%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : RNG125+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 08:45:45 AM UTC 2026 % Result : Theorem 0.40s 0.63s % Output : Proof 0.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : RNG125+1 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.18/0.35 % Computer : n020.cluster.edu % 0.18/0.35 % Model : x86_64 x86_64 % 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.35 % Memory : 8042.1875MB % 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.35 % CPULimit : 300 % 0.18/0.35 % WCLimit : 300 % 0.18/0.35 % DateTime : Tue Jun 2 14:09:10 EDT 2026 % 0.18/0.35 % CPUTime : % 0.32/0.52 %----Proving TF0_NAR, FOF, or CNF % 0.40/0.63 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.40/0.63 % SZS status Theorem % 0.40/0.63 % SZS output start Proof % 0.40/0.63 ( % 0.40/0.63 (declare-sort $$unsorted 0) % 0.40/0.63 (declare-const tptp.xu $$unsorted) % 0.40/0.63 (declare-const tptp.xc $$unsorted) % 0.40/0.63 (declare-const tptp.xa $$unsorted) % 0.40/0.63 (declare-const tptp.xI $$unsorted) % 0.40/0.63 (declare-const tptp.slsdtgt0 (-> $$unsorted $$unsorted)) % 0.40/0.63 (declare-const tptp.aDivisorOf0 (-> $$unsorted $$unsorted Bool)) % 0.40/0.63 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 0.40/0.63 (declare-const tptp.sbrdtbr0 (-> $$unsorted $$unsorted)) % 0.40/0.63 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 0.40/0.63 (declare-const tptp.sz00 $$unsorted) % 0.40/0.63 (declare-const tptp.sz10 $$unsorted) % 0.40/0.63 (declare-const tptp.aGcdOfAnd0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.40/0.63 (declare-const tptp.smndt0 (-> $$unsorted $$unsorted)) % 0.40/0.63 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.40/0.63 (declare-const tptp.sdtasasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.40/0.63 (declare-const tptp.aIdeal0 (-> $$unsorted Bool)) % 0.40/0.63 (declare-const tptp.misRelativelyPrime0 (-> $$unsorted $$unsorted Bool)) % 0.40/0.63 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.40/0.63 (declare-const tptp.doDivides0 (-> $$unsorted $$unsorted Bool)) % 0.40/0.63 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 0.40/0.63 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 0.40/0.63 (declare-const tptp.sdteqdtlpzmzozddtrp0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.40/0.63 (declare-const tptp.xb $$unsorted) % 0.40/0.63 (declare-const tptp.sdtpldt1 (-> $$unsorted $$unsorted $$unsorted)) % 0.40/0.63 (declare-const tptp.aNaturalNumber0 (-> $$unsorted Bool)) % 0.40/0.63 (define @t1 () (@var "W0" $$unsorted)) % 0.40/0.63 (define @t2 () (tptp.aElement0 @t1)) % 0.40/0.63 (define @t3 () (@list @t1)) % 0.40/0.63 (define @t4 () (tptp.smndt0 @t1)) % 0.40/0.63 (define @t5 () (@var "W1" $$unsorted)) % 0.40/0.63 (define @t6 () (tptp.sdtpldt0 @t1 @t5)) % 0.40/0.63 (define @t7 () (tptp.aElement0 @t5)) % 0.40/0.63 (define @t8 () (and @t2 @t7)) % 0.40/0.63 (define @t9 () (@list @t1 @t5)) % 0.40/0.63 (define @t10 () (tptp.sdtasdt0 @t1 @t5)) % 0.40/0.63 (define @t11 () (@var "W2" $$unsorted)) % 0.40/0.63 (define @t12 () (tptp.sdtpldt0 @t5 @t11)) % 0.40/0.63 (define @t13 () (tptp.aElement0 @t11)) % 0.40/0.63 (define @t14 () (and @t2 @t7 @t13)) % 0.40/0.63 (define @t15 () (@list @t1 @t5 @t11)) % 0.40/0.63 (define @t16 () (tptp.sdtasdt0 @t5 @t1)) % 0.40/0.63 (define @t17 () (tptp.sdtasdt0 @t1 @t11)) % 0.40/0.63 (define @t18 () (tptp.smndt0 tptp.sz10)) % 0.40/0.63 (define @t19 () (= @t5 tptp.sz00)) % 0.40/0.63 (define @t20 () (= @t1 tptp.sz00)) % 0.40/0.63 (define @t21 () (tptp.aSet0 @t1)) % 0.40/0.63 (define @t22 () (tptp.aElementOf0 @t5 @t1)) % 0.40/0.63 (define @t23 () (@list @t5)) % 0.40/0.63 (define @t24 () (forall @t23 (=> @t22 @t7))) % 0.40/0.63 (define @t25 () (=> @t21 @t24)) % 0.40/0.63 (define @t26 () (forall @t3 @t25)) % 0.40/0.63 (define @t27 () (tptp.aElementOf0 @t11 @t1)) % 0.40/0.63 (define @t28 () (tptp.aElementOf0 @t11 @t5)) % 0.40/0.63 (define @t29 () (@list @t11)) % 0.40/0.63 (define @t30 () (tptp.aSet0 @t5)) % 0.40/0.63 (define @t31 () (and @t21 @t30)) % 0.40/0.63 (define @t32 () (@var "W3" $$unsorted)) % 0.40/0.63 (define @t33 () (@var "W5" $$unsorted)) % 0.40/0.63 (define @t34 () (@var "W4" $$unsorted)) % 0.40/0.63 (define @t35 () (tptp.aElementOf0 @t32 @t11)) % 0.40/0.63 (define @t36 () (@list @t32)) % 0.40/0.63 (define @t37 () (tptp.aSet0 @t11)) % 0.40/0.63 (define @t38 () (tptp.sdtpldt1 @t1 @t5)) % 0.40/0.63 (define @t39 () (tptp.sdtasasdt0 @t1 @t5)) % 0.40/0.63 (define @t40 () (tptp.sdtasdt0 @t11 @t5)) % 0.40/0.63 (define @t41 () (tptp.aElementOf0 @t40 @t1)) % 0.40/0.63 (define @t42 () (forall @t29 (=> @t13 @t41))) % 0.40/0.63 (define @t43 () (tptp.aElementOf0 @t12 @t1)) % 0.40/0.63 (define @t44 () (forall @t29 (=> @t27 @t43))) % 0.40/0.63 (define @t45 () (and @t44 @t42)) % 0.40/0.63 (define @t46 () (=> @t22 @t45)) % 0.40/0.63 (define @t47 () (forall @t23 @t46)) % 0.40/0.63 (define @t48 () (and @t21 @t47)) % 0.40/0.63 (define @t49 () (tptp.aIdeal0 @t1)) % 0.40/0.63 (define @t50 () (= @t49 @t48)) % 0.40/0.63 (define @t51 () (forall @t3 @t50)) % 0.40/0.63 (define @t52 () (and @t49 (tptp.aIdeal0 @t5))) % 0.40/0.63 (define @t53 () (tptp.aElement0 @t32)) % 0.40/0.63 (define @t54 () (@list @t11 @t32)) % 0.40/0.63 (define @t55 () (tptp.aNaturalNumber0 @t1)) % 0.40/0.63 (define @t56 () (tptp.sbrdtbr0 @t1)) % 0.40/0.63 (define @t57 () (not @t20)) % 0.40/0.63 (define @t58 () (forall @t23 (= (tptp.aDivisorOf0 @t5 @t1) (and @t7 (tptp.doDivides0 @t5 @t1))))) % 0.40/0.63 (define @t59 () (forall @t3 (=> @t2 @t58))) % 0.40/0.63 (define @t60 () (tptp.slsdtgt0 @t1)) % 0.40/0.63 (define @t61 () (tptp.aElement0 tptp.xb)) % 0.40/0.63 (define @t62 () (tptp.aElement0 tptp.xa)) % 0.40/0.63 (define @t63 () (tptp.slsdtgt0 tptp.xb)) % 0.40/0.63 (define @t64 () (tptp.slsdtgt0 tptp.xa)) % 0.40/0.63 (define @t65 () (tptp.sdtpldt1 @t64 @t63)) % 0.40/0.63 (define @t66 () (tptp.aIdeal0 tptp.xI)) % 0.40/0.63 (define @t67 () (tptp.aElementOf0 tptp.xu tptp.xI)) % 0.40/0.63 (define @t68 () (tptp.aDivisorOf0 tptp.xu tptp.xb)) % 0.40/0.63 (define @t69 () (tptp.aDivisorOf0 tptp.xu tptp.xa)) % 0.40/0.63 (define @t70 () (tptp.doDivides0 tptp.xu tptp.xa)) % 0.40/0.63 (define @t71 () (not @t70)) % 0.40/0.63 (define @t72 () (tptp.doDivides0 tptp.xu tptp.xb)) % 0.40/0.63 (define @t73 () (not @t72)) % 0.40/0.63 (define @t74 () (@var "BOUND_VARIABLE_8109" $$unsorted)) % 0.40/0.63 (define @t75 () (= (tptp.aDivisorOf0 @t74 @t1) (and (tptp.aElement0 @t74) (tptp.doDivides0 @t74 @t1)))) % 0.40/0.63 (define @t76 () (not @t2)) % 0.40/0.63 (define @t77 () (or @t76 @t75)) % 0.40/0.63 (define @t78 () (@list @t74)) % 0.40/0.63 (define @t79 () (forall @t78 @t77)) % 0.40/0.63 (define @t80 () (forall @t78 @t75)) % 0.40/0.63 (define @t81 () (@list @t5)) % 0.40/0.63 (define @t82 () (or @t76 @t80)) % 0.40/0.63 (define @t83 () (tptp.aElement0 tptp.xu)) % 0.40/0.63 (define @t84 () (and @t83 @t70)) % 0.40/0.63 (define @t85 () (= @t69 @t84)) % 0.40/0.63 (define @t86 () (not @t62)) % 0.40/0.63 (define @t87 () (or @t86 @t85)) % 0.40/0.63 (define @t88 () (@list false false)) % 0.40/0.63 (define @t89 () (@var "BOUND_VARIABLE_7868" $$unsorted)) % 0.40/0.63 (define @t90 () (tptp.aElement0 @t89)) % 0.40/0.63 (define @t91 () (not (tptp.aElementOf0 @t89 @t1))) % 0.40/0.63 (define @t92 () (not @t21)) % 0.40/0.63 (define @t93 () (or @t91 @t90)) % 0.40/0.63 (define @t94 () (or @t92 @t93)) % 0.40/0.63 (define @t95 () (forall (@list @t1 @t89) @t94)) % 0.40/0.63 (define @t96 () (@list @t89)) % 0.40/0.63 (define @t97 () (forall @t96 @t94)) % 0.40/0.63 (define @t98 () (forall @t96 @t93)) % 0.40/0.63 (define @t99 () (or @t92 @t98)) % 0.40/0.63 (define @t100 () (not @t22)) % 0.40/0.63 (define @t101 () (forall @t23 (or @t100 @t7))) % 0.40/0.63 (define @t102 () (@var "BOUND_VARIABLE_7980" $$unsorted)) % 0.40/0.63 (define @t103 () (tptp.sdtasdt0 @t102 @t5)) % 0.40/0.63 (define @t104 () (not (tptp.aElement0 @t102))) % 0.40/0.63 (define @t105 () (or @t104 (tptp.aElementOf0 @t103 @t1))) % 0.40/0.63 (define @t106 () (@var "BOUND_VARIABLE_7973" $$unsorted)) % 0.40/0.63 (define @t107 () (tptp.sdtpldt0 @t5 @t106)) % 0.40/0.63 (define @t108 () (or (not (tptp.aElementOf0 @t106 @t1)) (tptp.aElementOf0 @t107 @t1))) % 0.40/0.63 (define @t109 () (and @t108 @t105)) % 0.40/0.63 (define @t110 () (or @t100 @t109)) % 0.40/0.63 (define @t111 () (@list @t5 @t106 @t102)) % 0.40/0.63 (define @t112 () (@list @t106 @t102)) % 0.40/0.63 (define @t113 () (forall @t112 @t110)) % 0.40/0.63 (define @t114 () (forall (@list @t102) @t105)) % 0.40/0.63 (define @t115 () (@list @t11)) % 0.40/0.63 (define @t116 () (forall @t112 @t105)) % 0.40/0.63 (define @t117 () (forall (@list @t106) @t108)) % 0.40/0.63 (define @t118 () (forall @t112 @t108)) % 0.40/0.63 (define @t119 () (and @t118 @t116)) % 0.40/0.63 (define @t120 () (forall @t112 @t109)) % 0.40/0.63 (define @t121 () (or @t100 @t120)) % 0.40/0.63 (define @t122 () (and (forall @t29 (or (not @t27) @t43)) (forall @t29 (or (not @t13) @t41)))) % 0.40/0.63 (define @t123 () (tptp.aSet0 tptp.xI)) % 0.40/0.63 (define @t124 () (and @t123 (forall @t111 (or (not (tptp.aElementOf0 @t5 tptp.xI)) (and (or (not (tptp.aElementOf0 @t106 tptp.xI)) (tptp.aElementOf0 @t107 tptp.xI)) (or @t104 (tptp.aElementOf0 @t103 tptp.xI))))))) % 0.40/0.63 (define @t125 () (= @t66 @t124)) % 0.40/0.63 (define @t126 () (not @t67)) % 0.40/0.63 (define @t127 () (not @t123)) % 0.40/0.63 (define @t128 () (or @t127 @t126 @t83)) % 0.40/0.63 (define @t129 () (not @t83)) % 0.40/0.63 (define @t130 () (and @t83 @t72)) % 0.40/0.63 (define @t131 () (= @t68 @t130)) % 0.40/0.63 (define @t132 () (not @t61)) % 0.40/0.63 (define @t133 () (or @t132 @t131)) % 0.40/0.63 (assume @p1 (forall @t3 (=> @t2 true))) % 0.40/0.63 (assume @p2 (tptp.aElement0 tptp.sz00)) % 0.40/0.63 (assume @p3 (tptp.aElement0 tptp.sz10)) % 0.40/0.63 (assume @p4 (forall @t3 (=> @t2 (tptp.aElement0 @t4)))) % 0.40/0.63 (assume @p5 (forall @t9 (=> @t8 (tptp.aElement0 @t6)))) % 0.40/0.63 (assume @p6 (forall @t9 (=> @t8 (tptp.aElement0 @t10)))) % 0.40/0.63 (assume @p7 (forall @t9 (=> @t8 (= @t6 (tptp.sdtpldt0 @t5 @t1))))) % 0.40/0.63 (assume @p8 (forall @t15 (=> @t14 (= (tptp.sdtpldt0 @t6 @t11) (tptp.sdtpldt0 @t1 @t12))))) % 0.40/0.63 (assume @p9 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 tptp.sz00) @t1) (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1)))))) % 0.40/0.63 (assume @p10 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 @t4) tptp.sz00) (= tptp.sz00 (tptp.sdtpldt0 @t4 @t1)))))) % 0.40/0.63 (assume @p11 (forall @t9 (=> @t8 (= @t10 @t16)))) % 0.40/0.63 (assume @p12 (forall @t15 (=> @t14 (= (tptp.sdtasdt0 @t10 @t11) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t5 @t11)))))) % 0.40/0.63 (assume @p13 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 0.40/0.63 (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))))))) % 0.40/0.63 (assume @p15 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t18 @t1) @t4) (= @t4 (tptp.sdtasdt0 @t1 @t18)))))) % 0.40/0.63 (assume @p16 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 0.40/0.63 (assume @p17 (forall @t9 (=> @t8 (=> (= @t10 tptp.sz00) (or @t20 @t19))))) % 0.40/0.63 (assume @p18 (not (= tptp.sz10 tptp.sz00))) % 0.40/0.63 (assume @p19 (forall @t3 (=> @t21 true))) % 0.40/0.63 (assume @p20 @t26) % 0.40/0.63 (assume @p21 (forall @t9 (=> @t31 (=> (and (forall @t29 (=> @t27 @t28)) (forall @t29 (=> @t28 @t27))) (= @t1 @t5))))) % 0.40/0.63 (assume @p22 (forall @t9 (=> @t31 (forall @t29 (= (= @t11 @t38) (and @t37 (forall @t36 (= @t35 (exists (@list @t34 @t33) (and (tptp.aElementOf0 @t34 @t1) (tptp.aElementOf0 @t33 @t5) (= (tptp.sdtpldt0 @t34 @t33) @t32))))))))))) % 0.40/0.63 (assume @p23 (forall @t9 (=> @t31 (forall @t29 (= (= @t11 @t39) (and @t37 (forall @t36 (= @t35 (and (tptp.aElementOf0 @t32 @t1) (tptp.aElementOf0 @t32 @t5)))))))))) % 0.40/0.63 (assume @p24 @t51) % 0.40/0.63 (assume @p25 (forall @t9 (=> @t52 (tptp.aIdeal0 @t38)))) % 0.40/0.63 (assume @p26 (forall @t9 (=> @t52 (tptp.aIdeal0 @t39)))) % 0.40/0.63 (assume @p27 (forall @t15 (=> (and @t2 @t7 (tptp.aIdeal0 @t11)) (= (tptp.sdteqdtlpzmzozddtrp0 @t1 @t5 @t11) (tptp.aElementOf0 (tptp.sdtpldt0 @t1 (tptp.smndt0 @t5)) @t11))))) % 0.40/0.63 (assume @p28 (forall @t9 (=> @t52 (=> (forall @t29 (=> @t13 (tptp.aElementOf0 @t11 @t38))) (forall @t54 (=> (and @t13 @t53) (exists (@list @t34) (and (tptp.aElement0 @t34) (tptp.sdteqdtlpzmzozddtrp0 @t34 @t11 @t1) (tptp.sdteqdtlpzmzozddtrp0 @t34 @t32 @t5))))))))) % 0.40/0.63 (assume @p29 (forall @t3 (=> @t55 true))) % 0.40/0.63 (assume @p30 (forall @t3 (=> (and @t2 @t57) (tptp.aNaturalNumber0 @t56)))) % 0.40/0.63 (assume @p31 (forall @t9 (=> (and @t55 (tptp.aNaturalNumber0 @t5)) (=> (tptp.iLess0 @t1 @t5) true)))) % 0.40/0.63 (assume @p32 (forall @t9 (=> (and @t2 @t7 (not @t19)) (exists @t54 (and @t13 @t53 (= @t1 (tptp.sdtpldt0 @t40 @t32)) (=> (not (= @t32 tptp.sz00)) (tptp.iLess0 (tptp.sbrdtbr0 @t32) (tptp.sbrdtbr0 @t5)))))))) % 0.40/0.63 (assume @p33 (forall @t9 (=> @t8 (= (tptp.doDivides0 @t1 @t5) (exists @t29 (and @t13 (= @t17 @t5))))))) % 0.40/0.63 (assume @p34 @t59) % 0.40/0.63 (assume @p35 (forall @t9 (=> @t8 (forall @t29 (= (tptp.aGcdOfAnd0 @t11 @t1 @t5) (and (tptp.aDivisorOf0 @t11 @t1) (tptp.aDivisorOf0 @t11 @t5) (forall @t36 (=> (and (tptp.aDivisorOf0 @t32 @t1) (tptp.aDivisorOf0 @t32 @t5)) (tptp.doDivides0 @t32 @t11))))))))) % 0.40/0.63 (assume @p36 (forall @t9 (=> @t8 (= (tptp.misRelativelyPrime0 @t1 @t5) (tptp.aGcdOfAnd0 tptp.sz10 @t1 @t5))))) % 0.40/0.63 (assume @p37 (forall @t3 (=> @t2 (forall @t23 (= (= @t5 @t60) (and @t30 (forall @t29 (= @t28 (exists @t36 (and @t53 (= (tptp.sdtasdt0 @t1 @t32) @t11))))))))))) % 0.40/0.63 (assume @p38 (forall @t3 (=> @t2 (tptp.aIdeal0 @t60)))) % 0.40/0.63 (assume @p39 (and @t62 @t61)) % 0.40/0.63 (assume @p40 (or (not (= tptp.xa tptp.sz00)) (not (= tptp.xb tptp.sz00)))) % 0.40/0.63 (assume @p41 (tptp.aGcdOfAnd0 tptp.xc tptp.xa tptp.xb)) % 0.40/0.63 (assume @p42 (and @t66 (= tptp.xI @t65))) % 0.40/0.63 (assume @p43 (and (tptp.aElementOf0 tptp.sz00 @t64) (tptp.aElementOf0 tptp.xa @t64) (tptp.aElementOf0 tptp.sz00 @t63) (tptp.aElementOf0 tptp.xb @t63))) % 0.40/0.63 (assume @p44 (exists @t3 (and (tptp.aElementOf0 @t1 @t65) @t57))) % 0.40/0.63 (assume @p45 (and @t67 (not (= tptp.xu tptp.sz00)) (forall @t3 (=> (and (tptp.aElementOf0 @t1 tptp.xI) @t57) (not (tptp.iLess0 @t56 (tptp.sbrdtbr0 tptp.xu))))))) % 0.40/0.63 (assume @p46 (not (and @t69 @t68))) % 0.40/0.63 (assume @p47 (exists @t9 (and @t2 @t7 (= tptp.xu (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xa @t1) (tptp.sdtasdt0 tptp.xb @t5)))))) % 0.40/0.63 (assume @p48 (not @t71)) % 0.40/0.63 (assume @p49 (not @t73)) % 0.40/0.63 (assume @p50 (not false)) % 0.40/0.63 (assume @p51 true) % 0.40/0.63 (step @p52 :rule quant-merge-prenex :args ((= (forall @t3 @t79) (forall (@list @t1 @t74) @t77)))) % 0.40/0.63 (step @p53 :rule alpha_equiv :args (@t80 (@list @t74) @t81)) % 0.40/0.63 (step @p54 :rule refl :args (@t76)) % 0.40/0.63 (step @p55 :rule nary_cong :premises (@p54 @p53) :args (@t82)) % 0.40/0.63 (step @p56 :rule quant-miniscope-or :args ((= @t79 @t82))) % 0.40/0.63 (step @p57 :rule trans :premises (@p56 @p55)) % 0.40/0.63 (step @p58 :rule symm :premises (@p57)) % 0.40/0.63 (step @p59 :rule cong :premises (@p58) :args ((forall @t3 (or @t76 @t58)))) % 0.40/0.63 (step @p60 :rule trans :premises (@p59 @p52)) % 0.40/0.63 (step @p61 :rule bool-impl-elim :args (@t2 @t58)) % 0.40/0.63 (step @p62 :rule cong :premises (@p61) :args (@t59)) % 0.40/0.63 (step @p63 :rule trans :premises (@p62 @p60)) % 0.40/0.63 (step @p64 :rule eq_resolve :premises (@p34 @p63)) % 0.40/0.63 (step @p65 :rule instantiate :premises (@p64) :args ((@list tptp.xa tptp.xu))) % 0.40/0.63 (step @p66 :rule and_elim :premises (@p39) :args (0)) % 0.40/0.63 (step @p67 :rule cnf_or_pos :args (@t87)) % 0.40/0.63 (step @p68 :rule reordering :premises (@p67) :args ((or @t86 @t85 (not @t87)))) % 0.40/0.63 (step @p69 :rule chain_m_resolution :premises (@p68 @p66 @p65) :args (@t85 @t88 (@list @t62 @t87))) % 0.40/0.63 (step @p70 :rule aci_norm :args ((= @t94 (or @t92 @t91 @t90)))) % 0.40/0.63 (step @p71 :rule cong :premises (@p70) :args (@t95)) % 0.40/0.63 (step @p72 :rule quant-merge-prenex :args ((= (forall @t3 @t97) @t95))) % 0.40/0.63 (step @p73 :rule alpha_equiv :args (@t98 (@list @t89) @t81)) % 0.40/0.63 (step @p74 :rule refl :args (@t92)) % 0.40/0.63 (step @p75 :rule nary_cong :premises (@p74 @p73) :args (@t99)) % 0.40/0.63 (step @p76 :rule quant-miniscope-or :args ((= @t97 @t99))) % 0.40/0.63 (step @p77 :rule trans :premises (@p76 @p75)) % 0.40/0.63 (step @p78 :rule symm :premises (@p77)) % 0.40/0.63 (step @p79 :rule cong :premises (@p78) :args ((forall @t3 (or @t92 @t101)))) % 0.40/0.63 (step @p80 :rule trans :premises (@p79 @p72)) % 0.40/0.63 (step @p81 :rule trans :premises (@p80 @p71)) % 0.40/0.63 (step @p82 :rule bool-impl-elim :args (@t21 @t101)) % 0.40/0.63 (step @p83 :rule cong :premises (@p82) :args ((forall @t3 (=> @t21 @t101)))) % 0.40/0.63 (step @p84 :rule trans :premises (@p83 @p81)) % 0.40/0.63 (step @p85 :rule bool-impl-elim :args (@t22 @t7)) % 0.40/0.63 (step @p86 :rule cong :premises (@p85) :args (@t24)) % 0.40/0.63 (step @p87 :rule refl :args (@t21)) % 0.40/0.63 (step @p88 :rule cong :premises (@p87 @p86) :args (@t25)) % 0.40/0.63 (step @p89 :rule cong :premises (@p88) :args (@t26)) % 0.40/0.63 (step @p90 :rule trans :premises (@p89 @p84)) % 0.40/0.63 (step @p91 :rule eq_resolve :premises (@p20 @p90)) % 0.40/0.63 (step @p92 :rule instantiate :premises (@p91) :args ((@list tptp.xI tptp.xu))) % 0.40/0.63 (step @p93 :rule quant-merge-prenex :args ((= (forall @t23 @t113) (forall @t111 @t110)))) % 0.40/0.63 (step @p94 :rule alpha_equiv :args (@t114 (@list @t102) @t115)) % 0.40/0.63 (step @p95 :rule quant-unused-vars :args ((= @t116 @t114))) % 0.40/0.63 (step @p96 :rule trans :premises (@p95 @p94)) % 0.40/0.63 (step @p97 :rule alpha_equiv :args (@t117 (@list @t106) @t115)) % 0.40/0.63 (step @p98 :rule quant-unused-vars :args ((= @t118 @t117))) % 0.40/0.63 (step @p99 :rule trans :premises (@p98 @p97)) % 0.40/0.63 (step @p100 :rule nary_cong :premises (@p99 @p96) :args (@t119)) % 0.40/0.63 (step @p101 :rule quant-miniscope-and :args ((= @t120 @t119))) % 0.40/0.63 (step @p102 :rule trans :premises (@p101 @p100)) % 0.40/0.63 (step @p103 :rule refl :args (@t100)) % 0.40/0.63 (step @p104 :rule nary_cong :premises (@p103 @p102) :args (@t121)) % 0.40/0.63 (step @p105 :rule quant-miniscope-or :args ((= @t113 @t121))) % 0.40/0.63 (step @p106 :rule trans :premises (@p105 @p104)) % 0.40/0.63 (step @p107 :rule symm :premises (@p106)) % 0.40/0.63 (step @p108 :rule cong :premises (@p107) :args ((forall @t23 (or @t100 @t122)))) % 0.40/0.63 (step @p109 :rule trans :premises (@p108 @p93)) % 0.40/0.63 (step @p110 :rule bool-impl-elim :args (@t22 @t122)) % 0.40/0.63 (step @p111 :rule cong :premises (@p110) :args ((forall @t23 (=> @t22 @t122)))) % 0.40/0.63 (step @p112 :rule trans :premises (@p111 @p109)) % 0.40/0.63 (step @p113 :rule bool-impl-elim :args (@t13 @t41)) % 0.40/0.63 (step @p114 :rule cong :premises (@p113) :args (@t42)) % 0.40/0.63 (step @p115 :rule bool-impl-elim :args (@t27 @t43)) % 0.40/0.63 (step @p116 :rule cong :premises (@p115) :args (@t44)) % 0.40/0.63 (step @p117 :rule nary_cong :premises (@p116 @p114) :args (@t45)) % 0.40/0.63 (step @p118 :rule refl :args (@t22)) % 0.40/0.63 (step @p119 :rule cong :premises (@p118 @p117) :args (@t46)) % 0.40/0.63 (step @p120 :rule cong :premises (@p119) :args (@t47)) % 0.40/0.63 (step @p121 :rule trans :premises (@p120 @p112)) % 0.40/0.63 (step @p122 :rule nary_cong :premises (@p87 @p121) :args (@t48)) % 0.40/0.63 (step @p123 :rule refl :args (@t49)) % 0.40/0.63 (step @p124 :rule cong :premises (@p123 @p122) :args (@t50)) % 0.40/0.63 (step @p125 :rule cong :premises (@p124) :args (@t51)) % 0.40/0.63 (step @p126 :rule eq_resolve :premises (@p24 @p125)) % 0.40/0.63 (step @p127 :rule instantiate :premises (@p126) :args ((@list tptp.xI))) % 0.40/0.63 (step @p128 :rule and_elim :premises (@p42) :args (0)) % 0.40/0.63 (step @p129 :rule cnf_equiv_pos1 :args (@t125)) % 0.40/0.63 (step @p130 :rule reordering :premises (@p129) :args ((or (not @t66) @t124 (not @t125)))) % 0.40/0.63 (step @p131 :rule chain_m_resolution :premises (@p130 @p128 @p127) :args (@t124 @t88 (@list @t66 @t125))) % 0.40/0.63 (step @p132 :rule cnf_and_pos :args (@t124 0)) % 0.40/0.63 (step @p133 :rule reordering :premises (@p132) :args ((or @t123 (not @t124)))) % 0.40/0.63 (step @p134 :rule chain_m_resolution :premises (@p133 @p131) :args (@t123 (@list false) (@list @t124))) % 0.40/0.63 (step @p135 :rule and_elim :premises (@p45) :args (0)) % 0.40/0.63 (step @p136 :rule cnf_or_pos :args (@t128)) % 0.40/0.63 (step @p137 :rule reordering :premises (@p136) :args ((or @t126 @t127 @t83 (not @t128)))) % 0.40/0.63 (step @p138 :rule chain_m_resolution :premises (@p137 @p135 @p134 @p92) :args (@t83 (@list false false false) (@list @t67 @t123 @t128))) % 0.40/0.63 (step @p139 :rule bool-double-not-elim :args (@t70)) % 0.40/0.63 (step @p140 :rule eq_resolve :premises (@p48 @p139)) % 0.40/0.63 (step @p141 :rule cnf_and_neg :args (@t84)) % 0.40/0.63 (step @p142 :rule reordering :premises (@p141) :args ((or @t71 @t129 @t84))) % 0.40/0.63 (step @p143 :rule chain_m_resolution :premises (@p142 @p140 @p138) :args (@t84 @t88 (@list @t70 @t83))) % 0.40/0.63 (step @p144 :rule cnf_equiv_pos2 :args (@t85)) % 0.40/0.63 (step @p145 :rule reordering :premises (@p144) :args ((or @t69 (not @t84) (not @t85)))) % 0.40/0.63 (step @p146 :rule chain_m_resolution :premises (@p145 @p143 @p69) :args (@t69 @t88 (@list @t84 @t85))) % 0.40/0.63 (step @p147 :rule instantiate :premises (@p64) :args ((@list tptp.xb tptp.xu))) % 0.40/0.63 (step @p148 :rule and_elim :premises (@p39) :args (1)) % 0.40/0.63 (step @p149 :rule cnf_or_pos :args (@t133)) % 0.40/0.63 (step @p150 :rule reordering :premises (@p149) :args ((or @t132 @t131 (not @t133)))) % 0.40/0.63 (step @p151 :rule chain_m_resolution :premises (@p150 @p148 @p147) :args (@t131 @t88 (@list @t61 @t133))) % 0.40/0.63 (step @p152 :rule bool-double-not-elim :args (@t72)) % 0.40/0.63 (step @p153 :rule eq_resolve :premises (@p49 @p152)) % 0.40/0.63 (step @p154 :rule cnf_and_neg :args (@t130)) % 0.40/0.63 (step @p155 :rule reordering :premises (@p154) :args ((or @t73 @t129 @t130))) % 0.40/0.63 (step @p156 :rule chain_m_resolution :premises (@p155 @p153 @p138) :args (@t130 @t88 (@list @t72 @t83))) % 0.40/0.63 (step @p157 :rule cnf_equiv_pos2 :args (@t131)) % 0.40/0.63 (step @p158 :rule reordering :premises (@p157) :args ((or @t68 (not @t130) (not @t131)))) % 0.40/0.63 (step @p159 :rule chain_m_resolution :premises (@p158 @p156 @p151) :args (@t68 @t88 (@list @t130 @t131))) % 0.40/0.63 (step @p160 :rule not_and :premises (@p46)) % 0.40/0.63 (step @p161 false :rule chain_m_resolution :premises (@p160 @p159 @p146) :args (false @t88 (@list @t68 @t69))) % 0.40/0.63 ) % 0.40/0.63 % SZS output end Proof % 0.40/0.63 % cvc5 exiting %------------------------------------------------------------------------------