%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : KRS255+1 : TPTP v9.2.1. Bugfixed v5.4.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n015.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 08:29:10 AM UTC 2026 % Result : Theorem 0.37s 0.59s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : KRS255+1 : TPTP v9.2.1. Bugfixed v5.4.0. % 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n015.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 05:35:04 EDT 2026 % 0.17/0.34 % CPUTime : % 0.28/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.37/0.59 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.37/0.59 % SZS status Theorem % 0.37/0.59 % SZS output start Proof % 0.37/0.59 ( % 0.37/0.59 (declare-sort $$unsorted 0) % 0.37/0.59 (declare-const tptp.xora (-> $$unsorted $$unsorted Bool)) % 0.37/0.59 (declare-const tptp.nevera (-> $$unsorted $$unsorted Bool)) % 0.37/0.59 (declare-const tptp.nota (-> $$unsorted $$unsorted Bool)) % 0.37/0.59 (declare-const tptp.mighta (-> $$unsorted $$unsorted Bool)) % 0.37/0.59 (declare-const tptp.noc $$unsorted) % 0.37/0.59 (declare-const tptp.uns $$unsorted) % 0.37/0.59 (declare-const tptp.not (-> $$unsorted $$unsorted)) % 0.37/0.59 (declare-const tptp.tca $$unsorted) % 0.37/0.59 (declare-const tptp.sca $$unsorted) % 0.37/0.59 (declare-const tptp.wth $$unsorted) % 0.37/0.59 (declare-const tptp.unp $$unsorted) % 0.37/0.59 (declare-const tptp.wca $$unsorted) % 0.37/0.59 (declare-const tptp.wec $$unsorted) % 0.37/0.59 (declare-const tptp.sap $$unsorted) % 0.37/0.59 (declare-const tptp.wtc $$unsorted) % 0.37/0.59 (declare-const tptp.model (-> $$unsorted $$unsorted Bool)) % 0.37/0.59 (declare-const tptp.sat $$unsorted) % 0.37/0.59 (declare-const tptp.cax $$unsorted) % 0.37/0.59 (declare-const tptp.eqv $$unsorted) % 0.37/0.59 (declare-const tptp.esa $$unsorted) % 0.37/0.59 (declare-const tptp.csa $$unsorted) % 0.37/0.59 (declare-const tptp.status (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.37/0.59 (declare-const tptp.thm $$unsorted) % 0.37/0.59 (declare-const tptp.isa (-> $$unsorted $$unsorted Bool)) % 0.37/0.59 (declare-const tptp.eth $$unsorted) % 0.37/0.59 (declare-const tptp.tac $$unsorted) % 0.37/0.59 (declare-const tptp.tau $$unsorted) % 0.37/0.59 (define @t1 () (@var "C" $$unsorted)) % 0.37/0.59 (define @t2 () (@var "Ax" $$unsorted)) % 0.37/0.59 (define @t3 () (@var "I2" $$unsorted)) % 0.37/0.59 (define @t4 () (tptp.model @t3 @t1)) % 0.37/0.59 (define @t5 () (@list @t3)) % 0.37/0.59 (define @t6 () (exists @t5 @t4)) % 0.37/0.59 (define @t7 () (@var "I1" $$unsorted)) % 0.37/0.59 (define @t8 () (tptp.model @t7 @t2)) % 0.37/0.59 (define @t9 () (@list @t7)) % 0.37/0.59 (define @t10 () (exists @t9 @t8)) % 0.37/0.59 (define @t11 () (not @t10)) % 0.37/0.59 (define @t12 () (@list @t2 @t1)) % 0.37/0.59 (define @t13 () (tptp.status @t2 @t1 tptp.sap)) % 0.37/0.59 (define @t14 () (=> @t10 @t6)) % 0.37/0.59 (define @t15 () (= @t14 @t13)) % 0.37/0.59 (define @t16 () (forall @t12 @t15)) % 0.37/0.59 (define @t17 () (tptp.model @t7 @t1)) % 0.37/0.59 (define @t18 () (and @t8 @t17)) % 0.37/0.59 (define @t19 () (exists @t9 @t18)) % 0.37/0.59 (define @t20 () (tptp.status @t2 @t1 tptp.thm)) % 0.37/0.59 (define @t21 () (forall @t9 (=> @t8 @t17))) % 0.37/0.59 (define @t22 () (= @t21 @t20)) % 0.37/0.59 (define @t23 () (forall @t12 @t22)) % 0.37/0.59 (define @t24 () (tptp.model @t3 @t2)) % 0.37/0.59 (define @t25 () (forall @t5 @t4)) % 0.37/0.59 (define @t26 () (@var "I3" $$unsorted)) % 0.37/0.59 (define @t27 () (tptp.model @t26 @t2)) % 0.37/0.59 (define @t28 () (not @t27)) % 0.37/0.59 (define @t29 () (tptp.model @t26 @t1)) % 0.37/0.59 (define @t30 () (@list @t26)) % 0.37/0.59 (define @t31 () (exists @t30 (and @t29 @t28))) % 0.37/0.59 (define @t32 () (forall @t5 (=> @t24 @t4))) % 0.37/0.59 (define @t33 () (not @t24)) % 0.37/0.59 (define @t34 () (exists @t5 @t33)) % 0.37/0.59 (define @t35 () (@var "I4" $$unsorted)) % 0.37/0.59 (define @t36 () (exists (@list @t35) (not (tptp.model @t35 @t1)))) % 0.37/0.59 (define @t37 () (tptp.not @t1)) % 0.37/0.59 (define @t38 () (tptp.model @t3 @t37)) % 0.37/0.59 (define @t39 () (@var "S2" $$unsorted)) % 0.37/0.59 (define @t40 () (@var "S1" $$unsorted)) % 0.37/0.59 (define @t41 () (tptp.mighta @t40 @t39)) % 0.37/0.59 (define @t42 () (tptp.status @t2 @t1 @t39)) % 0.37/0.59 (define @t43 () (tptp.status @t2 @t1 @t40)) % 0.37/0.59 (define @t44 () (and @t43 @t42)) % 0.37/0.59 (define @t45 () (exists @t12 @t44)) % 0.37/0.59 (define @t46 () (= @t45 @t41)) % 0.37/0.59 (define @t47 () (@list @t40 @t39)) % 0.37/0.59 (define @t48 () (forall @t47 @t46)) % 0.37/0.59 (define @t49 () (not @t42)) % 0.37/0.59 (define @t50 () (@var "F" $$unsorted)) % 0.37/0.59 (define @t51 () (@var "I" $$unsorted)) % 0.37/0.59 (define @t52 () (tptp.model @t51 (tptp.not @t50))) % 0.37/0.59 (define @t53 () (tptp.model @t51 @t50)) % 0.37/0.59 (define @t54 () (@list @t51 @t50)) % 0.37/0.59 (define @t55 () (@list @t51)) % 0.37/0.59 (define @t56 () (@list @t50)) % 0.37/0.59 (define @t57 () (not @t4)) % 0.37/0.59 (define @t58 () (tptp.mighta tptp.sap tptp.thm)) % 0.37/0.59 (define @t59 () (not (forall @t5 @t57))) % 0.37/0.59 (define @t60 () (not @t8)) % 0.37/0.59 (define @t61 () (forall @t9 @t60)) % 0.37/0.59 (define @t62 () (not @t61)) % 0.37/0.59 (define @t63 () (=> @t62 @t59)) % 0.37/0.59 (define @t64 () (= @t13 @t63)) % 0.37/0.59 (define @t65 () (@list tptp.thm tptp.thm)) % 0.37/0.59 (define @t66 () (forall @t12 (not @t44))) % 0.37/0.59 (define @t67 () (not @t66)) % 0.37/0.59 (define @t68 () (forall @t12 (or (not @t13) (not @t20)))) % 0.37/0.59 (define @t69 () (not @t68)) % 0.37/0.59 (define @t70 () (= @t58 @t69)) % 0.37/0.59 (define @t71 () (not @t70)) % 0.37/0.59 (define @t72 () (@list true false)) % 0.37/0.59 (define @t73 () (forall @t9 (or @t60 @t17))) % 0.37/0.59 (define @t74 () (tptp.status tptp.thm tptp.thm tptp.thm)) % 0.37/0.59 (define @t75 () (tptp.model @t7 tptp.thm)) % 0.37/0.59 (define @t76 () (not @t75)) % 0.37/0.59 (define @t77 () (forall @t9 (or @t76 @t75))) % 0.37/0.59 (define @t78 () (= @t74 @t77)) % 0.37/0.59 (define @t79 () (forall @t12 (= @t20 @t73))) % 0.37/0.59 (define @t80 () (not @t74)) % 0.37/0.59 (define @t81 () (tptp.status tptp.thm tptp.thm tptp.sap)) % 0.37/0.59 (define @t82 () (not @t81)) % 0.37/0.59 (define @t83 () (or @t82 @t80)) % 0.37/0.59 (define @t84 () (forall @t5 (not (tptp.model @t3 tptp.thm)))) % 0.37/0.59 (define @t85 () (not @t84)) % 0.37/0.59 (define @t86 () (forall @t9 @t76)) % 0.37/0.59 (define @t87 () (or @t86 @t85)) % 0.37/0.59 (define @t88 () (= @t81 @t87)) % 0.37/0.59 (define @t89 () (not @t87)) % 0.37/0.59 (define @t90 () (not @t86)) % 0.37/0.59 (define @t91 () (@list true)) % 0.37/0.59 (define @t92 () (@list @t87)) % 0.37/0.59 (assume @p1 (forall @t12 (= (=> @t11 (not @t6)) (tptp.status @t2 @t1 tptp.unp)))) % 0.37/0.59 (assume @p2 @t16) % 0.37/0.59 (assume @p3 (forall @t12 (= (= @t10 @t6) (tptp.status @t2 @t1 tptp.esa)))) % 0.37/0.59 (assume @p4 (forall @t12 (= @t19 (tptp.status @t2 @t1 tptp.sat)))) % 0.37/0.59 (assume @p5 @t23) % 0.37/0.59 (assume @p6 (forall @t12 (= (and @t10 (forall @t5 (= @t24 @t4))) (tptp.status @t2 @t1 tptp.eqv)))) % 0.37/0.59 (assume @p7 (forall @t12 (= (and @t10 @t25) (tptp.status @t2 @t1 tptp.tac)))) % 0.37/0.59 (assume @p8 (forall @t12 (= (and @t10 @t32 @t31) (tptp.status @t2 @t1 tptp.wec)))) % 0.37/0.59 (assume @p9 (forall @t12 (= (and @t10 @t34 (forall @t30 (= @t27 @t29))) (tptp.status @t2 @t1 tptp.eth)))) % 0.37/0.59 (assume @p10 (forall @t12 (= (forall @t9 @t18) (tptp.status @t2 @t1 tptp.tau)))) % 0.37/0.59 (assume @p11 (forall @t12 (= (and @t10 @t34 (forall @t30 @t29)) (tptp.status @t2 @t1 tptp.wtc)))) % 0.37/0.59 (assume @p12 (forall @t12 (= (and @t10 @t32 @t31 @t36) (tptp.status @t2 @t1 tptp.wth)))) % 0.37/0.59 (assume @p13 (forall @t12 (= @t11 (tptp.status @t2 @t1 tptp.cax)))) % 0.37/0.59 (assume @p14 (forall @t12 (= (and @t11 @t6) (tptp.status @t2 @t1 tptp.sca)))) % 0.37/0.59 (assume @p15 (forall @t12 (= (and @t11 @t25) (tptp.status @t2 @t1 tptp.tca)))) % 0.37/0.59 (assume @p16 (forall @t12 (= (and @t11 @t6 (exists @t30 (not @t29))) (tptp.status @t2 @t1 tptp.wca)))) % 0.37/0.59 (assume @p17 (forall @t12 (= (exists @t9 (and @t8 (tptp.model @t7 @t37))) (tptp.status @t2 @t1 tptp.csa)))) % 0.37/0.59 (assume @p18 (forall @t12 (= (and (forall @t9 @t8) (forall @t5 @t38)) (tptp.status @t2 @t1 tptp.uns)))) % 0.37/0.59 (assume @p19 (forall @t12 (= (and @t19 (exists @t5 (and @t24 @t38))) (tptp.status @t2 @t1 tptp.noc)))) % 0.37/0.59 (assume @p20 @t48) % 0.37/0.59 (assume @p21 (forall @t47 (= (forall @t12 (=> @t43 @t42)) (tptp.isa @t40 @t39)))) % 0.37/0.59 (assume @p22 (forall @t47 (= (exists @t12 (and @t43 @t49)) (tptp.nota @t40 @t39)))) % 0.37/0.59 (assume @p23 (forall @t47 (= (forall @t12 (=> @t43 @t49)) (tptp.nevera @t40 @t39)))) % 0.37/0.59 (assume @p24 (forall @t47 (= (forall @t12 (xor @t43 @t42)) (tptp.xora @t40 @t39)))) % 0.37/0.59 (assume @p25 (forall @t54 (xor @t53 @t52))) % 0.37/0.59 (assume @p26 (forall @t54 (= @t53 (not @t52)))) % 0.37/0.59 (assume @p27 (exists @t56 (forall @t55 @t53))) % 0.37/0.59 (assume @p28 (exists @t56 (and (exists @t9 (tptp.model @t7 @t50)) (exists @t5 (not (tptp.model @t3 @t50)))))) % 0.37/0.59 (assume @p29 (exists @t56 (forall @t55 (not @t53)))) % 0.37/0.59 (assume @p30 (exists @t12 (and @t19 (exists @t5 (or @t33 @t57))))) % 0.37/0.59 (assume @p31 (exists @t12 (and @t10 @t32 (exists @t30 (and @t28 @t29)) @t36))) % 0.37/0.59 (assume @p32 (exists (@list @t7 @t2 @t1) (and @t8 (not @t17) @t6))) % 0.37/0.59 (assume @p33 (not @t58)) % 0.37/0.59 (assume @p34 true) % 0.37/0.59 (step @p35 :rule refl :args (@t59)) % 0.37/0.59 (step @p36 :rule bool-double-not-elim :args (@t61)) % 0.37/0.59 (step @p37 :rule nary_cong :premises (@p36 @p35) :args ((or (not @t62) @t59))) % 0.37/0.59 (step @p38 :rule bool-impl-elim :args (@t62 @t59)) % 0.37/0.59 (step @p39 :rule trans :premises (@p38 @p37)) % 0.37/0.59 (step @p40 :rule refl :args (@t13)) % 0.37/0.59 (step @p41 :rule cong :premises (@p40 @p39) :args (@t64)) % 0.37/0.59 (step @p42 :rule cong :premises (@p41) :args ((forall @t12 @t64))) % 0.37/0.59 (step @p43 :rule eq-symm :args (@t63 @t13)) % 0.37/0.59 (step @p44 :rule refl :args (@t13)) % 0.37/0.59 (step @p45 :rule exists-elim :args ((= @t6 @t59))) % 0.37/0.59 (step @p46 :rule exists-elim :args ((= @t10 @t62))) % 0.37/0.59 (step @p47 :rule cong :premises (@p46 @p45) :args (@t14)) % 0.37/0.59 (step @p48 :rule cong :premises (@p47 @p44) :args (@t15)) % 0.37/0.59 (step @p49 :rule trans :premises (@p48 @p43)) % 0.37/0.59 (step @p50 :rule cong :premises (@p49) :args (@t16)) % 0.37/0.59 (step @p51 :rule trans :premises (@p50 @p42)) % 0.37/0.59 (step @p52 :rule eq_resolve :premises (@p2 @p51)) % 0.37/0.59 (step @p53 :rule instantiate :premises (@p52) :args (@t65)) % 0.37/0.59 (step @p54 :rule eq-symm :args ((not (forall @t12 (or (not @t43) @t49))) @t41)) % 0.37/0.59 (step @p55 :rule refl :args (@t41)) % 0.37/0.59 (step @p56 :rule bool-and-de-morgan :args (@t43 @t42 true)) % 0.37/0.59 (step @p57 :rule cong :premises (@p56) :args (@t66)) % 0.37/0.59 (step @p58 :rule cong :premises (@p57) :args (@t67)) % 0.37/0.59 (step @p59 :rule exists-elim :args ((= @t45 @t67))) % 0.37/0.59 (step @p60 :rule trans :premises (@p59 @p58)) % 0.37/0.59 (step @p61 :rule cong :premises (@p60 @p55) :args (@t46)) % 0.37/0.59 (step @p62 :rule trans :premises (@p61 @p54)) % 0.37/0.59 (step @p63 :rule cong :premises (@p62) :args (@t48)) % 0.37/0.59 (step @p64 :rule eq_resolve :premises (@p20 @p63)) % 0.37/0.59 (step @p65 :rule instantiate :premises (@p64) :args ((@list tptp.sap tptp.thm))) % 0.37/0.59 (step @p66 :rule bool-double-not-elim :args (@t68)) % 0.37/0.59 (step @p67 :rule refl :args (@t58)) % 0.37/0.59 (step @p68 :rule refl :args (@t71)) % 0.37/0.59 (step @p69 :rule nary_cong :premises (@p68 @p67 @p66) :args ((or @t71 @t58 (not @t69)))) % 0.37/0.59 (step @p70 :rule cnf_equiv_pos2 :args (@t70)) % 0.37/0.59 (step @p71 :rule eq_resolve :premises (@p70 @p69)) % 0.37/0.59 (step @p72 :rule reordering :premises (@p71) :args ((or @t58 @t68 @t71))) % 0.37/0.59 (step @p73 :rule chain_m_resolution :premises (@p72 @p33 @p65) :args (@t68 @t72 (@list @t58 @t70))) % 0.37/0.59 (step @p74 :rule instantiate :premises (@p73) :args (@t65)) % 0.37/0.59 (step @p75 :rule eq-symm :args (@t73 @t20)) % 0.37/0.59 (step @p76 :rule refl :args (@t20)) % 0.37/0.59 (step @p77 :rule bool-impl-elim :args (@t8 @t17)) % 0.37/0.59 (step @p78 :rule cong :premises (@p77) :args (@t21)) % 0.37/0.59 (step @p79 :rule cong :premises (@p78 @p76) :args (@t22)) % 0.37/0.59 (step @p80 :rule trans :premises (@p79 @p75)) % 0.37/0.59 (step @p81 :rule cong :premises (@p80) :args (@t23)) % 0.37/0.59 (step @p82 :rule eq_resolve :premises (@p5 @p81)) % 0.37/0.59 (step @p83 :rule bool-eq-true :args (@t74)) % 0.37/0.59 (step @p84 :rule quant-unused-vars :args ((= (forall @t9 true) true))) % 0.37/0.59 (step @p85 :rule bool-or-taut2 :args (false @t75 false false)) % 0.37/0.59 (step @p86 :rule cong :premises (@p85) :args (@t77)) % 0.37/0.59 (step @p87 :rule trans :premises (@p86 @p84)) % 0.37/0.59 (step @p88 :rule refl :args (@t74)) % 0.37/0.59 (step @p89 :rule cong :premises (@p88 @p87) :args (@t78)) % 0.37/0.59 (step @p90 :rule trans :premises (@p89 @p83)) % 0.37/0.59 (step @p91 :rule refl :args (@t79)) % 0.37/0.59 (step @p92 :rule cong :premises (@p91 @p90) :args ((=> @t79 @t78))) % 0.37/0.59 (assume-push @p119 @t79) % 0.37/0.59 (step @p94 :rule instantiate :premises (@p82) :args (@t65)) % 0.37/0.59 (step-pop @p120 :rule scope :premises (@p94)) % 0.37/0.59 (step @p95 :rule process_scope :premises (@p120) :args (@t78)) % 0.37/0.59 (step @p97 :rule eq_resolve :premises (@p95 @p92)) % 0.37/0.59 (step @p98 :rule implies_elim :premises (@p97)) % 0.37/0.59 (step @p99 :rule chain_m_resolution :premises (@p98 @p82) :args (@t74 (@list false) (@list @t79))) % 0.37/0.59 (step @p100 :rule cnf_or_pos :args (@t83)) % 0.37/0.59 (step @p101 :rule reordering :premises (@p100) :args ((or @t82 @t80 (not @t83)))) % 0.37/0.59 (step @p102 :rule chain_m_resolution :premises (@p101 @p99 @p74) :args (@t82 (@list false false) (@list @t74 @t83))) % 0.37/0.59 (step @p103 :rule cnf_equiv_pos2 :args (@t88)) % 0.37/0.59 (step @p104 :rule reordering :premises (@p103) :args ((or @t81 @t89 (not @t88)))) % 0.37/0.59 (step @p105 :rule chain_m_resolution :premises (@p104 @p102 @p53) :args (@t89 @t72 (@list @t81 @t88))) % 0.37/0.59 (step @p106 :rule cnf_or_neg :args (@t87 0)) % 0.37/0.59 (step @p107 :rule reordering :premises (@p106) :args ((or @t90 @t87))) % 0.37/0.59 (step @p108 :rule chain_m_resolution :premises (@p107 @p105) :args (@t90 @t91 @t92)) % 0.37/0.59 (step @p109 :rule bool-double-not-elim :args (@t84)) % 0.37/0.59 (step @p110 :rule refl :args (@t87)) % 0.37/0.59 (step @p111 :rule nary_cong :premises (@p110 @p109) :args ((or @t87 (not @t85)))) % 0.37/0.59 (step @p112 :rule cnf_or_neg :args (@t87 1)) % 0.37/0.59 (step @p113 :rule eq_resolve :premises (@p112 @p111)) % 0.37/0.59 (step @p114 :rule reordering :premises (@p113) :args ((or @t84 @t87))) % 0.37/0.59 (step @p115 :rule chain_m_resolution :premises (@p114 @p105) :args (@t84 @t91 @t92)) % 0.37/0.59 (step @p116 :rule alpha_equiv :args (@t86 (@list @t7) (@list @t3))) % 0.37/0.59 (step @p117 :rule equiv_elim2 :premises (@p116)) % 0.37/0.59 (step @p118 false :rule chain_m_resolution :premises (@p117 @p115 @p108) :args (false (@list false true) (@list @t84 @t86))) % 0.37/0.59 ) % 0.37/0.59 % SZS output end Proof % 0.37/0.59 % cvc5 exiting %------------------------------------------------------------------------------