall @t3 (= @t38 (and @t21 (forall @t23 (=> @t22 (and (forall @t26 (=> @t24 (tptp.aElementOf0 @t12 @t1))) (forall @t26 (=> @t13 (tptp.aElementOf0 @t37 @t1)))))))))) % 0.37/0.61 (assume @p25 (forall @t9 (=> @t39 (tptp.aIdeal0 @t35)))) % 0.37/0.61 (assume @p26 (forall @t9 (=> @t39 (tptp.aIdeal0 @t36)))) % 0.37/0.61 (assume @p27 (forall @t15 (=> (and @t2 @t7 (tptp.aIdeal0 @t11)) (= (tptp.sdteqdtlpzmzozddtrp0 @t1 @t5 @t11) (tptp.aElementOf0 (tptp.sdtpldt0 @t1 (tptp.smndt0 @t5)) @t11))))) % 0.37/0.61 (assume @p28 (forall @t9 (=> @t39 (=> (forall @t26 (=> @t13 (tptp.aElementOf0 @t11 @t35))) (forall @t41 (=> (and @t13 @t40) (exists (@list @t31) (and (tptp.aElement0 @t31) (tptp.sdteqdtlpzmzozddtrp0 @t31 @t11 @t1) (tptp.sdteqdtlpzmzozddtrp0 @t31 @t29 @t5))))))))) % 0.37/0.61 (assume @p29 (forall @t3 (=> @t42 true))) % 0.37/0.61 (assume @p30 (forall @t3 (=> (and @t2 @t44) (tptp.aNaturalNumber0 @t43)))) % 0.37/0.61 (assume @p31 (forall @t9 (=> (and @t42 (tptp.aNaturalNumber0 @t5)) (=> (tptp.iLess0 @t1 @t5) true)))) % 0.37/0.61 (assume @p32 (forall @t9 (=> (and @t2 @t7 @t46) (exists @t41 (and @t13 @t40 (= @t1 (tptp.sdtpldt0 @t37 @t29)) (=> (not (= @t29 tptp.sz00)) (tptp.iLess0 (tptp.sbrdtbr0 @t29) @t45))))))) % 0.37/0.61 (assume @p33 (forall @t9 (=> @t8 (= (tptp.doDivides0 @t1 @t5) (exists @t26 (and @t13 (= @t17 @t5))))))) % 0.37/0.61 (assume @p34 (forall @t3 (=> @t2 (forall @t23 (= (tptp.aDivisorOf0 @t5 @t1) (and @t7 (tptp.doDivides0 @t5 @t1))))))) % 0.37/0.61 (assume @p35 (forall @t9 (=> @t8 (forall @t26 (= (tptp.aGcdOfAnd0 @t11 @t1 @t5) (and (tptp.aDivisorOf0 @t11 @t1) (tptp.aDivisorOf0 @t11 @t5) (forall @t33 (=> (and (tptp.aDivisorOf0 @t29 @t1) (tptp.aDivisorOf0 @t29 @t5)) (tptp.doDivides0 @t29 @t11))))))))) % 0.37/0.61 (assume @p36 (forall @t9 (=> @t8 (= (tptp.misRelativelyPrime0 @t1 @t5) (tptp.aGcdOfAnd0 tptp.sz10 @t1 @t5))))) % 0.37/0.61 (assume @p37 (forall @t3 (=> @t2 (forall @t23 (= (= @t5 @t47) (and @t27 (forall @t26 (= @t25 (exists @t33 (and @t40 (= (tptp.sdtasdt0 @t1 @t29) @t11))))))))))) % 0.37/0.61 (assume @p38 (forall @t3 (=> @t2 (tptp.aIdeal0 @t47)))) % 0.37/0.61 (assume @p39 (and (tptp.aElement0 tptp.xa) (tptp.aElement0 tptp.xb))) % 0.37/0.61 (assume @p40 (or (not (= tptp.xa tptp.sz00)) (not (= tptp.xb tptp.sz00)))) % 0.37/0.61 (assume @p41 (tptp.aGcdOfAnd0 tptp.xc tptp.xa tptp.xb)) % 0.37/0.61 (assume @p42 (and (tptp.aIdeal0 tptp.xI) (= tptp.xI @t50))) % 0.37/0.61 (assume @p43 (and (tptp.aElementOf0 tptp.sz00 @t49) (tptp.aElementOf0 tptp.xa @t49) (tptp.aElementOf0 tptp.sz00 @t48) (tptp.aElementOf0 tptp.xb @t48))) % 0.37/0.61 (assume @p44 @t53) % 0.37/0.61 (assume @p45 @t66) % 0.37/0.61 (assume @p46 @t73) % 0.37/0.61 (assume @p47 true) % 0.37/0.61 (step @p48 :rule evaluate :args ((= true false))) % 0.37/0.61 (step @p49 :rule bool-double-not-elim :args (@t80)) % 0.37/0.61 (step @p50 :rule refl :args (@t78)) % 0.37/0.61 (step @p51 :rule bool-double-not-elim :args (@t20)) % 0.37/0.61 (step @p52 :rule refl :args (@t79)) % 0.37/0.61 (step @p53 :rule nary_cong :premises (@p52 @p51 @p50) :args (@t82)) % 0.37/0.61 (step @p54 :rule aci_norm :args ((= (or @t79 (or @t81 @t78)) @t82))) % 0.37/0.61 (step @p55 :rule trans :premises (@p54 @p53)) % 0.37/0.61 (step @p56 :rule bool-and-de-morgan :args (@t44 @t77 true)) % 0.37/0.61 (step @p57 :rule nary_cong :premises (@p52 @p56) :args ((or @t79 (not (and @t44 @t77))))) % 0.37/0.61 (step @p58 :rule bool-and-de-morgan :args (@t63 @t44 (and @t77))) % 0.37/0.61 (step @p59 :rule trans :premises (@p58 @p57)) % 0.37/0.61 (step @p60 :rule trans :premises (@p59 @p55)) % 0.37/0.61 (step @p61 :rule cong :premises (@p60) :args (@t84)) % 0.37/0.61 (step @p62 :rule cong :premises (@p61) :args (@t85)) % 0.37/0.61 (step @p63 :rule exists-elim :args ((= (exists @t3 @t83) @t85))) % 0.37/0.61 (step @p64 :rule trans :premises (@p63 @p62)) % 0.37/0.61 (step @p65 :rule aci_norm :args ((= (or (or @t75 @t74) @t67) @t76))) % 0.37/0.61 (step @p66 :rule refl :args (@t67)) % 0.37/0.61 (step @p67 :rule bool-double-not-elim :args (@t74)) % 0.37/0.61 (step @p68 :rule refl :args (@t75)) % 0.37/0.61 (step @p69 :rule nary_cong :premises (@p68 @p67) :args ((or @t75 @t87))) % 0.37/0.61 (step @p70 :rule bool-and-de-morgan :args (@t60 @t86 true)) % 0.37/0.61 (step @p71 :rule trans :premises (@p70 @p69)) % 0.37/0.61 (step @p72 :rule nary_cong :premises (@p71 @p66) :args ((or (not @t88) @t67))) % 0.37/0.61 (step @p73 :rule trans :premises (@p72 @p65)) % 0.37/0.61 (step @p74 :rule bool-impl-elim :args (@t88 @t67)) % 0.37/0.61 (step @p75 :rule trans :premises (@p74 @p73)) % 0.37/0.61 (step @p76 :rule cong :premises (@p75) :args ((forall @t23 (=> @t88 @t67)))) % 0.37/0.61 (step @p77 :rule refl :args (@t67)) % 0.37/0.61 (step @p78 :rule eq-symm :args (@t5 tptp.sz00)) % 0.37/0.61 (step @p79 :rule cong :premises (@p78) :args (@t46)) % 0.37/0.61 (step @p80 :rule refl :args (@t60)) % 0.37/0.61 (step @p81 :rule nary_cong :premises (@p80 @p79) :args (@t68)) % 0.37/0.61 (step @p82 :rule cong :premises (@p81 @p77) :args (@t69)) % 0.37/0.61 (step @p83 :rule cong :premises (@p82) :args (@t70)) % 0.37/0.61 (step @p84 :rule trans :premises (@p83 @p76)) % 0.37/0.61 (step @p85 :rule refl :args (@t44)) % 0.37/0.61 (step @p86 :rule refl :args (@t63)) % 0.37/0.61 (step @p87 :rule nary_cong :premises (@p86 @p85 @p84) :args (@t71)) % 0.37/0.61 (step @p88 :rule cong :premises (@p87) :args (@t72)) % 0.37/0.61 (step @p89 :rule trans :premises (@p88 @p64)) % 0.37/0.61 (step @p90 :rule cong :premises (@p89) :args (@t73)) % 0.37/0.61 (step @p91 :rule trans :premises (@p90 @p49)) % 0.37/0.61 (step @p92 :rule eq_resolve :premises (@p46 @p91)) % 0.37/0.61 (step @p93 :rule refl :args (@t78)) % 0.37/0.61 (step @p94 :rule eq-symm :args (tptp.sz00 @t1)) % 0.37/0.61 (step @p95 :rule refl :args (@t79)) % 0.37/0.61 (step @p96 :rule nary_cong :premises (@p95 @p94 @p93) :args (@t89)) % 0.37/0.61 (step @p97 :rule cong :premises (@p96) :args ((forall @t3 @t89))) % 0.37/0.61 (step @p98 :rule alpha_equiv :args ((forall (@list @t90) (or (not (tptp.aElementOf0 @t90 tptp.xI)) (= tptp.sz00 @t90) (not (forall (@list @t91) (or (not (tptp.aElementOf0 @t91 tptp.xI)) (= tptp.sz00 @t91) (not (tptp.iLess0 (tptp.sbrdtbr0 @t91) (tptp.sbrdtbr0 @t90)))))))) @t92 (@list @t1 @t5))) % 0.37/0.61 (step @p99 :rule alpha_equiv :args (@t98 (@list @t5 @t11) @t92)) % 0.37/0.61 (step @p100 :rule trans :premises (@p99 @p98 @p97)) % 0.37/0.61 (step @p101 :rule equiv_elim2 :premises (@p100)) % 0.37/0.61 (step @p102 :rule chain_m_resolution :premises (@p101 @p92) :args (@t98 @t99 (@list @t80))) % 0.37/0.61 (step @p103 :rule quant-miniscope-or :args ((= (forall @t3 @t103) (or @t102 @t101)))) % 0.37/0.61 (step @p104 :rule aci_norm :args ((= @t104 @t103))) % 0.37/0.61 (step @p105 :rule cong :premises (@p104) :args ((forall @t3 @t104))) % 0.37/0.61 (step @p106 :rule trans :premises (@p105 @p103)) % 0.37/0.61 (step @p107 :rule aci_norm :args ((= (or @t100 @t102) @t104))) % 0.37/0.61 (step @p108 :rule refl :args (@t102)) % 0.37/0.61 (step @p109 :rule nary_cong :premises (@p52 @p51) :args ((or @t79 @t81))) % 0.37/0.61 (step @p110 :rule bool-and-de-morgan :args (@t63 @t44 true)) % 0.37/0.61 (step @p111 :rule trans :premises (@p110 @p109)) % 0.37/0.61 (step @p112 :rule nary_cong :premises (@p111 @p108) :args ((or (not @t64) @t102))) % 0.37/0.61 (step @p113 :rule trans :premises (@p112 @p107)) % 0.37/0.61 (step @p114 :rule bool-impl-elim :args (@t64 @t102)) % 0.37/0.61 (step @p115 :rule trans :premises (@p114 @p113)) % 0.37/0.61 (step @p116 :rule cong :premises (@p115) :args ((forall @t3 (=> @t64 @t102)))) % 0.37/0.61 (step @p117 :rule trans :premises (@p116 @p106)) % 0.37/0.61 (step @p118 :rule refl :args (@t97)) % 0.37/0.61 (step @p119 :rule nary_cong :premises (@p68 @p67 @p118) :args (@t105)) % 0.37/0.61 (step @p120 :rule aci_norm :args ((= (or @t75 (or @t87 @t97)) @t105))) % 0.37/0.61 (step @p121 :rule trans :premises (@p120 @p119)) % 0.37/0.61 (step @p122 :rule bool-and-de-morgan :args (@t86 @t96 true)) % 0.37/0.61 (step @p123 :rule nary_cong :premises (@p68 @p122) :args ((or @t75 (not (and @t86 @t96))))) % 0.37/0.61 (step @p124 :rule bool-and-de-morgan :args (@t60 @t86 (and @t96))) % 0.37/0.61 (step @p125 :rule trans :premises (@p124 @p123)) % 0.37/0.61 (step @p126 :rule trans :premises (@p125 @p121)) % 0.37/0.61 (step @p127 :rule cong :premises (@p126) :args (@t107)) % 0.37/0.61 (step @p128 :rule cong :premises (@p127) :args (@t108)) % 0.37/0.61 (step @p129 :rule exists-elim :args ((= (exists @t23 @t106) @t108))) % 0.37/0.61 (step @p130 :rule trans :premises (@p129 @p128)) % 0.37/0.61 (step @p131 :rule aci_norm :args ((= (or (or @t94 @t93) @t54) @t95))) % 0.37/0.61 (step @p132 :rule refl :args (@t54)) % 0.37/0.61 (step @p133 :rule bool-double-not-elim :args (@t93)) % 0.37/0.61 (step @p134 :rule refl :args (@t94)) % 0.37/0.61 (step @p135 :rule nary_cong :premises (@p134 @p133) :args ((or @t94 (not @t109)))) % 0.37/0.61 (step @p136 :rule bool-and-de-morgan :args (@t56 @t109 true)) % 0.37/0.61 (step @p137 :rule trans :premises (@p136 @p135)) % 0.37/0.61 (step @p138 :rule nary_cong :premises (@p137 @p132) :args ((or (not @t110) @t54))) % 0.37/0.61 (step @p139 :rule trans :premises (@p138 @p131)) % 0.37/0.61 (step @p140 :rule bool-impl-elim :args (@t110 @t54)) % 0.37/0.61 (step @p141 :rule trans :premises (@p140 @p139)) % 0.37/0.61 (step @p142 :rule cong :premises (@p141) :args ((forall @t26 (=> @t110 @t54)))) % 0.37/0.61 (step @p143 :rule refl :args (@t54)) % 0.37/0.61 (step @p144 :rule eq-symm :args (@t11 tptp.sz00)) % 0.37/0.61 (step @p145 :rule cong :premises (@p144) :args (@t55)) % 0.37/0.61 (step @p146 :rule refl :args (@t56)) % 0.37/0.61 (step @p147 :rule nary_cong :premises (@p146 @p145) :args (@t57)) % 0.37/0.61 (step @p148 :rule cong :premises (@p147 @p143) :args (@t58)) % 0.37/0.61 (step @p149 :rule cong :premises (@p148) :args (@t59)) % 0.37/0.61 (step @p150 :rule trans :premises (@p149 @p142)) % 0.37/0.61 (step @p151 :rule nary_cong :premises (@p80 @p79 @p150) :args (@t61)) % 0.37/0.61 (step @p152 :rule cong :premises (@p151) :args (@t62)) % 0.37/0.61 (step @p153 :rule trans :premises (@p152 @p130)) % 0.37/0.61 (step @p154 :rule refl :args (@t64)) % 0.37/0.61 (step @p155 :rule cong :premises (@p154 @p153) :args (@t65)) % 0.37/0.61 (step @p156 :rule cong :premises (@p155) :args (@t66)) % 0.37/0.61 (step @p157 :rule trans :premises (@p156 @p117)) % 0.37/0.61 (step @p158 :rule eq_resolve :premises (@p45 @p157)) % 0.37/0.61 (step @p159 :rule chain_m_resolution :premises (@p158 @p102) :args (@t101 @t99 (@list @t98))) % 0.37/0.61 (step @p160 :rule eq-symm :args (@t113 tptp.sz00)) % 0.37/0.61 (step @p161 :rule refl :args (@t114)) % 0.37/0.61 (step @p162 :rule nary_cong :premises (@p161 @p160) :args (@t116)) % 0.37/0.61 (step @p163 :rule refl :args (@t101)) % 0.37/0.61 (step @p164 :rule cong :premises (@p163 @p162) :args ((=> @t101 @t116))) % 0.37/0.61 (assume-push @p218 @t101) % 0.37/0.61 (step @p166 :rule instantiate :premises (@p159) :args ((@list @t113))) % 0.37/0.61 (step-pop @p219 :rule scope :premises (@p166)) % 0.37/0.61 (step @p167 :rule process_scope :premises (@p219) :args (@t116)) % 0.37/0.61 (step @p169 :rule eq_resolve :premises (@p167 @p164)) % 0.37/0.61 (step @p170 :rule implies_elim :premises (@p169)) % 0.37/0.61 (step @p171 :rule chain_m_resolution :premises (@p170 @p159) :args (@t118 @t99 (@list @t101))) % 0.37/0.61 (step @p172 :rule refl :args (@t111)) % 0.37/0.61 (step @p173 :rule nary_cong :premises (@p172 @p51) :args ((or @t111 @t81))) % 0.37/0.61 (step @p174 :rule bool-and-de-morgan :args (@t51 @t44 true)) % 0.37/0.61 (step @p175 :rule trans :premises (@p174 @p173)) % 0.37/0.61 (step @p176 :rule cong :premises (@p175) :args (@t119)) % 0.37/0.61 (step @p177 :rule cong :premises (@p176) :args (@t120)) % 0.37/0.61 (step @p178 :rule exists-elim :args ((= @t53 @t120))) % 0.37/0.61 (step @p179 :rule trans :premises (@p178 @p177)) % 0.37/0.61 (step @p180 :rule eq_resolve :premises (@p44 @p179)) % 0.37/0.61 (step @p181 :rule refl :args (@t124)) % 0.37/0.61 (step @p182 :rule bool-double-not-elim :args (@t112)) % 0.37/0.61 (step @p183 :rule nary_cong :premises (@p182 @p181) :args ((or (not @t125) @t124))) % 0.37/0.61 (step @p184 :rule refl :args (@t122)) % 0.37/0.61 (step @p185 :rule nary_cong :premises (@p184 @p160) :args (@t126)) % 0.37/0.61 (step @p186 :rule cong :premises (@p185) :args (@t127)) % 0.37/0.61 (step @p187 :rule refl :args (@t125)) % 0.37/0.61 (step @p188 :rule cong :premises (@p187 @p186) :args ((=> @t125 @t127))) % 0.37/0.61 (assume-push @p220 @t125) % 0.37/0.61 (step @p190 :rule skolemize :premises (@p180)) % 0.37/0.61 (step-pop @p221 :rule scope :premises (@p190)) % 0.37/0.61 (step @p191 :rule process_scope :premises (@p221) :args (@t127)) % 0.37/0.61 (step @p193 :rule eq_resolve :premises (@p191 @p188)) % 0.37/0.61 (step @p194 :rule implies_elim :premises (@p193)) % 0.37/0.61 (step @p195 :rule eq_resolve :premises (@p194 @p183)) % 0.37/0.61 (step @p196 :rule chain_m_resolution :premises (@p195 @p180) :args (@t124 @t128 (@list @t112))) % 0.37/0.62 (step @p197 :rule cnf_or_neg :args (@t123 1)) % 0.37/0.62 (step @p198 :rule chain_m_resolution :premises (@p197 @p196) :args ((not @t117) @t128 @t129)) % 0.37/0.62 (step @p199 :rule cnf_or_pos :args (@t118)) % 0.37/0.62 (step @p200 :rule reordering :premises (@p199) :args ((or @t117 @t114 (not @t118)))) % 0.37/0.62 (step @p201 :rule chain_m_resolution :premises (@p200 @p198 @p171) :args (@t114 (@list true false) (@list @t117 @t118))) % 0.37/0.62 (step @p202 :rule false_intro :premises (@p201)) % 0.37/0.62 (step @p203 :rule and_elim :premises (@p42) :args (1)) % 0.37/0.62 (step @p204 :rule symm :premises (@p203)) % 0.37/0.62 (step @p205 :rule refl :args (@t113)) % 0.37/0.62 (step @p206 :rule cong :premises (@p205 @p204) :args (@t121)) % 0.37/0.62 (step @p207 :rule bool-double-not-elim :args (@t121)) % 0.37/0.62 (step @p208 :rule refl :args (@t123)) % 0.37/0.62 (step @p209 :rule nary_cong :premises (@p208 @p207) :args ((or @t123 (not @t122)))) % 0.37/0.62 (step @p210 :rule cnf_or_neg :args (@t123 0)) % 0.37/0.62 (step @p211 :rule eq_resolve :premises (@p210 @p209)) % 0.37/0.62 (step @p212 :rule reordering :premises (@p211) :args ((or @t121 @t123))) % 0.37/0.62 (step @p213 :rule chain_m_resolution :premises (@p212 @p196) :args (@t121 @t128 @t129)) % 0.37/0.62 (step @p214 :rule true_intro :premises (@p213)) % 0.37/0.62 (step @p215 :rule symm :premises (@p214)) % 0.37/0.62 (step @p216 :rule trans :premises (@p215 @p206 @p202)) % 0.37/0.62 (step @p217 false :rule eq_resolve :premises (@p216 @p48)) % 0.37/0.62 ) % 0.37/0.62 % SZS output end Proof % 0.37/0.62 % cvc5 exiting %------------------------------------------------------------------------------