%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM505+3 : 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 08:39:39 AM UTC 2026 % Result : Theorem 0.44s 0.66s % Output : Proof 0.44s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM505+3 : 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 % 0.15/0.34 % Computer : n023.cluster.edu % 0.15/0.34 % Model : x86_64 x86_64 % 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.34 % Memory : 8042.1875MB % 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.34 % CPULimit : 300 % 0.15/0.34 % WCLimit : 300 % 0.15/0.34 % DateTime : Tue Jun 2 11:26:13 EDT 2026 % 0.15/0.34 % CPUTime : % 0.30/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.44/0.66 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.44/0.66 % SZS status Theorem % 0.44/0.66 % SZS output start Proof % 0.44/0.66 ( % 0.44/0.66 (declare-sort $$unsorted 0) % 0.44/0.66 (declare-const tptp.xr $$unsorted) % 0.44/0.66 (declare-const tptp.xk $$unsorted) % 0.44/0.66 (declare-const tptp.doDivides0 (-> $$unsorted $$unsorted Bool)) % 0.44/0.66 (declare-const tptp.xm $$unsorted) % 0.44/0.66 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.66 (declare-const tptp.sdtlseqdt0 (-> $$unsorted $$unsorted Bool)) % 0.44/0.66 (declare-const tptp.xn $$unsorted) % 0.44/0.66 (declare-const tptp.aNaturalNumber0 (-> $$unsorted Bool)) % 0.44/0.66 (declare-const tptp.sz00 $$unsorted) % 0.44/0.66 (declare-const tptp.sdtsldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.66 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.66 (declare-const tptp.sdtmndt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.66 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 0.44/0.66 (declare-const tptp.isPrime0 (-> $$unsorted Bool)) % 0.44/0.66 (declare-const tptp.sz10 $$unsorted) % 0.44/0.66 (declare-const tptp.xp $$unsorted) % 0.44/0.66 (define @t1 () (@var "W0" $$unsorted)) % 0.44/0.66 (define @t2 () (tptp.aNaturalNumber0 @t1)) % 0.44/0.66 (define @t3 () (@list @t1)) % 0.44/0.66 (define @t4 () (@var "W1" $$unsorted)) % 0.44/0.66 (define @t5 () (tptp.sdtpldt0 @t1 @t4)) % 0.44/0.66 (define @t6 () (tptp.aNaturalNumber0 @t4)) % 0.44/0.66 (define @t7 () (and @t2 @t6)) % 0.44/0.66 (define @t8 () (@list @t1 @t4)) % 0.44/0.66 (define @t9 () (tptp.sdtasdt0 @t1 @t4)) % 0.44/0.66 (define @t10 () (tptp.sdtpldt0 @t4 @t1)) % 0.44/0.66 (define @t11 () (@var "W2" $$unsorted)) % 0.44/0.66 (define @t12 () (tptp.sdtpldt0 @t4 @t11)) % 0.44/0.66 (define @t13 () (tptp.sdtpldt0 @t5 @t11)) % 0.44/0.66 (define @t14 () (tptp.aNaturalNumber0 @t11)) % 0.44/0.66 (define @t15 () (and @t2 @t6 @t14)) % 0.44/0.66 (define @t16 () (@list @t1 @t4 @t11)) % 0.44/0.66 (define @t17 () (tptp.sdtasdt0 @t4 @t1)) % 0.44/0.66 (define @t18 () (tptp.sdtasdt0 @t11 @t1)) % 0.44/0.66 (define @t19 () (tptp.sdtasdt0 @t1 @t11)) % 0.44/0.66 (define @t20 () (= @t4 @t11)) % 0.44/0.66 (define @t21 () (tptp.sdtpldt0 @t11 @t1)) % 0.44/0.66 (define @t22 () (tptp.sdtpldt0 @t1 @t11)) % 0.44/0.66 (define @t23 () (= @t17 @t18)) % 0.44/0.66 (define @t24 () (= @t9 @t19)) % 0.44/0.66 (define @t25 () (= @t1 tptp.sz00)) % 0.44/0.66 (define @t26 () (not @t25)) % 0.44/0.66 (define @t27 () (= @t4 tptp.sz00)) % 0.44/0.66 (define @t28 () (and @t14 (= @t22 @t4))) % 0.44/0.66 (define @t29 () (@list @t11)) % 0.44/0.66 (define @t30 () (tptp.sdtlseqdt0 @t1 @t4)) % 0.44/0.66 (define @t31 () (= @t1 @t4)) % 0.44/0.66 (define @t32 () (tptp.sdtlseqdt0 @t4 @t1)) % 0.44/0.66 (define @t33 () (tptp.sdtlseqdt0 @t4 @t11)) % 0.44/0.66 (define @t34 () (= @t4 @t1)) % 0.44/0.66 (define @t35 () (not @t34)) % 0.44/0.66 (define @t36 () (and @t35 @t32)) % 0.44/0.66 (define @t37 () (or @t30 @t36)) % 0.44/0.66 (define @t38 () (=> @t7 @t37)) % 0.44/0.66 (define @t39 () (forall @t8 @t38)) % 0.44/0.66 (define @t40 () (tptp.sdtpldt0 @t11 @t4)) % 0.44/0.66 (define @t41 () (not @t31)) % 0.44/0.66 (define @t42 () (and @t41 @t30)) % 0.44/0.66 (define @t43 () (= @t1 tptp.sz10)) % 0.44/0.66 (define @t44 () (tptp.iLess0 @t1 @t4)) % 0.44/0.66 (define @t45 () (and @t14 (= @t4 @t19))) % 0.44/0.66 (define @t46 () (tptp.doDivides0 @t1 @t4)) % 0.44/0.66 (define @t47 () (tptp.sdtsldt0 @t4 @t1)) % 0.44/0.66 (define @t48 () (and @t26 @t46)) % 0.44/0.66 (define @t49 () (tptp.doDivides0 @t1 @t11)) % 0.44/0.66 (define @t50 () (tptp.doDivides0 @t1 @t12)) % 0.44/0.66 (define @t51 () (tptp.doDivides0 @t4 @t1)) % 0.44/0.66 (define @t52 () (@list @t4)) % 0.44/0.66 (define @t53 () (not @t43)) % 0.44/0.66 (define @t54 () (tptp.aNaturalNumber0 tptp.xp)) % 0.44/0.66 (define @t55 () (@var "W3" $$unsorted)) % 0.44/0.66 (define @t56 () (tptp.sdtasdt0 @t11 @t55)) % 0.44/0.66 (define @t57 () (tptp.aNaturalNumber0 @t55)) % 0.44/0.66 (define @t58 () (@list @t55)) % 0.44/0.66 (define @t59 () (@var "W4" $$unsorted)) % 0.44/0.66 (define @t60 () (tptp.sdtasdt0 tptp.xn tptp.xm)) % 0.44/0.66 (define @t61 () (tptp.sdtpldt0 tptp.xp @t1)) % 0.44/0.66 (define @t62 () (tptp.aNaturalNumber0 tptp.xk)) % 0.44/0.66 (define @t63 () (= tptp.xk tptp.sz10)) % 0.44/0.66 (define @t64 () (= tptp.xk tptp.sz00)) % 0.44/0.66 (define @t65 () (tptp.sdtasdt0 tptp.xr @t1)) % 0.44/0.66 (define @t66 () (tptp.sdtlseqdt0 tptp.xk tptp.xp)) % 0.44/0.66 (define @t67 () (tptp.sdtpldt0 tptp.xk @t1)) % 0.44/0.66 (define @t68 () (and @t2 (= @t67 tptp.xp))) % 0.44/0.66 (define @t69 () (exists @t3 @t68)) % 0.44/0.66 (define @t70 () (or @t69 @t66)) % 0.44/0.66 (define @t71 () (not (= tptp.xk tptp.xp))) % 0.44/0.66 (define @t72 () (and @t71 @t70)) % 0.44/0.66 (define @t73 () (tptp.sdtlseqdt0 tptp.xp tptp.xk)) % 0.44/0.66 (define @t74 () (= @t61 tptp.xk)) % 0.44/0.66 (define @t75 () (and @t2 @t74)) % 0.44/0.66 (define @t76 () (exists @t3 @t75)) % 0.44/0.66 (define @t77 () (or @t76 @t73)) % 0.44/0.66 (define @t78 () (not @t77)) % 0.44/0.66 (define @t79 () (=> @t78 @t72)) % 0.44/0.66 (define @t80 () (not @t79)) % 0.44/0.66 (define @t81 () (and @t41 @t32)) % 0.44/0.66 (define @t82 () (not @t6)) % 0.44/0.66 (define @t83 () (not @t2)) % 0.44/0.66 (define @t84 () (or @t83 @t82 @t30 @t81)) % 0.44/0.66 (define @t85 () (or @t30 @t81)) % 0.44/0.66 (define @t86 () (= tptp.xp @t67)) % 0.44/0.66 (define @t87 () (and @t2 @t86)) % 0.44/0.66 (define @t88 () (forall @t3 (not @t87))) % 0.44/0.66 (define @t89 () (not @t88)) % 0.44/0.66 (define @t90 () (forall @t3 (not @t75))) % 0.44/0.66 (define @t91 () (not @t90)) % 0.44/0.66 (define @t92 () (= tptp.xp tptp.xk)) % 0.44/0.66 (define @t93 () (not @t92)) % 0.44/0.66 (define @t94 () (and @t93 @t66)) % 0.44/0.66 (define @t95 () (not @t62)) % 0.44/0.66 (define @t96 () (not @t54)) % 0.44/0.66 (define @t97 () (or @t96 @t95 @t73 @t94)) % 0.44/0.66 (define @t98 () (@list false)) % 0.44/0.66 (define @t99 () (and @t71 @t73)) % 0.44/0.66 (define @t100 () (or @t95 @t96 @t66 @t99)) % 0.44/0.66 (define @t101 () (forall @t8 @t84)) % 0.44/0.66 (define @t102 () (and @t93 @t73)) % 0.44/0.66 (define @t103 () (or @t95 @t96 @t66 @t102)) % 0.44/0.66 (define @t104 () (not @t102)) % 0.44/0.66 (define @t105 () (or (not (forall @t3 (or @t83 (not @t86)))) @t66)) % 0.44/0.66 (define @t106 () (not @t105)) % 0.44/0.66 (assume @p1 (forall @t3 (=> @t2 true))) % 0.44/0.66 (assume @p2 (tptp.aNaturalNumber0 tptp.sz00)) % 0.44/0.66 (assume @p3 (and (tptp.aNaturalNumber0 tptp.sz10) (not (= tptp.sz10 tptp.sz00)))) % 0.44/0.66 (assume @p4 (forall @t8 (=> @t7 (tptp.aNaturalNumber0 @t5)))) % 0.44/0.66 (assume @p5 (forall @t8 (=> @t7 (tptp.aNaturalNumber0 @t9)))) % 0.44/0.66 (assume @p6 (forall @t8 (=> @t7 (= @t5 @t10)))) % 0.44/0.66 (assume @p7 (forall @t16 (=> @t15 (= @t13 (tptp.sdtpldt0 @t1 @t12))))) % 0.44/0.66 (assume @p8 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 tptp.sz00) @t1) (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1)))))) % 0.44/0.66 (assume @p9 (forall @t8 (=> @t7 (= @t9 @t17)))) % 0.44/0.66 (assume @p10 (forall @t16 (=> @t15 (= (tptp.sdtasdt0 @t9 @t11) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t4 @t11)))))) % 0.44/0.66 (assume @p11 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 0.44/0.66 (assume @p12 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 0.44/0.66 (assume @p13 (forall @t16 (=> @t15 (and (= (tptp.sdtasdt0 @t1 @t12) (tptp.sdtpldt0 @t9 @t19)) (= (tptp.sdtasdt0 @t12 @t1) (tptp.sdtpldt0 @t17 @t18)))))) % 0.44/0.66 (assume @p14 (forall @t16 (=> @t15 (=> (or (= @t5 @t22) (= @t10 @t21)) @t20)))) % 0.44/0.66 (assume @p15 (forall @t3 (=> @t2 (=> @t26 (forall (@list @t4 @t11) (=> (and @t6 @t14) (=> (or @t24 @t23) @t20))))))) % 0.44/0.66 (assume @p16 (forall @t8 (=> @t7 (=> (= @t5 tptp.sz00) (and @t25 @t27))))) % 0.44/0.66 (assume @p17 (forall @t8 (=> @t7 (=> (= @t9 tptp.sz00) (or @t25 @t27))))) % 0.44/0.66 (assume @p18 (forall @t8 (=> @t7 (= @t30 (exists @t29 @t28))))) % 0.44/0.66 (assume @p19 (forall @t8 (=> @t7 (=> @t30 (forall @t29 (= (= @t11 (tptp.sdtmndt0 @t4 @t1)) @t28)))))) % 0.44/0.66 (assume @p20 (forall @t3 (=> @t2 (tptp.sdtlseqdt0 @t1 @t1)))) % 0.44/0.66 (assume @p21 (forall @t8 (=> @t7 (=> (and @t30 @t32) @t31)))) % 0.44/0.66 (assume @p22 (forall @t16 (=> @t15 (=> (and @t30 @t33) (tptp.sdtlseqdt0 @t1 @t11))))) % 0.44/0.66 (assume @p23 @t39) % 0.44/0.66 (assume @p24 (forall @t8 (=> @t7 (=> @t42 (forall @t29 (=> @t14 (and (not (= @t21 @t40)) (tptp.sdtlseqdt0 @t21 @t40) (not (= @t22 @t12)) (tptp.sdtlseqdt0 @t22 @t12)))))))) % 0.44/0.66 (assume @p25 (forall @t16 (=> @t15 (=> (and @t26 (not @t20) @t33) (and (not @t24) (tptp.sdtlseqdt0 @t9 @t19) (not @t23) (tptp.sdtlseqdt0 @t17 @t18)))))) % 0.44/0.66 (assume @p26 (forall @t3 (=> @t2 (or @t25 @t43 (and (not (= tptp.sz10 @t1)) (tptp.sdtlseqdt0 tptp.sz10 @t1)))))) % 0.44/0.66 (assume @p27 (forall @t8 (=> @t7 (=> @t26 (tptp.sdtlseqdt0 @t4 @t17))))) % 0.44/0.66 (assume @p28 (forall @t8 (=> @t7 (=> @t44 true)))) % 0.44/0.66 (assume @p29 (forall @t8 (=> @t7 (=> @t42 @t44)))) % 0.44/0.66 (assume @p30 (forall @t8 (=> @t7 (= @t46 (exists @t29 @t45))))) % 0.44/0.66 (assume @p31 (forall @t8 (=> @t7 (=> @t48 (forall @t29 (= (= @t11 @t47) @t45)))))) % 0.44/0.66 (assume @p32 (forall @t16 (=> @t15 (=> (and @t46 (tptp.doDivides0 @t4 @t11)) @t49)))) % 0.44/0.66 (assume @p33 (forall @t16 (=> @t15 (=> (and @t46 @t49) @t50)))) % 0.44/0.66 (assume @p34 (forall @t16 (=> @t15 (=> (and @t46 @t50) @t49)))) % 0.44/0.66 (assume @p35 (forall @t8 (=> @t7 (=> (and @t46 (not @t27)) @t30)))) % 0.44/0.66 (assume @p36 (forall @t8 (=> @t7 (=> @t48 (forall @t29 (=> @t14 (= (tptp.sdtasdt0 @t11 @t47) (tptp.sdtsldt0 (tptp.sdtasdt0 @t11 @t4) @t1)))))))) % 0.44/0.66 (assume @p37 (forall @t3 (=> @t2 (= (tptp.isPrime0 @t1) (and @t26 @t53 (forall @t52 (=> (and @t6 @t51) (or (= @t4 tptp.sz10) @t34)))))))) % 0.44/0.66 (assume @p38 (forall @t3 (=> (and @t2 @t26 @t53) (exists @t52 (and @t6 @t51 (tptp.isPrime0 @t4)))))) % 0.44/0.66 (assume @p39 (and (tptp.aNaturalNumber0 tptp.xn) (tptp.aNaturalNumber0 tptp.xm) @t54)) % 0.44/0.66 (assume @p40 (forall @t16 (=> @t15 (=> (and (or (and (not (= @t11 tptp.sz00)) (not (= @t11 tptp.sz10)) (forall @t58 (=> (and @t57 (exists (@list @t59) (and (tptp.aNaturalNumber0 @t59) (= @t11 (tptp.sdtasdt0 @t55 @t59)))) (tptp.doDivides0 @t55 @t11)) (or (= @t55 tptp.sz10) (= @t55 @t11))))) (tptp.isPrime0 @t11)) (or (exists @t58 (and @t57 (= @t9 @t56))) (tptp.doDivides0 @t11 @t9))) (=> (tptp.iLess0 @t13 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)) (or (and (exists @t58 (and @t57 (= @t1 @t56))) (tptp.doDivides0 @t11 @t1)) (and (exists @t58 (and @t57 (= @t4 @t56))) (tptp.doDivides0 @t11 @t4)))))))) % 0.44/0.66 (assume @p41 (and (not (= tptp.xp tptp.sz00)) (not (= tptp.xp tptp.sz10)) (forall @t3 (=> (and @t2 (or (exists @t52 (and @t6 (= tptp.xp @t9))) (tptp.doDivides0 @t1 tptp.xp))) (or @t43 (= @t1 tptp.xp)))) (tptp.isPrime0 tptp.xp) (exists @t3 (and @t2 (= @t60 (tptp.sdtasdt0 tptp.xp @t1)))) (tptp.doDivides0 tptp.xp @t60))) % 0.44/0.66 (assume @p42 (not (or (exists @t3 (and @t2 (= @t61 tptp.xn))) (tptp.sdtlseqdt0 tptp.xp tptp.xn)))) % 0.44/0.66 (assume @p43 (not (or (exists @t3 (and @t2 (= @t61 tptp.xm))) (tptp.sdtlseqdt0 tptp.xp tptp.xm)))) % 0.44/0.66 (assume @p44 (and (not (= tptp.xn tptp.xp)) (exists @t3 (and @t2 (= (tptp.sdtpldt0 tptp.xn @t1) tptp.xp))) (tptp.sdtlseqdt0 tptp.xn tptp.xp) (not (= tptp.xm tptp.xp)) (exists @t3 (and @t2 (= (tptp.sdtpldt0 tptp.xm @t1) tptp.xp))) (tptp.sdtlseqdt0 tptp.xm tptp.xp))) % 0.44/0.66 (assume @p45 (and @t62 (= @t60 (tptp.sdtasdt0 tptp.xp tptp.xk)) (= tptp.xk (tptp.sdtsldt0 @t60 tptp.xp)))) % 0.44/0.66 (assume @p46 (not (or @t64 @t63))) % 0.44/0.66 (assume @p47 (and (not @t64) (not @t63))) % 0.44/0.66 (assume @p48 (and (tptp.aNaturalNumber0 tptp.xr) (exists @t3 (and @t2 (= tptp.xk @t65))) (tptp.doDivides0 tptp.xr tptp.xk) (not (= tptp.xr tptp.sz00)) (not (= tptp.xr tptp.sz10)) (forall @t3 (=> (and @t2 (or (exists @t52 (and @t6 (= tptp.xr @t9))) (tptp.doDivides0 @t1 tptp.xr))) (or @t43 (= @t1 tptp.xr)))) (tptp.isPrime0 tptp.xr))) % 0.44/0.66 (assume @p49 (and (exists @t3 (and @t2 (= (tptp.sdtpldt0 tptp.xr @t1) tptp.xk))) (exists @t3 (and @t2 (= @t60 @t65))) (tptp.doDivides0 tptp.xr @t60))) % 0.44/0.66 (assume @p50 @t80) % 0.44/0.66 (assume @p51 true) % 0.44/0.66 (step @p52 :rule aci_norm :args ((= (or (or @t83 @t82) @t85) @t84))) % 0.44/0.66 (step @p53 :rule refl :args (@t85)) % 0.44/0.66 (step @p54 :rule bool-and-de-morgan :args (@t2 @t6 true)) % 0.44/0.66 (step @p55 :rule nary_cong :premises (@p54 @p53) :args ((or (not @t7) @t85))) % 0.44/0.66 (step @p56 :rule trans :premises (@p55 @p52)) % 0.44/0.66 (step @p57 :rule bool-impl-elim :args (@t7 @t85)) % 0.44/0.66 (step @p58 :rule trans :premises (@p57 @p56)) % 0.44/0.66 (step @p59 :rule cong :premises (@p58) :args ((forall @t8 (=> @t7 @t85)))) % 0.44/0.66 (step @p60 :rule refl :args (@t32)) % 0.44/0.66 (step @p61 :rule eq-symm :args (@t4 @t1)) % 0.44/0.66 (step @p62 :rule cong :premises (@p61) :args (@t35)) % 0.44/0.66 (step @p63 :rule nary_cong :premises (@p62 @p60) :args (@t36)) % 0.44/0.66 (step @p64 :rule refl :args (@t30)) % 0.44/0.66 (step @p65 :rule nary_cong :premises (@p64 @p63) :args (@t37)) % 0.44/0.66 (step @p66 :rule refl :args (@t7)) % 0.44/0.66 (step @p67 :rule cong :premises (@p66 @p65) :args (@t38)) % 0.44/0.66 (step @p68 :rule cong :premises (@p67) :args (@t39)) % 0.44/0.66 (step @p69 :rule trans :premises (@p68 @p59)) % 0.44/0.66 (step @p70 :rule eq_resolve :premises (@p23 @p69)) % 0.44/0.66 (step @p71 :rule instantiate :premises (@p70) :args ((@list tptp.xp tptp.xk))) % 0.44/0.66 (step @p72 :rule and_elim :premises (@p45) :args (0)) % 0.44/0.66 (step @p73 :rule and_elim :premises (@p39) :args (2)) % 0.44/0.66 (step @p74 :rule refl :args (@t66)) % 0.44/0.66 (step @p75 :rule bool-and-de-morgan :args (@t2 @t86 true)) % 0.44/0.66 (step @p76 :rule cong :premises (@p75) :args (@t88)) % 0.44/0.66 (step @p77 :rule cong :premises (@p76) :args (@t89)) % 0.44/0.66 (step @p78 :rule exists-elim :args ((= (exists @t3 @t87) @t89))) % 0.44/0.66 (step @p79 :rule trans :premises (@p78 @p77)) % 0.44/0.66 (step @p80 :rule eq-symm :args (@t67 tptp.xp)) % 0.44/0.66 (step @p81 :rule refl :args (@t2)) % 0.44/0.66 (step @p82 :rule nary_cong :premises (@p81 @p80) :args (@t68)) % 0.44/0.66 (step @p83 :rule cong :premises (@p82) :args (@t69)) % 0.44/0.66 (step @p84 :rule trans :premises (@p83 @p79)) % 0.44/0.66 (step @p85 :rule nary_cong :premises (@p84 @p74) :args (@t70)) % 0.44/0.66 (step @p86 :rule eq-symm :args (tptp.xk tptp.xp)) % 0.44/0.66 (step @p87 :rule cong :premises (@p86) :args (@t71)) % 0.44/0.66 (step @p88 :rule nary_cong :premises (@p87 @p85) :args (@t72)) % 0.44/0.66 (step @p89 :rule refl :args (@t73)) % 0.44/0.66 (step @p90 :rule bool-and-de-morgan :args (@t2 @t74 true)) % 0.44/0.66 (step @p91 :rule cong :premises (@p90) :args (@t90)) % 0.44/0.66 (step @p92 :rule cong :premises (@p91) :args (@t91)) % 0.44/0.66 (step @p93 :rule exists-elim :args ((= @t76 @t91))) % 0.44/0.66 (step @p94 :rule trans :premises (@p93 @p92)) % 0.44/0.66 (step @p95 :rule nary_cong :premises (@p94 @p89) :args (@t77)) % 0.44/0.66 (step @p96 :rule cong :premises (@p95) :args (@t78)) % 0.44/0.66 (step @p97 :rule cong :premises (@p96 @p88) :args (@t79)) % 0.44/0.66 (step @p98 :rule cong :premises (@p97) :args (@t80)) % 0.44/0.66 (step @p99 :rule eq_resolve :premises (@p50 @p98)) % 0.44/0.66 (step @p100 :rule not_implies_elim1 :premises (@p99)) % 0.44/0.66 (step @p101 :rule not_or_elim :premises (@p100) :args (1)) % 0.44/0.66 (step @p102 :rule cnf_or_pos :args (@t97)) % 0.44/0.66 (step @p103 :rule reordering :premises (@p102) :args ((or @t73 @t96 @t95 @t94 (not @t97)))) % 0.44/0.66 (step @p104 :rule chain_m_resolution :premises (@p103 @p101 @p73 @p72 @p71) :args (@t94 (@list true false false false) (@list @t73 @t54 @t62 @t97))) % 0.44/0.66 (step @p105 :rule cnf_and_pos :args (@t94 0)) % 0.44/0.66 (step @p106 :rule reordering :premises (@p105) :args ((or @t93 (not @t94)))) % 0.44/0.66 (step @p107 :rule chain_m_resolution :premises (@p106 @p104) :args (@t93 @t98 (@list @t94))) % 0.44/0.66 (step @p108 :rule nary_cong :premises (@p87 @p89) :args (@t99)) % 0.44/0.66 (step @p109 :rule refl :args (@t96)) % 0.44/0.66 (step @p110 :rule refl :args (@t95)) % 0.44/0.66 (step @p111 :rule nary_cong :premises (@p110 @p109 @p74 @p108) :args (@t100)) % 0.44/0.66 (step @p112 :rule refl :args (@t101)) % 0.44/0.66 (step @p113 :rule cong :premises (@p112 @p111) :args ((=> @t101 @t100))) % 0.44/0.66 (assume-push @p136 @t101) % 0.44/0.66 (step @p115 :rule instantiate :premises (@p70) :args ((@list tptp.xk tptp.xp))) % 0.44/0.66 (step-pop @p137 :rule scope :premises (@p115)) % 0.44/0.66 (step @p116 :rule process_scope :premises (@p137) :args (@t100)) % 0.44/0.66 (step @p118 :rule eq_resolve :premises (@p116 @p113)) % 0.44/0.66 (step @p119 :rule implies_elim :premises (@p118)) % 0.44/0.66 (step @p120 :rule chain_m_resolution :premises (@p119 @p70) :args (@t103 @t98 (@list @t101))) % 0.44/0.66 (step @p121 :rule cnf_and_pos :args (@t102 1)) % 0.44/0.66 (step @p122 :rule reordering :premises (@p121) :args ((or @t73 @t104))) % 0.44/0.66 (step @p123 :rule chain_m_resolution :premises (@p122 @p101) :args (@t104 (@list true) (@list @t73))) % 0.44/0.66 (step @p124 :rule cnf_or_pos :args (@t103)) % 0.44/0.66 (step @p125 :rule reordering :premises (@p124) :args ((or @t66 @t96 @t95 @t102 (not @t103)))) % 0.44/0.66 (step @p126 :rule chain_m_resolution :premises (@p125 @p73 @p72 @p123 @p120) :args (@t66 (@list false false true false) (@list @t54 @t62 @t102 @t103))) % 0.44/0.66 (step @p127 :rule cnf_or_neg :args (@t105 1)) % 0.44/0.66 (step @p128 :rule chain_m_resolution :premises (@p127 @p126) :args (@t105 @t98 (@list @t66))) % 0.44/0.66 (step @p129 :rule refl :args (@t106)) % 0.44/0.66 (step @p130 :rule bool-double-not-elim :args (@t92)) % 0.44/0.66 (step @p131 :rule nary_cong :premises (@p130 @p129) :args ((or (not @t93) @t106))) % 0.44/0.66 (step @p132 :rule not_implies_elim2 :premises (@p99)) % 0.44/0.66 (step @p133 :rule not_and :premises (@p132)) % 0.44/0.66 (step @p134 :rule eq_resolve :premises (@p133 @p131)) % 0.44/0.66 (step @p135 false :rule chain_m_resolution :premises (@p134 @p128 @p107) :args (false (@list false true) (@list @t105 @t92))) % 0.44/0.66 ) % 0.44/0.66 % SZS output end Proof % 0.44/0.66 % cvc5 exiting %------------------------------------------------------------------------------