%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM492+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 : n005.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 08:39:36 AM UTC 2026 % Result : Theorem 5.12s 5.31s % Output : Proof 5.12s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM492+1 : TPTP v9.2.1. Released v4.0.0. % 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n005.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 11:24:03 EDT 2026 % 0.16/0.34 % CPUTime : % 0.27/0.50 %----Proving TF0_NAR, FOF, or CNF % 5.12/5.31 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 5.12/5.31 % SZS status Theorem % 5.12/5.31 % SZS output start Proof % 5.12/5.31 ( % 5.12/5.31 (declare-sort $$unsorted 0) % 5.12/5.31 (declare-const tptp.doDivides0 (-> $$unsorted $$unsorted Bool)) % 5.12/5.31 (declare-const tptp.xm $$unsorted) % 5.12/5.31 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 5.12/5.31 (declare-const tptp.xr $$unsorted) % 5.12/5.31 (declare-const tptp.sdtlseqdt0 (-> $$unsorted $$unsorted Bool)) % 5.12/5.31 (declare-const tptp.xn $$unsorted) % 5.12/5.31 (declare-const tptp.aNaturalNumber0 (-> $$unsorted Bool)) % 5.12/5.31 (declare-const tptp.sz00 $$unsorted) % 5.12/5.31 (declare-const tptp.sdtsldt0 (-> $$unsorted $$unsorted $$unsorted)) % 5.12/5.31 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 5.12/5.31 (declare-const tptp.sdtmndt0 (-> $$unsorted $$unsorted $$unsorted)) % 5.12/5.31 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 5.12/5.31 (declare-const tptp.isPrime0 (-> $$unsorted Bool)) % 5.12/5.31 (declare-const tptp.sz10 $$unsorted) % 5.12/5.31 (declare-const tptp.xp $$unsorted) % 5.12/5.31 (define @t1 () (@var "W0" $$unsorted)) % 5.12/5.31 (define @t2 () (tptp.aNaturalNumber0 @t1)) % 5.12/5.31 (define @t3 () (@list @t1)) % 5.12/5.31 (define @t4 () (@var "W1" $$unsorted)) % 5.12/5.31 (define @t5 () (tptp.sdtpldt0 @t1 @t4)) % 5.12/5.31 (define @t6 () (tptp.aNaturalNumber0 @t4)) % 5.12/5.31 (define @t7 () (and @t2 @t6)) % 5.12/5.31 (define @t8 () (@list @t1 @t4)) % 5.12/5.31 (define @t9 () (tptp.sdtasdt0 @t1 @t4)) % 5.12/5.31 (define @t10 () (tptp.aNaturalNumber0 @t9)) % 5.12/5.31 (define @t11 () (forall @t8 (=> @t7 @t10))) % 5.12/5.31 (define @t12 () (tptp.sdtpldt0 @t4 @t1)) % 5.12/5.31 (define @t13 () (@var "W2" $$unsorted)) % 5.12/5.31 (define @t14 () (tptp.sdtpldt0 @t4 @t13)) % 5.12/5.31 (define @t15 () (tptp.sdtpldt0 @t5 @t13)) % 5.12/5.31 (define @t16 () (tptp.aNaturalNumber0 @t13)) % 5.12/5.31 (define @t17 () (and @t2 @t6 @t16)) % 5.12/5.31 (define @t18 () (@list @t1 @t4 @t13)) % 5.12/5.31 (define @t19 () (tptp.sdtasdt0 @t4 @t1)) % 5.12/5.31 (define @t20 () (tptp.sdtasdt0 @t13 @t1)) % 5.12/5.31 (define @t21 () (tptp.sdtasdt0 @t1 @t13)) % 5.12/5.31 (define @t22 () (= @t4 @t13)) % 5.12/5.31 (define @t23 () (tptp.sdtpldt0 @t13 @t1)) % 5.12/5.31 (define @t24 () (tptp.sdtpldt0 @t1 @t13)) % 5.12/5.31 (define @t25 () (= @t19 @t20)) % 5.12/5.31 (define @t26 () (= @t9 @t21)) % 5.12/5.31 (define @t27 () (and @t6 @t16)) % 5.12/5.31 (define @t28 () (= @t1 tptp.sz00)) % 5.12/5.31 (define @t29 () (not @t28)) % 5.12/5.31 (define @t30 () (= @t4 tptp.sz00)) % 5.12/5.31 (define @t31 () (and @t16 (= @t24 @t4))) % 5.12/5.31 (define @t32 () (@list @t13)) % 5.12/5.31 (define @t33 () (tptp.sdtlseqdt0 @t1 @t4)) % 5.12/5.31 (define @t34 () (tptp.sdtmndt0 @t4 @t1)) % 5.12/5.31 (define @t35 () (= @t13 @t34)) % 5.12/5.31 (define @t36 () (forall @t32 (= @t35 @t31))) % 5.12/5.31 (define @t37 () (=> @t33 @t36)) % 5.12/5.31 (define @t38 () (=> @t7 @t37)) % 5.12/5.31 (define @t39 () (forall @t8 @t38)) % 5.12/5.31 (define @t40 () (= @t1 @t4)) % 5.12/5.31 (define @t41 () (tptp.sdtlseqdt0 @t4 @t1)) % 5.12/5.31 (define @t42 () (tptp.sdtlseqdt0 @t4 @t13)) % 5.12/5.31 (define @t43 () (= @t4 @t1)) % 5.12/5.31 (define @t44 () (tptp.sdtpldt0 @t13 @t4)) % 5.12/5.31 (define @t45 () (and (not @t40) @t33)) % 5.12/5.31 (define @t46 () (= @t1 tptp.sz10)) % 5.12/5.31 (define @t47 () (tptp.iLess0 @t1 @t4)) % 5.12/5.31 (define @t48 () (and @t16 (= @t4 @t21))) % 5.12/5.31 (define @t49 () (tptp.doDivides0 @t1 @t4)) % 5.12/5.31 (define @t50 () (tptp.sdtsldt0 @t4 @t1)) % 5.12/5.31 (define @t51 () (and @t29 @t49)) % 5.12/5.31 (define @t52 () (tptp.doDivides0 @t1 @t13)) % 5.12/5.31 (define @t53 () (tptp.doDivides0 @t1 @t14)) % 5.12/5.31 (define @t54 () (and @t49 @t53)) % 5.12/5.31 (define @t55 () (=> @t54 @t52)) % 5.12/5.31 (define @t56 () (forall @t18 (=> @t17 @t55))) % 5.12/5.31 (define @t57 () (tptp.doDivides0 @t4 @t1)) % 5.12/5.31 (define @t58 () (@list @t4)) % 5.12/5.31 (define @t59 () (not @t46)) % 5.12/5.31 (define @t60 () (tptp.aNaturalNumber0 tptp.xp)) % 5.12/5.31 (define @t61 () (tptp.aNaturalNumber0 tptp.xm)) % 5.12/5.31 (define @t62 () (tptp.aNaturalNumber0 tptp.xn)) % 5.12/5.31 (define @t63 () (tptp.sdtasdt0 tptp.xn tptp.xm)) % 5.12/5.31 (define @t64 () (tptp.doDivides0 tptp.xp @t63)) % 5.12/5.31 (define @t65 () (tptp.sdtlseqdt0 tptp.xp tptp.xn)) % 5.12/5.31 (define @t66 () (tptp.sdtmndt0 tptp.xn tptp.xp)) % 5.12/5.31 (define @t67 () (= tptp.xr @t66)) % 5.12/5.31 (define @t68 () (= tptp.xn (tptp.sdtpldt0 tptp.xp tptp.xr))) % 5.12/5.31 (define @t69 () (tptp.sdtasdt0 tptp.xr tptp.xm)) % 5.12/5.31 (define @t70 () (tptp.sdtasdt0 tptp.xp tptp.xm)) % 5.12/5.31 (define @t71 () (tptp.sdtpldt0 @t70 @t69)) % 5.12/5.31 (define @t72 () (tptp.doDivides0 tptp.xp @t70)) % 5.12/5.31 (define @t73 () (tptp.doDivides0 tptp.xp @t69)) % 5.12/5.31 (define @t74 () (@var "BOUND_VARIABLE_7869" $$unsorted)) % 5.12/5.31 (define @t75 () (and (tptp.aNaturalNumber0 @t74) (= @t4 (tptp.sdtpldt0 @t1 @t74)))) % 5.12/5.31 (define @t76 () (= @t74 @t34)) % 5.12/5.31 (define @t77 () (not @t33)) % 5.12/5.31 (define @t78 () (not @t6)) % 5.12/5.31 (define @t79 () (not @t2)) % 5.12/5.31 (define @t80 () (= @t76 @t75)) % 5.12/5.31 (define @t81 () (or @t79 @t78 @t77 @t80)) % 5.12/5.31 (define @t82 () (@list @t1 @t4 @t74)) % 5.12/5.31 (define @t83 () (forall @t82 @t81)) % 5.12/5.31 (define @t84 () (@list @t74)) % 5.12/5.31 (define @t85 () (forall @t84 @t81)) % 5.12/5.31 (define @t86 () (forall @t84 @t80)) % 5.12/5.31 (define @t87 () (or @t79 @t78 @t77 @t86)) % 5.12/5.31 (define @t88 () (and @t16 (= @t4 @t24))) % 5.12/5.31 (define @t89 () (forall @t32 (= @t35 @t88))) % 5.12/5.31 (define @t90 () (or @t79 @t78 @t77 @t89)) % 5.12/5.31 (define @t91 () (or @t79 @t78)) % 5.12/5.31 (define @t92 () (=> @t33 @t89)) % 5.12/5.31 (define @t93 () (not @t7)) % 5.12/5.31 (define @t94 () (tptp.aNaturalNumber0 tptp.xr)) % 5.12/5.31 (define @t95 () (and @t94 @t68)) % 5.12/5.31 (define @t96 () (= @t95 (= @t66 tptp.xr))) % 5.12/5.31 (define @t97 () (not @t65)) % 5.12/5.31 (define @t98 () (not @t62)) % 5.12/5.31 (define @t99 () (not @t60)) % 5.12/5.31 (define @t100 () (or @t99 @t98 @t97 @t96)) % 5.12/5.31 (define @t101 () (forall @t82 (or @t79 @t78 @t77 (= @t75 (= @t34 @t74))))) % 5.12/5.31 (define @t102 () (= @t67 @t95)) % 5.12/5.31 (define @t103 () (or @t99 @t98 @t97 @t102)) % 5.12/5.31 (define @t104 () (not @t53)) % 5.12/5.31 (define @t105 () (not @t49)) % 5.12/5.31 (define @t106 () (not @t16)) % 5.12/5.31 (define @t107 () (or @t105 @t104 @t52)) % 5.12/5.31 (define @t108 () (or @t79 @t78 @t106)) % 5.12/5.31 (define @t109 () (tptp.doDivides0 tptp.xp @t71)) % 5.12/5.31 (define @t110 () (tptp.aNaturalNumber0 @t70)) % 5.12/5.31 (define @t111 () (not @t61)) % 5.12/5.31 (define @t112 () (or @t99 @t111 @t110)) % 5.12/5.31 (define @t113 () (not @t109)) % 5.12/5.31 (define @t114 () (not @t72)) % 5.12/5.31 (define @t115 () (tptp.aNaturalNumber0 @t69)) % 5.12/5.31 (define @t116 () (not @t115)) % 5.12/5.31 (define @t117 () (not @t110)) % 5.12/5.31 (define @t118 () (or @t99 @t117 @t116 @t114 @t113 @t73)) % 5.12/5.31 (define @t119 () (not @t94)) % 5.12/5.31 (define @t120 () (or @t119 @t111 @t115)) % 5.12/5.31 (define @t121 () (not @t95)) % 5.12/5.31 (define @t122 () (not @t102)) % 5.12/5.31 (assume @p1 (forall @t3 (=> @t2 true))) % 5.12/5.31 (assume @p2 (tptp.aNaturalNumber0 tptp.sz00)) % 5.12/5.31 (assume @p3 (and (tptp.aNaturalNumber0 tptp.sz10) (not (= tptp.sz10 tptp.sz00)))) % 5.12/5.31 (assume @p4 (forall @t8 (=> @t7 (tptp.aNaturalNumber0 @t5)))) % 5.12/5.31 (assume @p5 @t11) % 5.12/5.31 (assume @p6 (forall @t8 (=> @t7 (= @t5 @t12)))) % 5.12/5.31 (assume @p7 (forall @t18 (=> @t17 (= @t15 (tptp.sdtpldt0 @t1 @t14))))) % 5.12/5.31 (assume @p8 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 tptp.sz00) @t1) (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1)))))) % 5.12/5.31 (assume @p9 (forall @t8 (=> @t7 (= @t9 @t19)))) % 5.12/5.31 (assume @p10 (forall @t18 (=> @t17 (= (tptp.sdtasdt0 @t9 @t13) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t4 @t13)))))) % 5.12/5.31 (assume @p11 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 5.12/5.31 (assume @p12 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 5.12/5.31 (assume @p13 (forall @t18 (=> @t17 (and (= (tptp.sdtasdt0 @t1 @t14) (tptp.sdtpldt0 @t9 @t21)) (= (tptp.sdtasdt0 @t14 @t1) (tptp.sdtpldt0 @t19 @t20)))))) % 5.12/5.31 (assume @p14 (forall @t18 (=> @t17 (=> (or (= @t5 @t24) (= @t12 @t23)) @t22)))) % 5.12/5.31 (assume @p15 (forall @t3 (=> @t2 (=> @t29 (forall (@list @t4 @t13) (=> @t27 (=> (or @t26 @t25) @t22))))))) % 5.12/5.31 (assume @p16 (forall @t8 (=> @t7 (=> (= @t5 tptp.sz00) (and @t28 @t30))))) % 5.12/5.31 (assume @p17 (forall @t8 (=> @t7 (=> (= @t9 tptp.sz00) (or @t28 @t30))))) % 5.12/5.31 (assume @p18 (forall @t8 (=> @t7 (= @t33 (exists @t32 @t31))))) % 5.12/5.31 (assume @p19 @t39) % 5.12/5.31 (assume @p20 (forall @t3 (=> @t2 (tptp.sdtlseqdt0 @t1 @t1)))) % 5.12/5.31 (assume @p21 (forall @t8 (=> @t7 (=> (and @t33 @t41) @t40)))) % 5.12/5.31 (assume @p22 (forall @t18 (=> @t17 (=> (and @t33 @t42) (tptp.sdtlseqdt0 @t1 @t13))))) % 5.12/5.31 (assume @p23 (forall @t8 (=> @t7 (or @t33 (and (not @t43) @t41))))) % 5.12/5.31 (assume @p24 (forall @t8 (=> @t7 (=> @t45 (forall @t32 (=> @t16 (and (not (= @t23 @t44)) (tptp.sdtlseqdt0 @t23 @t44) (not (= @t24 @t14)) (tptp.sdtlseqdt0 @t24 @t14)))))))) % 5.12/5.31 (assume @p25 (forall @t18 (=> @t17 (=> (and @t29 (not @t22) @t42) (and (not @t26) (tptp.sdtlseqdt0 @t9 @t21) (not @t25) (tptp.sdtlseqdt0 @t19 @t20)))))) % 5.12/5.31 (assume @p26 (forall @t3 (=> @t2 (or @t28 @t46 (and (not (= tptp.sz10 @t1)) (tptp.sdtlseqdt0 tptp.sz10 @t1)))))) % 5.12/5.31 (assume @p27 (forall @t8 (=> @t7 (=> @t29 (tptp.sdtlseqdt0 @t4 @t19))))) % 5.12/5.31 (assume @p28 (forall @t8 (=> @t7 (=> @t47 true)))) % 5.12/5.31 (assume @p29 (forall @t8 (=> @t7 (=> @t45 @t47)))) % 5.12/5.31 (assume @p30 (forall @t8 (=> @t7 (= @t49 (exists @t32 @t48))))) % 5.12/5.31 (assume @p31 (forall @t8 (=> @t7 (=> @t51 (forall @t32 (= (= @t13 @t50) @t48)))))) % 5.12/5.31 (assume @p32 (forall @t18 (=> @t17 (=> (and @t49 (tptp.doDivides0 @t4 @t13)) @t52)))) % 5.12/5.31 (assume @p33 (forall @t18 (=> @t17 (=> (and @t49 @t52) @t53)))) % 5.12/5.31 (assume @p34 @t56) % 5.12/5.31 (assume @p35 (forall @t8 (=> @t7 (=> (and @t49 (not @t30)) @t33)))) % 5.12/5.31 (assume @p36 (forall @t8 (=> @t7 (=> @t51 (forall @t32 (=> @t16 (= (tptp.sdtasdt0 @t13 @t50) (tptp.sdtsldt0 (tptp.sdtasdt0 @t13 @t4) @t1)))))))) % 5.12/5.31 (assume @p37 (forall @t3 (=> @t2 (= (tptp.isPrime0 @t1) (and @t29 @t59 (forall @t58 (=> (and @t6 @t57) (or (= @t4 tptp.sz10) @t43)))))))) % 5.12/5.31 (assume @p38 (forall @t3 (=> (and @t2 @t29 @t59) (exists @t58 (and @t6 @t57 (tptp.isPrime0 @t4)))))) % 5.12/5.31 (assume @p39 (and @t62 @t61 @t60)) % 5.12/5.31 (assume @p40 (forall @t18 (=> @t17 (=> (and (tptp.isPrime0 @t13) (tptp.doDivides0 @t13 @t9)) (=> (tptp.iLess0 @t15 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)) (or (tptp.doDivides0 @t13 @t1) (tptp.doDivides0 @t13 @t4))))))) % 5.12/5.31 (assume @p41 (and (tptp.isPrime0 tptp.xp) @t64)) % 5.12/5.31 (assume @p42 @t65) % 5.12/5.31 (assume @p43 @t67) % 5.12/5.31 (assume @p44 (and (not (= tptp.xr tptp.xn)) (tptp.sdtlseqdt0 tptp.xr tptp.xn))) % 5.12/5.31 (assume @p45 @t68) % 5.12/5.31 (assume @p46 (= @t63 @t71)) % 5.12/5.31 (assume @p47 (= @t69 (tptp.sdtmndt0 @t63 @t70))) % 5.12/5.31 (assume @p48 (and @t64 @t72)) % 5.12/5.31 (assume @p49 (not @t73)) % 5.12/5.31 (assume @p50 true) % 5.12/5.31 (step @p51 :rule and_elim :premises (@p39) :args (0)) % 5.12/5.31 (step @p52 :rule and_elim :premises (@p39) :args (2)) % 5.12/5.31 (step @p53 :rule eq-symm :args (@t74 @t34)) % 5.12/5.31 (step @p54 :rule refl :args (@t75)) % 5.12/5.31 (step @p55 :rule cong :premises (@p54 @p53) :args ((= @t75 @t76))) % 5.12/5.31 (step @p56 :rule eq-symm :args (@t76 @t75)) % 5.12/5.31 (step @p57 :rule trans :premises (@p56 @p55)) % 5.12/5.31 (step @p58 :rule refl :args (@t77)) % 5.12/5.31 (step @p59 :rule refl :args (@t78)) % 5.12/5.31 (step @p60 :rule refl :args (@t79)) % 5.12/5.31 (step @p61 :rule nary_cong :premises (@p60 @p59 @p58 @p57) :args (@t81)) % 5.12/5.31 (step @p62 :rule cong :premises (@p61) :args (@t83)) % 5.12/5.31 (step @p63 :rule quant-merge-prenex :args ((= (forall @t8 @t85) @t83))) % 5.12/5.31 (step @p64 :rule alpha_equiv :args (@t86 (@list @t74) (@list @t13))) % 5.12/5.31 (step @p65 :rule refl :args (@t77)) % 5.12/5.31 (step @p66 :rule refl :args (@t78)) % 5.12/5.31 (step @p67 :rule refl :args (@t79)) % 5.12/5.31 (step @p68 :rule nary_cong :premises (@p67 @p66 @p65 @p64) :args (@t87)) % 5.12/5.31 (step @p69 :rule quant-miniscope-or :args ((= @t85 @t87))) % 5.12/5.31 (step @p70 :rule trans :premises (@p69 @p68)) % 5.12/5.31 (step @p71 :rule symm :premises (@p70)) % 5.12/5.31 (step @p72 :rule cong :premises (@p71) :args ((forall @t8 @t90))) % 5.12/5.31 (step @p73 :rule trans :premises (@p72 @p63)) % 5.12/5.31 (step @p74 :rule trans :premises (@p73 @p62)) % 5.12/5.31 (step @p75 :rule aci_norm :args ((= (or @t91 (or @t77 @t89)) @t90))) % 5.12/5.31 (step @p76 :rule bool-impl-elim :args (@t33 @t89)) % 5.12/5.31 (step @p77 :rule bool-and-de-morgan :args (@t2 @t6 true)) % 5.12/5.31 (step @p78 :rule nary_cong :premises (@p77 @p76) :args ((or @t93 @t92))) % 5.12/5.31 (step @p79 :rule trans :premises (@p78 @p75)) % 5.12/5.31 (step @p80 :rule bool-impl-elim :args (@t7 @t92)) % 5.12/5.31 (step @p81 :rule trans :premises (@p80 @p79)) % 5.12/5.31 (step @p82 :rule cong :premises (@p81) :args ((forall @t8 (=> @t7 @t92)))) % 5.12/5.31 (step @p83 :rule trans :premises (@p82 @p74)) % 5.12/5.31 (step @p84 :rule eq-symm :args (@t88 @t35)) % 5.12/5.31 (step @p85 :rule refl :args (@t35)) % 5.12/5.31 (step @p86 :rule eq-symm :args (@t24 @t4)) % 5.12/5.31 (step @p87 :rule refl :args (@t16)) % 5.12/5.31 (step @p88 :rule nary_cong :premises (@p87 @p86) :args (@t31)) % 5.12/5.31 (step @p89 :rule cong :premises (@p88 @p85) :args ((= @t31 @t35))) % 5.12/5.31 (step @p90 :rule trans :premises (@p89 @p84)) % 5.12/5.31 (step @p91 :rule eq-symm :args (@t35 @t31)) % 5.12/5.31 (step @p92 :rule trans :premises (@p91 @p90)) % 5.12/5.31 (step @p93 :rule cong :premises (@p92) :args (@t36)) % 5.12/5.31 (step @p94 :rule refl :args (@t33)) % 5.12/5.31 (step @p95 :rule cong :premises (@p94 @p93) :args (@t37)) % 5.12/5.31 (step @p96 :rule refl :args (@t7)) % 5.12/5.31 (step @p97 :rule cong :premises (@p96 @p95) :args (@t38)) % 5.12/5.31 (step @p98 :rule cong :premises (@p97) :args (@t39)) % 5.12/5.31 (step @p99 :rule trans :premises (@p98 @p83)) % 5.12/5.31 (step @p100 :rule eq_resolve :premises (@p19 @p99)) % 5.12/5.31 (step @p101 :rule eq-symm :args (@t95 @t67)) % 5.12/5.31 (step @p102 :rule eq-symm :args (@t66 tptp.xr)) % 5.12/5.31 (step @p103 :rule refl :args (@t95)) % 5.12/5.31 (step @p104 :rule cong :premises (@p103 @p102) :args (@t96)) % 5.12/5.31 (step @p105 :rule trans :premises (@p104 @p101)) % 5.12/5.31 (step @p106 :rule refl :args (@t97)) % 5.12/5.31 (step @p107 :rule refl :args (@t98)) % 5.12/5.31 (step @p108 :rule refl :args (@t99)) % 5.12/5.31 (step @p109 :rule nary_cong :premises (@p108 @p107 @p106 @p105) :args (@t100)) % 5.12/5.31 (step @p110 :rule refl :args (@t101)) % 5.12/5.31 (step @p111 :rule cong :premises (@p110 @p109) :args ((=> @t101 @t100))) % 5.12/5.31 (assume-push @p177 @t101) % 5.12/5.31 (step @p113 :rule instantiate :premises (@p100) :args ((@list tptp.xp tptp.xn tptp.xr))) % 5.12/5.31 (step-pop @p178 :rule scope :premises (@p113)) % 5.12/5.31 (step @p114 :rule process_scope :premises (@p178) :args (@t100)) % 5.12/5.31 (step @p116 :rule eq_resolve :premises (@p114 @p111)) % 5.12/5.31 (step @p117 :rule implies_elim :premises (@p116)) % 5.12/5.31 (step @p118 :rule chain_m_resolution :premises (@p117 @p100) :args (@t103 (@list false) (@list @t101))) % 5.12/5.31 (step @p119 :rule aci_norm :args ((= (or @t91 @t10) (or @t79 @t78 @t10)))) % 5.12/5.31 (step @p120 :rule refl :args (@t10)) % 5.12/5.31 (step @p121 :rule nary_cong :premises (@p77 @p120) :args ((or @t93 @t10))) % 5.12/5.31 (step @p122 :rule trans :premises (@p121 @p119)) % 5.12/5.31 (step @p123 :rule bool-impl-elim :args (@t7 @t10)) % 5.12/5.31 (step @p124 :rule trans :premises (@p123 @p122)) % 5.12/5.31 (step @p125 :rule cong :premises (@p124) :args (@t11)) % 5.12/5.31 (step @p126 :rule eq_resolve :premises (@p5 @p125)) % 5.12/5.31 (step @p127 :rule instantiate :premises (@p126) :args ((@list tptp.xr tptp.xm))) % 5.12/5.31 (step @p128 :rule aci_norm :args ((= (or @t108 @t107) (or @t79 @t78 @t106 @t105 @t104 @t52)))) % 5.12/5.31 (step @p129 :rule aci_norm :args ((= (or (or @t105 @t104) @t52) @t107))) % 5.12/5.31 (step @p130 :rule refl :args (@t52)) % 5.12/5.31 (step @p131 :rule bool-and-de-morgan :args (@t49 @t53 true)) % 5.12/5.31 (step @p132 :rule nary_cong :premises (@p131 @p130) :args ((or (not @t54) @t52))) % 5.12/5.31 (step @p133 :rule trans :premises (@p132 @p129)) % 5.12/5.31 (step @p134 :rule bool-impl-elim :args (@t54 @t52)) % 5.12/5.31 (step @p135 :rule trans :premises (@p134 @p133)) % 5.12/5.31 (step @p136 :rule aci_norm :args ((= (or @t79 (or @t78 @t106)) @t108))) % 5.12/5.31 (step @p137 :rule bool-and-de-morgan :args (@t6 @t16 true)) % 5.12/5.31 (step @p138 :rule nary_cong :premises (@p67 @p137) :args ((or @t79 (not @t27)))) % 5.12/5.31 (step @p139 :rule bool-and-de-morgan :args (@t2 @t6 (and @t16))) % 5.12/5.31 (step @p140 :rule trans :premises (@p139 @p138)) % 5.12/5.31 (step @p141 :rule trans :premises (@p140 @p136)) % 5.12/5.31 (step @p142 :rule nary_cong :premises (@p141 @p135) :args ((or (not @t17) @t55))) % 5.12/5.31 (step @p143 :rule trans :premises (@p142 @p128)) % 5.12/5.31 (step @p144 :rule bool-impl-elim :args (@t17 @t55)) % 5.12/5.31 (step @p145 :rule trans :premises (@p144 @p143)) % 5.12/5.31 (step @p146 :rule cong :premises (@p145) :args (@t56)) % 5.12/5.31 (step @p147 :rule eq_resolve :premises (@p34 @p146)) % 5.12/5.31 (step @p148 :rule instantiate :premises (@p147) :args ((@list tptp.xp @t70 @t69))) % 5.12/5.31 (step @p149 :rule and_elim :premises (@p41) :args (1)) % 5.12/5.31 (step @p150 :rule true_intro :premises (@p149)) % 5.12/5.31 (step @p151 :rule symm :premises (@p46)) % 5.12/5.31 (step @p152 :rule refl :args (tptp.xp)) % 5.12/5.31 (step @p153 :rule cong :premises (@p152 @p151) :args (@t109)) % 5.12/5.31 (step @p154 :rule trans :premises (@p153 @p150)) % 5.12/5.31 (step @p155 :rule true_elim :premises (@p154)) % 5.12/5.31 (step @p156 :rule instantiate :premises (@p126) :args ((@list tptp.xp tptp.xm))) % 5.12/5.31 (step @p157 :rule and_elim :premises (@p39) :args (1)) % 5.12/5.31 (step @p158 :rule cnf_or_pos :args (@t112)) % 5.12/5.31 (step @p159 :rule reordering :premises (@p158) :args ((or @t111 @t99 @t110 (not @t112)))) % 5.12/5.31 (step @p160 :rule chain_m_resolution :premises (@p159 @p157 @p52 @p156) :args (@t110 (@list false false false) (@list @t61 @t60 @t112))) % 5.12/5.31 (step @p161 :rule and_elim :premises (@p48) :args (1)) % 5.12/5.31 (step @p162 :rule cnf_or_pos :args (@t118)) % 5.12/5.31 (step @p163 :rule reordering :premises (@p162) :args ((or @t73 @t99 @t114 @t117 @t116 @t113 (not @t118)))) % 5.12/5.31 (step @p164 :rule chain_m_resolution :premises (@p163 @p49 @p52 @p161 @p160 @p155 @p148) :args (@t116 (@list true false false false false false) (@list @t73 @t60 @t72 @t110 @t109 @t118))) % 5.12/5.31 (step @p165 :rule cnf_or_pos :args (@t120)) % 5.12/5.31 (step @p166 :rule reordering :premises (@p165) :args ((or @t111 @t115 @t119 (not @t120)))) % 5.12/5.31 (step @p167 :rule chain_m_resolution :premises (@p166 @p157 @p164 @p127) :args (@t119 (@list false true false) (@list @t61 @t115 @t120))) % 5.12/5.31 (step @p168 :rule cnf_and_pos :args (@t95 0)) % 5.12/5.31 (step @p169 :rule reordering :premises (@p168) :args ((or @t94 @t121))) % 5.12/5.31 (step @p170 :rule chain_m_resolution :premises (@p169 @p167) :args (@t121 (@list true) (@list @t94))) % 5.12/5.34 (step @p171 :rule cnf_equiv_pos1 :args (@t102)) % 5.12/5.34 (step @p172 :rule reordering :premises (@p171) :args ((or (not @t67) @t95 @t122))) % 5.12/5.34 (step @p173 :rule chain_m_resolution :premises (@p172 @p43 @p170) :args (@t122 (@list false true) (@list @t67 @t95))) % 5.12/5.34 (step @p174 :rule cnf_or_pos :args (@t103)) % 5.12/5.34 (step @p175 :rule reordering :premises (@p174) :args ((or @t98 @t99 @t97 @t102 (not @t103)))) % 5.12/5.34 (step @p176 false :rule chain_m_resolution :premises (@p175 @p173 @p118 @p42 @p52 @p51) :args (false (@list true false false false false) (@list @t102 @t103 @t65 @t60 @t62))) % 5.12/5.34 ) % 5.12/5.34 % SZS output end Proof % 5.12/5.34 % cvc5 exiting %------------------------------------------------------------------------------