%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : ITP010_2 : TPTP v9.2.1. Bugfixed v7.5.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n027.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 08:24:30 AM UTC 2026 % Result : Theorem 0.38s 0.57s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ITP010_2 : TPTP v9.2.1. Bugfixed v7.5.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n027.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 03:47:21 EDT 2026 % 0.17/0.34 % CPUTime : % 0.31/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.38/0.57 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.38/0.57 % SZS status Theorem % 0.38/0.57 % SZS output start Proof % 0.38/0.57 ( % 0.38/0.57 (declare-sort tptp.tp__o 0) % 0.38/0.57 (declare-sort tptp.del 0) % 0.38/0.57 (declare-sort $$unsorted 0) % 0.38/0.57 (declare-const tptp.c_2Ebool_2E_21 (-> tptp.del $$unsorted)) % 0.38/0.57 (declare-const tptp.c_2Emin_2E_3D (-> tptp.del $$unsorted)) % 0.38/0.57 (declare-const tptp.fo__c_2Ebool_2E_7E (-> tptp.tp__o tptp.tp__o)) % 0.38/0.57 (declare-const tptp.fo__c_2Ebool_2E_5C_2F (-> tptp.tp__o tptp.tp__o tptp.tp__o)) % 0.38/0.57 (declare-const tptp.c_2Ebool_2E_5C_2F $$unsorted) % 0.38/0.57 (declare-const tptp.fo__c_2Emin_2E_3D_3D_3E (-> tptp.tp__o tptp.tp__o tptp.tp__o)) % 0.38/0.57 (declare-const tptp.c_2Emin_2E_3D_3D_3E $$unsorted) % 0.38/0.57 (declare-const tptp.fo__c_2Ebool_2EF tptp.tp__o) % 0.38/0.57 (declare-const tptp.c_2Ebool_2E_2F_5C $$unsorted) % 0.38/0.57 (declare-const tptp.ap (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.57 (declare-const tptp.mem (-> $$unsorted tptp.del Bool)) % 0.38/0.57 (declare-const tptp.p (-> $$unsorted Bool)) % 0.38/0.57 (declare-const tptp.bool tptp.del) % 0.38/0.57 (declare-const tptp.arr (-> tptp.del tptp.del tptp.del)) % 0.38/0.57 (declare-const tptp.c_2Ecardinal_2Ecardleq (-> tptp.del tptp.del $$unsorted)) % 0.38/0.57 (declare-const tptp.fo__c_2Ebool_2E_2F_5C (-> tptp.tp__o tptp.tp__o tptp.tp__o)) % 0.38/0.57 (declare-const tptp.k (-> tptp.del $$unsorted $$unsorted)) % 0.38/0.57 (declare-const tptp.i (-> tptp.del $$unsorted)) % 0.38/0.57 (declare-const tptp.c_2Ebool_2EF $$unsorted) % 0.38/0.57 (declare-const tptp.inj__o (-> tptp.tp__o $$unsorted)) % 0.38/0.57 (declare-const tptp.surj__o (-> $$unsorted tptp.tp__o)) % 0.38/0.57 (declare-const tptp.c_2Ebool_2E_7E $$unsorted) % 0.38/0.57 (declare-const tptp.c_2Ebool_2ET $$unsorted) % 0.38/0.57 (declare-const tptp.fo__c_2Ebool_2ET tptp.tp__o) % 0.38/0.57 (define @t1 () (@var "B" tptp.del)) % 0.38/0.57 (define @t2 () (@var "X" $$unsorted)) % 0.38/0.57 (define @t3 () (@var "F" $$unsorted)) % 0.38/0.57 (define @t4 () (tptp.ap @t3 @t2)) % 0.38/0.57 (define @t5 () (@var "A" tptp.del)) % 0.38/0.57 (define @t6 () (tptp.mem @t2 @t5)) % 0.38/0.57 (define @t7 () (@list @t2)) % 0.38/0.57 (define @t8 () (tptp.arr @t5 @t1)) % 0.38/0.57 (define @t9 () (tptp.mem @t3 @t8)) % 0.38/0.57 (define @t10 () (@list @t5 @t1 @t3)) % 0.38/0.57 (define @t11 () (@var "R" $$unsorted)) % 0.38/0.57 (define @t12 () (@var "Q" $$unsorted)) % 0.38/0.57 (define @t13 () (tptp.p @t11)) % 0.38/0.57 (define @t14 () (tptp.p @t12)) % 0.38/0.57 (define @t15 () (tptp.mem @t11 tptp.bool)) % 0.38/0.57 (define @t16 () (@list @t11)) % 0.38/0.57 (define @t17 () (tptp.mem @t12 tptp.bool)) % 0.38/0.57 (define @t18 () (@list @t12)) % 0.38/0.57 (define @t19 () (@var "G" $$unsorted)) % 0.38/0.57 (define @t20 () (@var "Y" $$unsorted)) % 0.38/0.57 (define @t21 () (@list @t5 @t2)) % 0.38/0.57 (define @t22 () (@var "X" tptp.tp__o)) % 0.38/0.57 (define @t23 () (tptp.inj__o @t22)) % 0.38/0.57 (define @t24 () (@list @t22)) % 0.38/0.57 (define @t25 () (@var "A_27b" tptp.del)) % 0.38/0.57 (define @t26 () (tptp.arr @t25 tptp.bool)) % 0.38/0.57 (define @t27 () (@var "A_27a" tptp.del)) % 0.38/0.57 (define @t28 () (tptp.arr @t27 tptp.bool)) % 0.38/0.57 (define @t29 () (tptp.c_2Ecardinal_2Ecardleq @t27 @t25)) % 0.38/0.57 (define @t30 () (tptp.arr tptp.bool tptp.bool)) % 0.38/0.57 (define @t31 () (tptp.arr tptp.bool @t30)) % 0.38/0.57 (define @t32 () (@var "X1" tptp.tp__o)) % 0.38/0.57 (define @t33 () (tptp.inj__o @t32)) % 0.38/0.57 (define @t34 () (@var "X0" tptp.tp__o)) % 0.38/0.57 (define @t35 () (tptp.inj__o @t34)) % 0.38/0.57 (define @t36 () (@list @t34 @t32)) % 0.38/0.57 (define @t37 () (@list @t27)) % 0.38/0.57 (define @t38 () (@var "V0t" tptp.tp__o)) % 0.38/0.57 (define @t39 () (tptp.p (tptp.inj__o @t38))) % 0.38/0.57 (define @t40 () (=> false @t39)) % 0.38/0.57 (define @t41 () (@list @t38)) % 0.38/0.57 (define @t42 () (@var "V1x" $$unsorted)) % 0.38/0.57 (define @t43 () (not @t39)) % 0.38/0.57 (define @t44 () (not true)) % 0.38/0.57 (define @t45 () (forall @t41 (= (not @t43) @t39))) % 0.38/0.57 (define @t46 () (@var "V0x" $$unsorted)) % 0.38/0.57 (define @t47 () (@var "V0s" $$unsorted)) % 0.38/0.57 (define @t48 () (@var "V1t" $$unsorted)) % 0.38/0.57 (define @t49 () (tptp.p (tptp.ap (tptp.ap @t29 @t47) @t48))) % 0.38/0.57 (define @t50 () (tptp.mem @t48 @t26)) % 0.38/0.57 (define @t51 () (@list @t48)) % 0.38/0.57 (define @t52 () (tptp.mem @t47 @t28)) % 0.38/0.57 (define @t53 () (@list @t27 @t25 @t47)) % 0.38/0.57 (define @t54 () (@var "V0A" tptp.tp__o)) % 0.38/0.57 (define @t55 () (tptp.p (tptp.inj__o @t54))) % 0.38/0.57 (define @t56 () (not @t55)) % 0.38/0.57 (define @t57 () (=> @t56 false)) % 0.38/0.57 (define @t58 () (@list @t54)) % 0.38/0.57 (define @t59 () (@var "V1B" tptp.tp__o)) % 0.38/0.57 (define @t60 () (tptp.p (tptp.inj__o @t59))) % 0.38/0.57 (define @t61 () (=> (not @t60) false)) % 0.38/0.57 (define @t62 () (=> @t55 false)) % 0.38/0.57 (define @t63 () (@list @t54 @t59)) % 0.38/0.57 (define @t64 () (@var "V0p" tptp.tp__o)) % 0.38/0.57 (define @t65 () (tptp.p (tptp.inj__o @t64))) % 0.38/0.57 (define @t66 () (not @t65)) % 0.38/0.57 (define @t67 () (@var "V1q" tptp.tp__o)) % 0.38/0.57 (define @t68 () (tptp.p (tptp.inj__o @t67))) % 0.38/0.57 (define @t69 () (not @t68)) % 0.38/0.57 (define @t70 () (@var "V2r" tptp.tp__o)) % 0.38/0.57 (define @t71 () (tptp.p (tptp.inj__o @t70))) % 0.38/0.57 (define @t72 () (not @t71)) % 0.38/0.57 (define @t73 () (not @t49)) % 0.38/0.57 (define @t74 () (=> @t50 (= @t73 @t73))) % 0.38/0.57 (define @t75 () (forall @t51 @t74)) % 0.38/0.57 (define @t76 () (=> @t52 @t75)) % 0.38/0.57 (define @t77 () (forall @t53 @t76)) % 0.38/0.57 (define @t78 () (not @t77)) % 0.38/0.57 (assume @p1 (forall @t10 (=> @t9 (forall @t7 (=> @t6 (tptp.mem @t4 @t1)))))) % 0.38/0.57 (assume @p2 (forall @t18 (=> @t17 (forall @t16 (=> @t15 (=> (= @t14 @t13) (= @t12 @t11))))))) % 0.38/0.57 (assume @p3 (forall @t10 (=> @t9 (forall (@list @t19) (=> (tptp.mem @t19 @t8) (=> (forall @t7 (=> @t6 (= @t4 (tptp.ap @t19 @t2)))) (= @t3 @t19))))))) % 0.38/0.57 (assume @p4 (forall (@list @t5 @t20 @t2) (=> @t6 (= (tptp.ap (tptp.k @t5 @t20) @t2) @t20)))) % 0.38/0.57 (assume @p5 (forall @t21 (=> @t6 (= (tptp.ap (tptp.i @t5) @t2) @t2)))) % 0.38/0.57 (assume @p6 (forall @t24 (= (tptp.surj__o @t23) @t22))) % 0.38/0.57 (assume @p7 (forall @t24 (tptp.mem @t23 tptp.bool))) % 0.38/0.57 (assume @p8 (forall @t7 (=> (tptp.mem @t2 tptp.bool) (= @t2 (tptp.inj__o (tptp.surj__o @t2)))))) % 0.38/0.57 (assume @p9 (tptp.mem tptp.c_2Ebool_2ET tptp.bool)) % 0.38/0.57 (assume @p10 (= (tptp.inj__o tptp.fo__c_2Ebool_2ET) tptp.c_2Ebool_2ET)) % 0.38/0.57 (assume @p11 (tptp.p tptp.c_2Ebool_2ET)) % 0.38/0.57 (assume @p12 (forall (@list @t27 @t25) (tptp.mem @t29 (tptp.arr @t28 (tptp.arr @t26 tptp.bool))))) % 0.38/0.57 (assume @p13 (tptp.mem tptp.c_2Ebool_2EF tptp.bool)) % 0.38/0.57 (assume @p14 (= (tptp.inj__o tptp.fo__c_2Ebool_2EF) tptp.c_2Ebool_2EF)) % 0.38/0.57 (assume @p15 (not (tptp.p tptp.c_2Ebool_2EF))) % 0.38/0.57 (assume @p16 (tptp.mem tptp.c_2Emin_2E_3D_3D_3E @t31)) % 0.38/0.57 (assume @p17 (forall @t36 (= (tptp.inj__o (tptp.fo__c_2Emin_2E_3D_3D_3E @t34 @t32)) (tptp.ap (tptp.ap tptp.c_2Emin_2E_3D_3D_3E @t35) @t33)))) % 0.38/0.57 (assume @p18 (forall @t18 (=> @t17 (forall @t16 (=> @t15 (= (tptp.p (tptp.ap (tptp.ap tptp.c_2Emin_2E_3D_3D_3E @t12) @t11)) (=> @t14 @t13))))))) % 0.38/0.57 (assume @p19 (tptp.mem tptp.c_2Ebool_2E_5C_2F @t31)) % 0.38/0.57 (assume @p20 (forall @t36 (= (tptp.inj__o (tptp.fo__c_2Ebool_2E_5C_2F @t34 @t32)) (tptp.ap (tptp.ap tptp.c_2Ebool_2E_5C_2F @t35) @t33)))) % 0.38/0.57 (assume @p21 (forall @t18 (=> @t17 (forall @t16 (=> @t15 (= (tptp.p (tptp.ap (tptp.ap tptp.c_2Ebool_2E_5C_2F @t12) @t11)) (or @t14 @t13))))))) % 0.38/0.57 (assume @p22 (tptp.mem tptp.c_2Ebool_2E_2F_5C @t31)) % 0.38/0.57 (assume @p23 (forall @t36 (= (tptp.inj__o (tptp.fo__c_2Ebool_2E_2F_5C @t34 @t32)) (tptp.ap (tptp.ap tptp.c_2Ebool_2E_2F_5C @t35) @t33)))) % 0.38/0.57 (assume @p24 (forall @t18 (=> @t17 (forall @t16 (=> @t15 (= (tptp.p (tptp.ap (tptp.ap tptp.c_2Ebool_2E_2F_5C @t12) @t11)) (and @t14 @t13))))))) % 0.38/0.57 (assume @p25 (tptp.mem tptp.c_2Ebool_2E_7E @t30)) % 0.38/0.57 (assume @p26 (forall (@list @t34) (= (tptp.inj__o (tptp.fo__c_2Ebool_2E_7E @t34)) (tptp.ap tptp.c_2Ebool_2E_7E @t35)))) % 0.38/0.57 (assume @p27 (forall @t18 (=> @t17 (= (tptp.p (tptp.ap tptp.c_2Ebool_2E_7E @t12)) (not @t14))))) % 0.38/0.57 (assume @p28 (forall @t37 (tptp.mem (tptp.c_2Emin_2E_3D @t27) (tptp.arr @t27 @t28)))) % 0.38/0.57 (assume @p29 (forall @t21 (=> @t6 (forall (@list @t20) (=> (tptp.mem @t20 @t5) (= (tptp.p (tptp.ap (tptp.ap (tptp.c_2Emin_2E_3D @t5) @t2) @t20)) (= @t2 @t20))))))) % 0.38/0.57 (assume @p30 (forall @t37 (tptp.mem (tptp.c_2Ebool_2E_21 @t27) (tptp.arr @t28 tptp.bool)))) % 0.38/0.57 (assume @p31 (forall (@list @t5 @t12) (=> (tptp.mem @t12 (tptp.arr @t5 tptp.bool)) (= (tptp.p (tptp.ap (tptp.c_2Ebool_2E_21 @t5) @t12)) (forall @t7 (=> @t6 (tptp.p (tptp.ap @t12 @t2)))))))) % 0.38/0.57 (assume @p32 true) % 0.38/0.57 (assume @p33 (forall @t41 @t40)) % 0.38/0.57 (assume @p34 (forall (@list @t27 @t38) (= (forall (@list @t42) (=> (tptp.mem @t42 @t27) @t39)) @t39))) % 0.38/0.57 (assume @p35 (forall @t41 (and (= (=> true @t39) @t39) (= (=> @t39 true) true) (= @t40 true) (= (=> @t39 @t39) true) (= (=> @t39 false) @t43)))) % 0.38/0.57 (assume @p36 (and @t45 (= @t44 false) (= (not false) true))) % 0.38/0.57 (assume @p37 (forall (@list @t27 @t46) (=> (tptp.mem @t46 @t27) (= (= @t46 @t46) true)))) % 0.38/0.57 (assume @p38 (forall @t41 (and (= (= true @t39) @t39) (= (= @t39 true) @t39) (= (= false @t39) @t43) (= (= @t39 false) @t43)))) % 0.38/0.57 (assume @p39 (forall @t53 (=> @t52 (forall @t51 (=> @t50 (or @t49 (tptp.p (tptp.ap (tptp.ap (tptp.c_2Ecardinal_2Ecardleq @t25 @t27) @t48) @t47)))))))) % 0.38/0.57 (assume @p40 @t45) % 0.38/0.57 (assume @p41 (forall @t58 (=> @t55 @t57))) % 0.38/0.57 (assume @p42 (forall @t63 (= (=> (not (or @t55 @t60)) false) (=> @t62 @t61)))) % 0.38/0.57 (assume @p43 (forall @t63 (= (=> (not (or @t56 @t60)) false) (=> @t55 @t61)))) % 0.38/0.57 (assume @p44 (forall @t58 (=> @t57 (=> @t62 false)))) % 0.38/0.57 (assume @p45 (forall (@list @t64 @t67 @t70) (= (= @t65 (= @t68 @t71)) (and (or @t65 @t68 @t71) (or @t65 @t72 @t69) (or @t68 @t72 @t66) (or @t71 @t69 @t66))))) % 0.38/0.57 (assume @p46 (forall (@list @t64 @t67) (= (= @t65 @t69) (and (or @t65 @t68) (or @t69 @t66))))) % 0.38/0.57 (assume @p47 @t78) % 0.38/0.57 (step @p48 :rule evaluate :args (@t44)) % 0.38/0.57 (step @p49 :rule quant-unused-vars :args ((= (forall @t53 true) true))) % 0.38/0.57 (step @p50 :rule bool-impl-true1 :args (@t52)) % 0.38/0.57 (step @p51 :rule quant-unused-vars :args ((= (forall @t51 true) true))) % 0.38/0.57 (step @p52 :rule bool-impl-true1 :args (@t50)) % 0.38/0.57 (step @p53 :rule eq-refl :args (@t73)) % 0.38/0.57 (step @p54 :rule refl :args (@t50)) % 0.38/0.57 (step @p55 :rule cong :premises (@p54 @p53) :args (@t74)) % 0.38/0.57 (step @p56 :rule trans :premises (@p55 @p52)) % 0.38/0.57 (step @p57 :rule cong :premises (@p56) :args (@t75)) % 0.38/0.57 (step @p58 :rule trans :premises (@p57 @p51)) % 0.38/0.57 (step @p59 :rule refl :args (@t52)) % 0.38/0.57 (step @p60 :rule cong :premises (@p59 @p58) :args (@t76)) % 0.38/0.57 (step @p61 :rule trans :premises (@p60 @p50)) % 0.38/0.57 (step @p62 :rule cong :premises (@p61) :args (@t77)) % 0.38/0.57 (step @p63 :rule trans :premises (@p62 @p49)) % 0.38/0.57 (step @p64 :rule cong :premises (@p63) :args (@t78)) % 0.38/0.57 (step @p65 :rule trans :premises (@p64 @p48)) % 0.38/0.57 (step @p66 false :rule eq_resolve :premises (@p47 @p65)) % 0.38/0.57 ) % 0.38/0.57 % SZS output end Proof % 0.38/0.57 % cvc5 exiting %------------------------------------------------------------------------------