%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM488+3 : 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 : 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 08:39:35 AM UTC 2026 % Result : Theorem 73.44s 73.75s % Output : Proof 73.44s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM488+3 : TPTP v9.2.1. Released v4.0.0. % 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n023.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 11:24:13 EDT 2026 % 0.17/0.34 % CPUTime : % 0.31/0.50 %----Proving TF0_NAR, FOF, or CNF % 73.44/73.75 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 73.44/73.75 --- Run --no-e-matching --full-saturate-quant at 6... % 73.44/73.75 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 6... % 73.44/73.75 --- Run --finite-model-find --uf-ss=no-minimal at 6... % 73.44/73.75 --- Run --multi-trigger-when-single --full-saturate-quant at 30... % 73.44/73.75 --- Run --trigger-sel=max --full-saturate-quant at 15... % 73.44/73.75 % SZS status Theorem % 73.44/73.75 % SZS output start Proof % 73.44/73.75 ( % 73.44/73.75 (declare-sort $$unsorted 0) % 73.44/73.75 (declare-const tptp.xr $$unsorted) % 73.44/73.75 (declare-const tptp.doDivides0 (-> $$unsorted $$unsorted Bool)) % 73.44/73.75 (declare-const tptp.xm $$unsorted) % 73.44/73.75 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 73.44/73.75 (declare-const tptp.sdtlseqdt0 (-> $$unsorted $$unsorted Bool)) % 73.44/73.75 (declare-const tptp.xn $$unsorted) % 73.44/73.75 (declare-const tptp.aNaturalNumber0 (-> $$unsorted Bool)) % 73.44/73.75 (declare-const tptp.sz00 $$unsorted) % 73.44/73.75 (declare-const tptp.sdtsldt0 (-> $$unsorted $$unsorted $$unsorted)) % 73.44/73.75 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 73.44/73.75 (declare-const tptp.sdtmndt0 (-> $$unsorted $$unsorted $$unsorted)) % 73.44/73.75 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 73.44/73.75 (declare-const tptp.isPrime0 (-> $$unsorted Bool)) % 73.44/73.75 (declare-const tptp.sz10 $$unsorted) % 73.44/73.75 (declare-const tptp.xp $$unsorted) % 73.44/73.75 (define @t1 () (@var "W0" $$unsorted)) % 73.44/73.75 (define @t2 () (tptp.aNaturalNumber0 @t1)) % 73.44/73.75 (define @t3 () (@list @t1)) % 73.44/73.75 (define @t4 () (@var "W1" $$unsorted)) % 73.44/73.75 (define @t5 () (tptp.sdtpldt0 @t1 @t4)) % 73.44/73.75 (define @t6 () (tptp.aNaturalNumber0 @t4)) % 73.44/73.75 (define @t7 () (and @t2 @t6)) % 73.44/73.75 (define @t8 () (@list @t1 @t4)) % 73.44/73.75 (define @t9 () (tptp.sdtasdt0 @t1 @t4)) % 73.44/73.75 (define @t10 () (tptp.aNaturalNumber0 @t9)) % 73.44/73.75 (define @t11 () (forall @t8 (=> @t7 @t10))) % 73.44/73.75 (define @t12 () (tptp.sdtpldt0 @t4 @t1)) % 73.44/73.75 (define @t13 () (@var "W2" $$unsorted)) % 73.44/73.75 (define @t14 () (tptp.sdtpldt0 @t4 @t13)) % 73.44/73.75 (define @t15 () (tptp.sdtpldt0 @t5 @t13)) % 73.44/73.75 (define @t16 () (tptp.aNaturalNumber0 @t13)) % 73.44/73.75 (define @t17 () (and @t2 @t6 @t16)) % 73.44/73.75 (define @t18 () (@list @t1 @t4 @t13)) % 73.44/73.75 (define @t19 () (tptp.sdtasdt0 @t4 @t1)) % 73.44/73.75 (define @t20 () (= @t9 @t19)) % 73.44/73.75 (define @t21 () (forall @t8 (=> @t7 @t20))) % 73.44/73.75 (define @t22 () (tptp.sdtasdt0 @t13 @t1)) % 73.44/73.75 (define @t23 () (tptp.sdtasdt0 @t1 @t13)) % 73.44/73.75 (define @t24 () (and (= (tptp.sdtasdt0 @t1 @t14) (tptp.sdtpldt0 @t9 @t23)) (= (tptp.sdtasdt0 @t14 @t1) (tptp.sdtpldt0 @t19 @t22)))) % 73.44/73.75 (define @t25 () (forall @t18 (=> @t17 @t24))) % 73.44/73.75 (define @t26 () (= @t4 @t13)) % 73.44/73.75 (define @t27 () (tptp.sdtpldt0 @t13 @t1)) % 73.44/73.75 (define @t28 () (tptp.sdtpldt0 @t1 @t13)) % 73.44/73.75 (define @t29 () (= @t19 @t22)) % 73.44/73.75 (define @t30 () (= @t9 @t23)) % 73.44/73.75 (define @t31 () (and @t6 @t16)) % 73.44/73.75 (define @t32 () (= @t1 tptp.sz00)) % 73.44/73.75 (define @t33 () (not @t32)) % 73.44/73.75 (define @t34 () (= @t4 tptp.sz00)) % 73.44/73.75 (define @t35 () (and @t16 (= @t28 @t4))) % 73.44/73.75 (define @t36 () (@list @t13)) % 73.44/73.75 (define @t37 () (tptp.sdtlseqdt0 @t1 @t4)) % 73.44/73.75 (define @t38 () (= @t1 @t4)) % 73.44/73.75 (define @t39 () (tptp.sdtlseqdt0 @t4 @t1)) % 73.44/73.75 (define @t40 () (tptp.sdtlseqdt0 @t4 @t13)) % 73.44/73.75 (define @t41 () (= @t4 @t1)) % 73.44/73.75 (define @t42 () (tptp.sdtpldt0 @t13 @t4)) % 73.44/73.75 (define @t43 () (and (not @t38) @t37)) % 73.44/73.75 (define @t44 () (= @t1 tptp.sz10)) % 73.44/73.75 (define @t45 () (tptp.iLess0 @t1 @t4)) % 73.44/73.75 (define @t46 () (= @t4 @t23)) % 73.44/73.75 (define @t47 () (and @t16 @t46)) % 73.44/73.75 (define @t48 () (exists @t36 @t47)) % 73.44/73.75 (define @t49 () (tptp.doDivides0 @t1 @t4)) % 73.44/73.75 (define @t50 () (= @t49 @t48)) % 73.44/73.75 (define @t51 () (=> @t7 @t50)) % 73.44/73.75 (define @t52 () (forall @t8 @t51)) % 73.44/73.75 (define @t53 () (tptp.sdtsldt0 @t4 @t1)) % 73.44/73.75 (define @t54 () (and @t33 @t49)) % 73.44/73.75 (define @t55 () (tptp.doDivides0 @t1 @t13)) % 73.44/73.75 (define @t56 () (tptp.doDivides0 @t1 @t14)) % 73.44/73.75 (define @t57 () (and @t49 @t56)) % 73.44/73.75 (define @t58 () (=> @t57 @t55)) % 73.44/73.75 (define @t59 () (forall @t18 (=> @t17 @t58))) % 73.44/73.75 (define @t60 () (tptp.doDivides0 @t4 @t1)) % 73.44/73.75 (define @t61 () (@list @t4)) % 73.44/73.75 (define @t62 () (not @t44)) % 73.44/73.75 (define @t63 () (tptp.aNaturalNumber0 tptp.xp)) % 73.44/73.75 (define @t64 () (tptp.aNaturalNumber0 tptp.xm)) % 73.44/73.75 (define @t65 () (@var "W3" $$unsorted)) % 73.44/73.75 (define @t66 () (tptp.sdtasdt0 @t13 @t65)) % 73.44/73.75 (define @t67 () (tptp.aNaturalNumber0 @t65)) % 73.44/73.75 (define @t68 () (@list @t65)) % 73.44/73.75 (define @t69 () (@var "W4" $$unsorted)) % 73.44/73.75 (define @t70 () (tptp.sdtasdt0 tptp.xn tptp.xm)) % 73.44/73.75 (define @t71 () (tptp.doDivides0 tptp.xp @t70)) % 73.44/73.75 (define @t72 () (tptp.sdtasdt0 tptp.xp @t1)) % 73.44/73.75 (define @t73 () (tptp.sdtpldt0 tptp.xp tptp.xr)) % 73.44/73.75 (define @t74 () (tptp.aNaturalNumber0 tptp.xr)) % 73.44/73.75 (define @t75 () (tptp.sdtasdt0 tptp.xr tptp.xm)) % 73.44/73.75 (define @t76 () (tptp.doDivides0 tptp.xp @t75)) % 73.44/73.75 (define @t77 () (and @t2 (= @t75 @t72))) % 73.44/73.75 (define @t78 () (exists @t3 @t77)) % 73.44/73.75 (define @t79 () (or @t78 @t76)) % 73.44/73.75 (define @t80 () (not @t79)) % 73.44/73.75 (define @t81 () (not @t16)) % 73.44/73.75 (define @t82 () (= @t49 (not (forall @t36 (or @t81 (not @t46)))))) % 73.44/73.75 (define @t83 () (not @t6)) % 73.44/73.75 (define @t84 () (not @t2)) % 73.44/73.75 (define @t85 () (or @t84 @t83)) % 73.44/73.75 (define @t86 () (not @t7)) % 73.44/73.75 (define @t87 () (forall @t36 (not @t47))) % 73.44/73.75 (define @t88 () (not @t87)) % 73.44/73.75 (define @t89 () (tptp.sdtasdt0 tptp.xp tptp.xm)) % 73.44/73.75 (define @t90 () (@list tptp.xm tptp.xp)) % 73.44/73.75 (define @t91 () (tptp.sdtasdt0 tptp.xm tptp.xp)) % 73.44/73.75 (define @t92 () (tptp.aNaturalNumber0 @t91)) % 73.44/73.75 (define @t93 () (not @t63)) % 73.44/73.75 (define @t94 () (not @t64)) % 73.44/73.75 (define @t95 () (or @t94 @t93 @t92)) % 73.44/73.75 (define @t96 () (@list false false false)) % 73.44/73.75 (define @t97 () (or @t84 @t83 @t20)) % 73.44/73.75 (define @t98 () (or @t94 @t93 (= @t91 @t89))) % 73.44/73.75 (define @t99 () (forall @t8 @t97)) % 73.44/73.75 (define @t100 () (= @t89 @t91)) % 73.44/73.75 (define @t101 () (or @t94 @t93 @t100)) % 73.44/73.75 (define @t102 () (@list false)) % 73.44/73.75 (define @t103 () (tptp.aNaturalNumber0 @t89)) % 73.44/73.75 (define @t104 () (forall @t36 (or @t81 (not (= @t89 (tptp.sdtasdt0 tptp.xp @t13)))))) % 73.44/73.75 (define @t105 () (not @t104)) % 73.44/73.75 (define @t106 () (tptp.doDivides0 tptp.xp @t89)) % 73.44/73.75 (define @t107 () (= @t106 @t105)) % 73.44/73.75 (define @t108 () (not @t103)) % 73.44/73.75 (define @t109 () (or @t93 @t108 @t107)) % 73.44/73.75 (define @t110 () (not @t56)) % 73.44/73.75 (define @t111 () (not @t49)) % 73.44/73.75 (define @t112 () (or @t111 @t110 @t55)) % 73.44/73.75 (define @t113 () (or @t84 @t83 @t81)) % 73.44/73.75 (define @t114 () (not @t17)) % 73.44/73.75 (define @t115 () (tptp.sdtpldt0 @t89 @t75)) % 73.44/73.75 (define @t116 () (= (tptp.sdtasdt0 @t73 tptp.xm) @t115)) % 73.44/73.75 (define @t117 () (tptp.sdtasdt0 tptp.xm tptp.xr)) % 73.44/73.75 (define @t118 () (and (= (tptp.sdtasdt0 tptp.xm @t73) (tptp.sdtpldt0 @t91 @t117)) @t116)) % 73.44/73.75 (define @t119 () (not @t74)) % 73.44/73.75 (define @t120 () (or @t94 @t93 @t119 @t118)) % 73.44/73.75 (define @t121 () (tptp.doDivides0 tptp.xp @t115)) % 73.44/73.75 (define @t122 () (tptp.aNaturalNumber0 @t117)) % 73.44/73.75 (define @t123 () (or @t94 @t119 @t122)) % 73.44/73.75 (define @t124 () (= @t75 @t117)) % 73.44/73.75 (define @t125 () (or @t119 @t94 @t124)) % 73.44/73.75 (define @t126 () (tptp.aNaturalNumber0 @t75)) % 73.44/73.75 (define @t127 () (= @t72 @t75)) % 73.44/73.75 (define @t128 () (and @t2 @t127)) % 73.44/73.75 (define @t129 () (forall @t3 (not @t128))) % 73.44/73.75 (define @t130 () (not @t129)) % 73.44/73.75 (define @t131 () (not @t121)) % 73.44/73.75 (define @t132 () (not @t106)) % 73.44/73.75 (define @t133 () (not @t126)) % 73.44/73.75 (define @t134 () (or @t93 @t108 @t133 @t132 @t131 @t76)) % 73.44/73.75 (define @t135 () (not @t107)) % 73.44/73.75 (define @t136 () (not (= @t89 @t89))) % 73.44/73.75 (define @t137 () (or @t94 @t136)) % 73.44/73.75 (assume @p1 (forall @t3 (=> @t2 true))) % 73.44/73.75 (assume @p2 (tptp.aNaturalNumber0 tptp.sz00)) % 73.44/73.75 (assume @p3 (and (tptp.aNaturalNumber0 tptp.sz10) (not (= tptp.sz10 tptp.sz00)))) % 73.44/73.75 (assume @p4 (forall @t8 (=> @t7 (tptp.aNaturalNumber0 @t5)))) % 73.44/73.75 (assume @p5 @t11) % 73.44/73.75 (assume @p6 (forall @t8 (=> @t7 (= @t5 @t12)))) % 73.44/73.75 (assume @p7 (forall @t18 (=> @t17 (= @t15 (tptp.sdtpldt0 @t1 @t14))))) % 73.44/73.75 (assume @p8 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 tptp.sz00) @t1) (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1)))))) % 73.44/73.75 (assume @p9 @t21) % 73.44/73.75 (assume @p10 (forall @t18 (=> @t17 (= (tptp.sdtasdt0 @t9 @t13) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t4 @t13)))))) % 73.44/73.75 (assume @p11 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 73.44/73.75 (assume @p12 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 73.44/73.75 (assume @p13 @t25) % 73.44/73.75 (assume @p14 (forall @t18 (=> @t17 (=> (or (= @t5 @t28) (= @t12 @t27)) @t26)))) % 73.44/73.75 (assume @p15 (forall @t3 (=> @t2 (=> @t33 (forall (@list @t4 @t13) (=> @t31 (=> (or @t30 @t29) @t26))))))) % 73.44/73.75 (assume @p16 (forall @t8 (=> @t7 (=> (= @t5 tptp.sz00) (and @t32 @t34))))) % 73.44/73.75 (assume @p17 (forall @t8 (=> @t7 (=> (= @t9 tptp.sz00) (or @t32 @t34))))) % 73.44/73.75 (assume @p18 (forall @t8 (=> @t7 (= @t37 (exists @t36 @t35))))) % 73.44/73.75 (assume @p19 (forall @t8 (=> @t7 (=> @t37 (forall @t36 (= (= @t13 (tptp.sdtmndt0 @t4 @t1)) @t35)))))) % 73.44/73.75 (assume @p20 (forall @t3 (=> @t2 (tptp.sdtlseqdt0 @t1 @t1)))) % 73.44/73.75 (assume @p21 (forall @t8 (=> @t7 (=> (and @t37 @t39) @t38)))) % 73.44/73.75 (assume @p22 (forall @t18 (=> @t17 (=> (and @t37 @t40) (tptp.sdtlseqdt0 @t1 @t13))))) % 73.44/73.75 (assume @p23 (forall @t8 (=> @t7 (or @t37 (and (not @t41) @t39))))) % 73.44/73.75 (assume @p24 (forall @t8 (=> @t7 (=> @t43 (forall @t36 (=> @t16 (and (not (= @t27 @t42)) (tptp.sdtlseqdt0 @t27 @t42) (not (= @t28 @t14)) (tptp.sdtlseqdt0 @t28 @t14)))))))) % 73.44/73.75 (assume @p25 (forall @t18 (=> @t17 (=> (and @t33 (not @t26) @t40) (and (not @t30) (tptp.sdtlseqdt0 @t9 @t23) (not @t29) (tptp.sdtlseqdt0 @t19 @t22)))))) % 73.44/73.75 (assume @p26 (forall @t3 (=> @t2 (or @t32 @t44 (and (not (= tptp.sz10 @t1)) (tptp.sdtlseqdt0 tptp.sz10 @t1)))))) % 73.44/73.75 (assume @p27 (forall @t8 (=> @t7 (=> @t33 (tptp.sdtlseqdt0 @t4 @t19))))) % 73.44/73.75 (assume @p28 (forall @t8 (=> @t7 (=> @t45 true)))) % 73.44/73.75 (assume @p29 (forall @t8 (=> @t7 (=> @t43 @t45)))) % 73.44/73.75 (assume @p30 @t52) % 73.44/73.75 (assume @p31 (forall @t8 (=> @t7 (=> @t54 (forall @t36 (= (= @t13 @t53) @t47)))))) % 73.44/73.75 (assume @p32 (forall @t18 (=> @t17 (=> (and @t49 (tptp.doDivides0 @t4 @t13)) @t55)))) % 73.44/73.75 (assume @p33 (forall @t18 (=> @t17 (=> (and @t49 @t55) @t56)))) % 73.44/73.75 (assume @p34 @t59) % 73.44/73.75 (assume @p35 (forall @t8 (=> @t7 (=> (and @t49 (not @t34)) @t37)))) % 73.44/73.75 (assume @p36 (forall @t8 (=> @t7 (=> @t54 (forall @t36 (=> @t16 (= (tptp.sdtasdt0 @t13 @t53) (tptp.sdtsldt0 (tptp.sdtasdt0 @t13 @t4) @t1)))))))) % 73.44/73.75 (assume @p37 (forall @t3 (=> @t2 (= (tptp.isPrime0 @t1) (and @t33 @t62 (forall @t61 (=> (and @t6 @t60) (or (= @t4 tptp.sz10) @t41)))))))) % 73.44/73.75 (assume @p38 (forall @t3 (=> (and @t2 @t33 @t62) (exists @t61 (and @t6 @t60 (tptp.isPrime0 @t4)))))) % 73.44/73.75 (assume @p39 (and (tptp.aNaturalNumber0 tptp.xn) @t64 @t63)) % 73.44/73.75 (assume @p40 (forall @t18 (=> @t17 (=> (and (or (and (not (= @t13 tptp.sz00)) (not (= @t13 tptp.sz10)) (forall @t68 (=> (and @t67 (exists (@list @t69) (and (tptp.aNaturalNumber0 @t69) (= @t13 (tptp.sdtasdt0 @t65 @t69)))) (tptp.doDivides0 @t65 @t13)) (or (= @t65 tptp.sz10) (= @t65 @t13))))) (tptp.isPrime0 @t13)) (or (exists @t68 (and @t67 (= @t9 @t66))) (tptp.doDivides0 @t13 @t9))) (=> (tptp.iLess0 @t15 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)) (or (and (exists @t68 (and @t67 (= @t1 @t66))) (tptp.doDivides0 @t13 @t1)) (and (exists @t68 (and @t67 (= @t4 @t66))) (tptp.doDivides0 @t13 @t4)))))))) % 73.44/73.75 (assume @p41 (and (not (= tptp.xp tptp.sz00)) (not (= tptp.xp tptp.sz10)) (forall @t3 (=> (and @t2 (or (exists @t61 (and @t6 (= tptp.xp @t9))) (tptp.doDivides0 @t1 tptp.xp))) (or @t44 (= @t1 tptp.xp)))) (tptp.isPrime0 tptp.xp) (exists @t3 (and @t2 (= @t70 @t72))) @t71)) % 73.44/73.75 (assume @p42 (and (exists @t3 (and @t2 (= (tptp.sdtpldt0 tptp.xp @t1) tptp.xn))) (tptp.sdtlseqdt0 tptp.xp tptp.xn))) % 73.44/73.75 (assume @p43 (and @t74 (= @t73 tptp.xn) (= tptp.xr (tptp.sdtmndt0 tptp.xn tptp.xp)))) % 73.44/73.75 (assume @p44 (and (not (= tptp.xr tptp.xn)) (exists @t3 (and @t2 (= (tptp.sdtpldt0 tptp.xr @t1) tptp.xn))) (tptp.sdtlseqdt0 tptp.xr tptp.xn))) % 73.44/73.75 (assume @p45 @t80) % 73.44/73.75 (assume @p46 true) % 73.44/73.75 (step @p47 :rule and_elim :premises (@p39) :args (1)) % 73.44/73.75 (step @p48 :rule aci_norm :args ((= (or @t85 @t82) (or @t84 @t83 @t82)))) % 73.44/73.75 (step @p49 :rule refl :args (@t82)) % 73.44/73.75 (step @p50 :rule bool-and-de-morgan :args (@t2 @t6 true)) % 73.44/73.75 (step @p51 :rule nary_cong :premises (@p50 @p49) :args ((or @t86 @t82))) % 73.44/73.75 (step @p52 :rule trans :premises (@p51 @p48)) % 73.44/73.75 (step @p53 :rule bool-impl-elim :args (@t7 @t82)) % 73.44/73.75 (step @p54 :rule trans :premises (@p53 @p52)) % 73.44/73.75 (step @p55 :rule cong :premises (@p54) :args ((forall @t8 (=> @t7 @t82)))) % 73.44/73.75 (step @p56 :rule bool-and-de-morgan :args (@t16 @t46 true)) % 73.44/73.75 (step @p57 :rule cong :premises (@p56) :args (@t87)) % 73.44/73.75 (step @p58 :rule cong :premises (@p57) :args (@t88)) % 73.44/73.75 (step @p59 :rule exists-elim :args ((= @t48 @t88))) % 73.44/73.75 (step @p60 :rule trans :premises (@p59 @p58)) % 73.44/73.75 (step @p61 :rule refl :args (@t49)) % 73.44/73.75 (step @p62 :rule cong :premises (@p61 @p60) :args (@t50)) % 73.44/73.75 (step @p63 :rule refl :args (@t7)) % 73.44/73.75 (step @p64 :rule cong :premises (@p63 @p62) :args (@t51)) % 73.44/73.75 (step @p65 :rule cong :premises (@p64) :args (@t52)) % 73.44/73.75 (step @p66 :rule trans :premises (@p65 @p55)) % 73.44/73.75 (step @p67 :rule eq_resolve :premises (@p30 @p66)) % 73.44/73.75 (step @p68 :rule instantiate :premises (@p67) :args ((@list tptp.xp @t89))) % 73.44/73.75 (step @p69 :rule aci_norm :args ((= (or @t85 @t10) (or @t84 @t83 @t10)))) % 73.44/73.75 (step @p70 :rule refl :args (@t10)) % 73.44/73.75 (step @p71 :rule nary_cong :premises (@p50 @p70) :args ((or @t86 @t10))) % 73.44/73.75 (step @p72 :rule trans :premises (@p71 @p69)) % 73.44/73.75 (step @p73 :rule bool-impl-elim :args (@t7 @t10)) % 73.44/73.75 (step @p74 :rule trans :premises (@p73 @p72)) % 73.44/73.75 (step @p75 :rule cong :premises (@p74) :args (@t11)) % 73.44/73.75 (step @p76 :rule eq_resolve :premises (@p5 @p75)) % 73.44/73.75 (step @p77 :rule instantiate :premises (@p76) :args (@t90)) % 73.44/73.75 (step @p78 :rule and_elim :premises (@p39) :args (2)) % 73.44/73.75 (step @p79 :rule cnf_or_pos :args (@t95)) % 73.44/73.75 (step @p80 :rule reordering :premises (@p79) :args ((or @t94 @t93 @t92 (not @t95)))) % 73.44/73.75 (step @p81 :rule chain_m_resolution :premises (@p80 @p47 @p78 @p77) :args (@t92 @t96 (@list @t64 @t63 @t95))) % 73.44/73.75 (step @p82 :rule true_intro :premises (@p81)) % 73.44/73.75 (step @p83 :rule aci_norm :args ((= (or @t85 @t20) @t97))) % 73.44/73.75 (step @p84 :rule refl :args (@t20)) % 73.44/73.75 (step @p85 :rule nary_cong :premises (@p50 @p84) :args ((or @t86 @t20))) % 73.44/73.75 (step @p86 :rule trans :premises (@p85 @p83)) % 73.44/73.75 (step @p87 :rule bool-impl-elim :args (@t7 @t20)) % 73.44/73.75 (step @p88 :rule trans :premises (@p87 @p86)) % 73.44/73.75 (step @p89 :rule cong :premises (@p88) :args (@t21)) % 73.44/73.75 (step @p90 :rule eq_resolve :premises (@p9 @p89)) % 73.44/73.75 (step @p91 :rule eq-symm :args (@t91 @t89)) % 73.44/73.75 (step @p92 :rule refl :args (@t93)) % 73.44/73.75 (step @p93 :rule refl :args (@t94)) % 73.44/73.75 (step @p94 :rule nary_cong :premises (@p93 @p92 @p91) :args (@t98)) % 73.44/73.75 (step @p95 :rule refl :args (@t99)) % 73.44/73.75 (step @p96 :rule cong :premises (@p95 @p94) :args ((=> @t99 @t98))) % 73.44/73.75 (assume-push @p219 @t99) % 73.44/73.75 (step @p98 :rule instantiate :premises (@p90) :args (@t90)) % 73.44/73.75 (step-pop @p220 :rule scope :premises (@p98)) % 73.44/73.75 (step @p99 :rule process_scope :premises (@p220) :args (@t98)) % 73.44/73.75 (step @p101 :rule eq_resolve :premises (@p99 @p96)) % 73.44/73.75 (step @p102 :rule implies_elim :premises (@p101)) % 73.44/73.75 (step @p103 :rule chain_m_resolution :premises (@p102 @p90) :args (@t101 @t102 (@list @t99))) % 73.44/73.75 (step @p104 :rule cnf_or_pos :args (@t101)) % 73.44/73.75 (step @p105 :rule reordering :premises (@p104) :args ((or @t94 @t93 @t100 (not @t101)))) % 73.44/73.75 (step @p106 :rule chain_m_resolution :premises (@p105 @p47 @p78 @p103) :args (@t100 @t96 (@list @t64 @t63 @t101))) % 73.44/73.75 (step @p107 :rule cong :premises (@p106) :args (@t103)) % 73.44/73.75 (step @p108 :rule trans :premises (@p107 @p82)) % 73.44/73.75 (step @p109 :rule true_elim :premises (@p108)) % 73.44/73.75 (step @p110 :rule cnf_or_pos :args (@t109)) % 73.44/73.75 (step @p111 :rule reordering :premises (@p110) :args ((or @t93 @t108 @t107 (not @t109)))) % 73.44/73.75 (step @p112 :rule chain_m_resolution :premises (@p111 @p78 @p109 @p68) :args (@t107 @t96 (@list @t63 @t103 @t109))) % 73.44/73.75 (step @p113 :rule aci_norm :args ((= (or @t113 @t112) (or @t84 @t83 @t81 @t111 @t110 @t55)))) % 73.44/73.75 (step @p114 :rule aci_norm :args ((= (or (or @t111 @t110) @t55) @t112))) % 73.44/73.75 (step @p115 :rule refl :args (@t55)) % 73.44/73.75 (step @p116 :rule bool-and-de-morgan :args (@t49 @t56 true)) % 73.44/73.75 (step @p117 :rule nary_cong :premises (@p116 @p115) :args ((or (not @t57) @t55))) % 73.44/73.75 (step @p118 :rule trans :premises (@p117 @p114)) % 73.44/73.75 (step @p119 :rule bool-impl-elim :args (@t57 @t55)) % 73.44/73.75 (step @p120 :rule trans :premises (@p119 @p118)) % 73.44/73.75 (step @p121 :rule aci_norm :args ((= (or @t84 (or @t83 @t81)) @t113))) % 73.44/73.75 (step @p122 :rule bool-and-de-morgan :args (@t6 @t16 true)) % 73.44/73.75 (step @p123 :rule refl :args (@t84)) % 73.44/73.75 (step @p124 :rule nary_cong :premises (@p123 @p122) :args ((or @t84 (not @t31)))) % 73.44/73.75 (step @p125 :rule bool-and-de-morgan :args (@t2 @t6 (and @t16))) % 73.44/73.75 (step @p126 :rule trans :premises (@p125 @p124)) % 73.44/73.75 (step @p127 :rule trans :premises (@p126 @p121)) % 73.44/73.75 (step @p128 :rule nary_cong :premises (@p127 @p120) :args ((or @t114 @t58))) % 73.44/73.75 (step @p129 :rule trans :premises (@p128 @p113)) % 73.44/73.75 (step @p130 :rule bool-impl-elim :args (@t17 @t58)) % 73.44/73.75 (step @p131 :rule trans :premises (@p130 @p129)) % 73.44/73.75 (step @p132 :rule cong :premises (@p131) :args (@t59)) % 73.44/73.75 (step @p133 :rule eq_resolve :premises (@p34 @p132)) % 73.44/73.75 (step @p134 :rule instantiate :premises (@p133) :args ((@list tptp.xp @t89 @t75))) % 73.44/73.75 (step @p135 :rule refl :args (tptp.xm)) % 73.44/73.75 (step @p136 :rule and_elim :premises (@p43) :args (1)) % 73.44/73.75 (step @p137 :rule symm :premises (@p136)) % 73.44/73.75 (step @p138 :rule cong :premises (@p137 @p135) :args (@t70)) % 73.44/73.75 (step @p139 :rule refl :args (tptp.xp)) % 73.44/73.75 (step @p140 :rule cong :premises (@p139 @p138) :args (@t71)) % 73.44/73.75 (step @p141 :rule and_elim :premises (@p41) :args (5)) % 73.44/73.75 (step @p142 :rule eq_resolve :premises (@p141 @p140)) % 73.44/73.75 (step @p143 :rule true_intro :premises (@p142)) % 73.44/73.75 (step @p144 :rule aci_norm :args ((= (or @t113 @t24) (or @t84 @t83 @t81 @t24)))) % 73.44/73.75 (step @p145 :rule refl :args (@t24)) % 73.44/73.75 (step @p146 :rule nary_cong :premises (@p127 @p145) :args ((or @t114 @t24))) % 73.44/73.75 (step @p147 :rule trans :premises (@p146 @p144)) % 73.44/73.75 (step @p148 :rule bool-impl-elim :args (@t17 @t24)) % 73.44/73.75 (step @p149 :rule trans :premises (@p148 @p147)) % 73.44/73.75 (step @p150 :rule cong :premises (@p149) :args (@t25)) % 73.44/73.75 (step @p151 :rule eq_resolve :premises (@p13 @p150)) % 73.44/73.75 (step @p152 :rule instantiate :premises (@p151) :args ((@list tptp.xm tptp.xp tptp.xr))) % 73.44/73.75 (step @p153 :rule and_elim :premises (@p43) :args (0)) % 73.44/73.75 (step @p154 :rule cnf_or_pos :args (@t120)) % 73.44/73.75 (step @p155 :rule reordering :premises (@p154) :args ((or @t94 @t93 @t119 @t118 (not @t120)))) % 73.44/73.75 (step @p156 :rule chain_m_resolution :premises (@p155 @p47 @p78 @p153 @p152) :args (@t118 (@list false false false false) (@list @t64 @t63 @t74 @t120))) % 73.44/73.75 (step @p157 :rule cnf_and_pos :args (@t118 1)) % 73.44/73.75 (step @p158 :rule reordering :premises (@p157) :args ((or @t116 (not @t118)))) % 73.44/73.75 (step @p159 :rule chain_m_resolution :premises (@p158 @p156) :args (@t116 @t102 (@list @t118))) % 73.44/73.75 (step @p160 :rule symm :premises (@p159)) % 73.44/73.75 (step @p161 :rule cong :premises (@p139 @p160) :args (@t121)) % 73.44/73.75 (step @p162 :rule trans :premises (@p161 @p143)) % 73.44/73.75 (step @p163 :rule true_elim :premises (@p162)) % 73.44/73.75 (step @p164 :rule instantiate :premises (@p76) :args ((@list tptp.xm tptp.xr))) % 73.44/73.75 (step @p165 :rule cnf_or_pos :args (@t123)) % 73.44/73.75 (step @p166 :rule reordering :premises (@p165) :args ((or @t94 @t119 @t122 (not @t123)))) % 73.44/73.75 (step @p167 :rule chain_m_resolution :premises (@p166 @p47 @p153 @p164) :args (@t122 @t96 (@list @t64 @t74 @t123))) % 73.44/73.75 (step @p168 :rule true_intro :premises (@p167)) % 73.44/73.75 (step @p169 :rule instantiate :premises (@p90) :args ((@list tptp.xr tptp.xm))) % 73.44/73.75 (step @p170 :rule cnf_or_pos :args (@t125)) % 73.44/73.75 (step @p171 :rule reordering :premises (@p170) :args ((or @t94 @t119 @t124 (not @t125)))) % 73.44/73.75 (step @p172 :rule chain_m_resolution :premises (@p171 @p47 @p153 @p169) :args (@t124 @t96 (@list @t64 @t74 @t125))) % 73.44/73.75 (step @p173 :rule cong :premises (@p172) :args (@t126)) % 73.44/73.75 (step @p174 :rule trans :premises (@p173 @p168)) % 73.44/73.75 (step @p175 :rule true_elim :premises (@p174)) % 73.44/73.75 (step @p176 :rule refl :args (@t76)) % 73.44/73.75 (step @p177 :rule bool-and-de-morgan :args (@t2 @t127 true)) % 73.44/73.75 (step @p178 :rule cong :premises (@p177) :args (@t129)) % 73.44/73.75 (step @p179 :rule cong :premises (@p178) :args (@t130)) % 73.44/73.75 (step @p180 :rule exists-elim :args ((= (exists @t3 @t128) @t130))) % 73.44/73.75 (step @p181 :rule trans :premises (@p180 @p179)) % 73.44/73.75 (step @p182 :rule eq-symm :args (@t75 @t72)) % 73.44/73.75 (step @p183 :rule refl :args (@t2)) % 73.44/73.75 (step @p184 :rule nary_cong :premises (@p183 @p182) :args (@t77)) % 73.44/73.75 (step @p185 :rule cong :premises (@p184) :args (@t78)) % 73.44/73.75 (step @p186 :rule trans :premises (@p185 @p181)) % 73.44/73.75 (step @p187 :rule nary_cong :premises (@p186 @p176) :args (@t79)) % 73.44/73.75 (step @p188 :rule cong :premises (@p187) :args (@t80)) % 73.44/73.75 (step @p189 :rule eq_resolve :premises (@p45 @p188)) % 73.44/73.75 (step @p190 :rule not_or_elim :premises (@p189) :args (1)) % 73.44/73.75 (step @p191 :rule cnf_or_pos :args (@t134)) % 73.44/73.75 (step @p192 :rule reordering :premises (@p191) :args ((or @t76 @t93 @t133 @t108 @t132 @t131 (not @t134)))) % 73.44/73.75 (step @p193 :rule chain_m_resolution :premises (@p192 @p190 @p78 @p175 @p109 @p163 @p134) :args (@t132 (@list true false false false false false) (@list @t76 @t63 @t126 @t103 @t121 @t134))) % 73.44/73.75 (step @p194 :rule bool-double-not-elim :args (@t104)) % 73.44/73.75 (step @p195 :rule refl :args (@t106)) % 73.44/73.75 (step @p196 :rule refl :args (@t135)) % 73.44/73.75 (step @p197 :rule nary_cong :premises (@p196 @p195 @p194) :args ((or @t135 @t106 (not @t105)))) % 73.44/73.75 (step @p198 :rule cnf_equiv_pos2 :args (@t107)) % 73.44/73.75 (step @p199 :rule eq_resolve :premises (@p198 @p197)) % 73.44/73.75 (step @p200 :rule reordering :premises (@p199) :args ((or @t106 @t104 @t135))) % 73.44/73.75 (step @p201 :rule chain_m_resolution :premises (@p200 @p193 @p112) :args (@t104 (@list true false) (@list @t106 @t107))) % 73.44/73.75 (step @p202 :rule aci_norm :args ((= (or @t94 false) @t94))) % 73.44/73.76 (step @p203 :rule evaluate :args ((not true))) % 73.44/73.76 (step @p204 :rule eq-refl :args (@t89)) % 73.44/73.76 (step @p205 :rule cong :premises (@p204) :args (@t136)) % 73.44/73.76 (step @p206 :rule trans :premises (@p205 @p203)) % 73.44/73.76 (step @p207 :rule nary_cong :premises (@p93 @p206) :args (@t137)) % 73.44/73.76 (step @p208 :rule trans :premises (@p207 @p202)) % 73.44/73.76 (step @p209 :rule refl :args (@t104)) % 73.44/73.76 (step @p210 :rule cong :premises (@p209 @p208) :args ((=> @t104 @t137))) % 73.44/73.76 (assume-push @p221 @t104) % 73.44/73.76 (step @p212 :rule instantiate :premises (@p201) :args ((@list tptp.xm))) % 73.44/73.76 (step-pop @p222 :rule scope :premises (@p212)) % 73.44/73.76 (step @p213 :rule process_scope :premises (@p222) :args (@t137)) % 73.44/73.76 (step @p215 :rule eq_resolve :premises (@p213 @p210)) % 73.44/73.76 (step @p216 :rule implies_elim :premises (@p215)) % 73.44/73.76 (step @p217 :rule reordering :premises (@p216) :args ((or @t94 @t105))) % 73.44/73.76 (step @p218 false :rule chain_m_resolution :premises (@p217 @p201 @p47) :args (false (@list false false) (@list @t104 @t64))) % 73.44/73.76 ) % 73.44/73.76 % SZS output end Proof % 73.44/73.76 % cvc5 exiting %------------------------------------------------------------------------------