%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : ITP010+2 : TPTP v9.2.1. Bugfixed v7.5.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n025.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 0.36s 0.57s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : ITP010+2 : TPTP v9.2.1. Bugfixed v7.5.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.15/0.33 % Computer : n025.cluster.edu % 0.15/0.33 % Model : x86_64 x86_64 % 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.33 % Memory : 8042.1875MB % 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.33 % CPULimit : 300 % 0.15/0.33 % WCLimit : 300 % 0.15/0.33 % DateTime : Tue Jun 2 03:47:16 EDT 2026 % 0.15/0.33 % CPUTime : % 0.28/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.36/0.57 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.36/0.57 % SZS status Theorem % 0.36/0.57 % SZS output start Proof % 0.36/0.57 ( % 0.36/0.57 (declare-sort $$unsorted 0) % 0.36/0.57 (declare-const tptp.c_2Emin_2E_3D (-> $$unsorted $$unsorted)) % 0.36/0.57 (declare-const tptp.c_2Ebool_2E_7E $$unsorted) % 0.36/0.57 (declare-const tptp.c_2Ebool_2E_2F_5C $$unsorted) % 0.36/0.57 (declare-const tptp.c_2Ebool_2E_5C_2F $$unsorted) % 0.36/0.57 (declare-const tptp.c_2Ecardinal_2Ecardleq (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.57 (declare-const tptp.ne (-> $$unsorted Bool)) % 0.36/0.57 (declare-const tptp.ind $$unsorted) % 0.36/0.57 (declare-const tptp.c_2Ebool_2EF $$unsorted) % 0.36/0.57 (declare-const tptp.mem (-> $$unsorted $$unsorted Bool)) % 0.36/0.57 (declare-const tptp.i (-> $$unsorted $$unsorted)) % 0.36/0.57 (declare-const tptp.bool $$unsorted) % 0.36/0.57 (declare-const tptp.arr (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.57 (declare-const tptp.p (-> $$unsorted Bool)) % 0.36/0.57 (declare-const tptp.k (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.57 (declare-const tptp.c_2Ebool_2E_21 (-> $$unsorted $$unsorted)) % 0.36/0.57 (declare-const tptp.ap (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.57 (declare-const tptp.c_2Ebool_2ET $$unsorted) % 0.36/0.57 (declare-const tptp.c_2Emin_2E_3D_3D_3E $$unsorted) % 0.36/0.57 (define @t1 () (@var "B" $$unsorted)) % 0.36/0.57 (define @t2 () (@var "A" $$unsorted)) % 0.36/0.57 (define @t3 () (tptp.arr @t2 @t1)) % 0.36/0.57 (define @t4 () (tptp.ne @t2)) % 0.36/0.57 (define @t5 () (@list @t2)) % 0.36/0.57 (define @t6 () (@var "X" $$unsorted)) % 0.36/0.57 (define @t7 () (@var "F" $$unsorted)) % 0.36/0.57 (define @t8 () (tptp.ap @t7 @t6)) % 0.36/0.57 (define @t9 () (tptp.mem @t6 @t2)) % 0.36/0.57 (define @t10 () (@list @t6)) % 0.36/0.57 (define @t11 () (tptp.mem @t7 @t3)) % 0.36/0.57 (define @t12 () (@list @t2 @t1 @t7)) % 0.36/0.57 (define @t13 () (@var "R" $$unsorted)) % 0.36/0.57 (define @t14 () (@var "Q" $$unsorted)) % 0.36/0.57 (define @t15 () (tptp.p @t13)) % 0.36/0.57 (define @t16 () (tptp.p @t14)) % 0.36/0.57 (define @t17 () (tptp.mem @t13 tptp.bool)) % 0.36/0.57 (define @t18 () (@list @t13)) % 0.36/0.57 (define @t19 () (tptp.mem @t14 tptp.bool)) % 0.36/0.57 (define @t20 () (@list @t14)) % 0.36/0.57 (define @t21 () (@var "G" $$unsorted)) % 0.36/0.57 (define @t22 () (@var "Y" $$unsorted)) % 0.36/0.57 (define @t23 () (@var "A_27b" $$unsorted)) % 0.36/0.57 (define @t24 () (tptp.arr @t23 tptp.bool)) % 0.36/0.57 (define @t25 () (@var "A_27a" $$unsorted)) % 0.36/0.57 (define @t26 () (tptp.arr @t25 tptp.bool)) % 0.36/0.57 (define @t27 () (tptp.c_2Ecardinal_2Ecardleq @t25 @t23)) % 0.36/0.57 (define @t28 () (tptp.ne @t23)) % 0.36/0.57 (define @t29 () (@list @t23)) % 0.36/0.57 (define @t30 () (tptp.ne @t25)) % 0.36/0.57 (define @t31 () (@list @t25)) % 0.36/0.57 (define @t32 () (tptp.arr tptp.bool tptp.bool)) % 0.36/0.57 (define @t33 () (tptp.arr tptp.bool @t32)) % 0.36/0.57 (define @t34 () (@var "V0t" $$unsorted)) % 0.36/0.57 (define @t35 () (tptp.p @t34)) % 0.36/0.57 (define @t36 () (=> false @t35)) % 0.36/0.57 (define @t37 () (tptp.mem @t34 tptp.bool)) % 0.36/0.57 (define @t38 () (@list @t34)) % 0.36/0.57 (define @t39 () (@var "V1x" $$unsorted)) % 0.36/0.57 (define @t40 () (not @t35)) % 0.36/0.57 (define @t41 () (not true)) % 0.36/0.57 (define @t42 () (forall @t38 (=> @t37 (= (not @t40) @t35)))) % 0.36/0.57 (define @t43 () (@var "V0x" $$unsorted)) % 0.36/0.57 (define @t44 () (@var "V0s" $$unsorted)) % 0.36/0.57 (define @t45 () (@var "V1t" $$unsorted)) % 0.36/0.57 (define @t46 () (tptp.p (tptp.ap (tptp.ap @t27 @t44) @t45))) % 0.36/0.57 (define @t47 () (tptp.mem @t45 @t24)) % 0.36/0.57 (define @t48 () (@list @t45)) % 0.36/0.57 (define @t49 () (tptp.mem @t44 @t26)) % 0.36/0.57 (define @t50 () (@list @t44)) % 0.36/0.57 (define @t51 () (@var "V0A" $$unsorted)) % 0.36/0.57 (define @t52 () (tptp.p @t51)) % 0.36/0.57 (define @t53 () (not @t52)) % 0.36/0.57 (define @t54 () (=> @t53 false)) % 0.36/0.57 (define @t55 () (tptp.mem @t51 tptp.bool)) % 0.36/0.57 (define @t56 () (@list @t51)) % 0.36/0.57 (define @t57 () (@var "V1B" $$unsorted)) % 0.36/0.57 (define @t58 () (tptp.p @t57)) % 0.36/0.57 (define @t59 () (=> (not @t58) false)) % 0.36/0.57 (define @t60 () (=> @t52 false)) % 0.36/0.57 (define @t61 () (tptp.mem @t57 tptp.bool)) % 0.36/0.57 (define @t62 () (@list @t57)) % 0.36/0.57 (define @t63 () (@var "V0p" $$unsorted)) % 0.36/0.57 (define @t64 () (tptp.p @t63)) % 0.36/0.57 (define @t65 () (not @t64)) % 0.36/0.57 (define @t66 () (@var "V1q" $$unsorted)) % 0.36/0.57 (define @t67 () (tptp.p @t66)) % 0.36/0.57 (define @t68 () (not @t67)) % 0.36/0.57 (define @t69 () (@var "V2r" $$unsorted)) % 0.36/0.57 (define @t70 () (tptp.p @t69)) % 0.36/0.57 (define @t71 () (not @t70)) % 0.36/0.57 (define @t72 () (tptp.mem @t66 tptp.bool)) % 0.36/0.57 (define @t73 () (@list @t66)) % 0.36/0.57 (define @t74 () (tptp.mem @t63 tptp.bool)) % 0.36/0.57 (define @t75 () (@list @t63)) % 0.36/0.57 (define @t76 () (not @t46)) % 0.36/0.57 (define @t77 () (=> @t47 (= @t76 @t76))) % 0.36/0.57 (define @t78 () (forall @t48 @t77)) % 0.36/0.57 (define @t79 () (=> @t49 @t78)) % 0.36/0.57 (define @t80 () (forall @t50 @t79)) % 0.36/0.57 (define @t81 () (=> @t28 @t80)) % 0.36/0.57 (define @t82 () (forall @t29 @t81)) % 0.36/0.58 (define @t83 () (=> @t30 @t82)) % 0.36/0.58 (define @t84 () (forall @t31 @t83)) % 0.36/0.58 (define @t85 () (not @t84)) % 0.36/0.58 (assume @p1 (tptp.ne tptp.bool)) % 0.36/0.58 (assume @p2 (tptp.ne tptp.ind)) % 0.36/0.58 (assume @p3 (forall @t5 (=> @t4 (forall (@list @t1) (=> (tptp.ne @t1) (tptp.ne @t3)))))) % 0.36/0.58 (assume @p4 (forall @t12 (=> @t11 (forall @t10 (=> @t9 (tptp.mem @t8 @t1)))))) % 0.36/0.58 (assume @p5 (forall @t20 (=> @t19 (forall @t18 (=> @t17 (=> (= @t16 @t15) (= @t14 @t13))))))) % 0.36/0.58 (assume @p6 (forall @t12 (=> @t11 (forall (@list @t21) (=> (tptp.mem @t21 @t3) (=> (forall @t10 (=> @t9 (= @t8 (tptp.ap @t21 @t6)))) (= @t7 @t21))))))) % 0.36/0.58 (assume @p7 (forall (@list @t2 @t22 @t6) (=> @t9 (= (tptp.ap (tptp.k @t2 @t22) @t6) @t22)))) % 0.36/0.58 (assume @p8 (forall (@list @t2 @t6) (=> @t9 (= (tptp.ap (tptp.i @t2) @t6) @t6)))) % 0.36/0.58 (assume @p9 (tptp.mem tptp.c_2Ebool_2ET tptp.bool)) % 0.36/0.58 (assume @p10 (tptp.p tptp.c_2Ebool_2ET)) % 0.36/0.58 (assume @p11 (forall @t31 (=> @t30 (forall @t29 (=> @t28 (tptp.mem @t27 (tptp.arr @t26 (tptp.arr @t24 tptp.bool)))))))) % 0.36/0.58 (assume @p12 (tptp.mem tptp.c_2Ebool_2EF tptp.bool)) % 0.36/0.58 (assume @p13 (not (tptp.p tptp.c_2Ebool_2EF))) % 0.36/0.58 (assume @p14 (tptp.mem tptp.c_2Emin_2E_3D_3D_3E @t33)) % 0.36/0.58 (assume @p15 (forall @t20 (=> @t19 (forall @t18 (=> @t17 (= (tptp.p (tptp.ap (tptp.ap tptp.c_2Emin_2E_3D_3D_3E @t14) @t13)) (=> @t16 @t15))))))) % 0.36/0.58 (assume @p16 (tptp.mem tptp.c_2Ebool_2E_5C_2F @t33)) % 0.36/0.58 (assume @p17 (forall @t20 (=> @t19 (forall @t18 (=> @t17 (= (tptp.p (tptp.ap (tptp.ap tptp.c_2Ebool_2E_5C_2F @t14) @t13)) (or @t16 @t15))))))) % 0.36/0.58 (assume @p18 (tptp.mem tptp.c_2Ebool_2E_2F_5C @t33)) % 0.36/0.58 (assume @p19 (forall @t20 (=> @t19 (forall @t18 (=> @t17 (= (tptp.p (tptp.ap (tptp.ap tptp.c_2Ebool_2E_2F_5C @t14) @t13)) (and @t16 @t15))))))) % 0.36/0.58 (assume @p20 (tptp.mem tptp.c_2Ebool_2E_7E @t32)) % 0.36/0.58 (assume @p21 (forall @t20 (=> @t19 (= (tptp.p (tptp.ap tptp.c_2Ebool_2E_7E @t14)) (not @t16))))) % 0.36/0.58 (assume @p22 (forall @t31 (=> @t30 (tptp.mem (tptp.c_2Emin_2E_3D @t25) (tptp.arr @t25 @t26))))) % 0.36/0.58 (assume @p23 (forall @t5 (=> @t4 (forall @t10 (=> @t9 (forall (@list @t22) (=> (tptp.mem @t22 @t2) (= (tptp.p (tptp.ap (tptp.ap (tptp.c_2Emin_2E_3D @t2) @t6) @t22)) (= @t6 @t22))))))))) % 0.36/0.58 (assume @p24 (forall @t31 (=> @t30 (tptp.mem (tptp.c_2Ebool_2E_21 @t25) (tptp.arr @t26 tptp.bool))))) % 0.36/0.58 (assume @p25 (forall @t5 (=> @t4 (forall @t20 (=> (tptp.mem @t14 (tptp.arr @t2 tptp.bool)) (= (tptp.p (tptp.ap (tptp.c_2Ebool_2E_21 @t2) @t14)) (forall @t10 (=> @t9 (tptp.p (tptp.ap @t14 @t6)))))))))) % 0.36/0.58 (assume @p26 true) % 0.36/0.58 (assume @p27 (forall @t38 (=> @t37 @t36))) % 0.36/0.58 (assume @p28 (forall @t31 (=> @t30 (forall @t38 (=> @t37 (= (forall (@list @t39) (=> (tptp.mem @t39 @t25) @t35)) @t35)))))) % 0.36/0.58 (assume @p29 (forall @t38 (=> @t37 (and (= (=> true @t35) @t35) (= (=> @t35 true) true) (= @t36 true) (= (=> @t35 @t35) true) (= (=> @t35 false) @t40))))) % 0.36/0.58 (assume @p30 (and @t42 (= @t41 false) (= (not false) true))) % 0.36/0.58 (assume @p31 (forall @t31 (=> @t30 (forall (@list @t43) (=> (tptp.mem @t43 @t25) (= (= @t43 @t43) true)))))) % 0.36/0.58 (assume @p32 (forall @t38 (=> @t37 (and (= (= true @t35) @t35) (= (= @t35 true) @t35) (= (= false @t35) @t40) (= (= @t35 false) @t40))))) % 0.36/0.58 (assume @p33 (forall @t31 (=> @t30 (forall @t29 (=> @t28 (forall @t50 (=> @t49 (forall @t48 (=> @t47 (or @t46 (tptp.p (tptp.ap (tptp.ap (tptp.c_2Ecardinal_2Ecardleq @t23 @t25) @t45) @t44)))))))))))) % 0.36/0.58 (assume @p34 @t42) % 0.36/0.58 (assume @p35 (forall @t56 (=> @t55 (=> @t52 @t54)))) % 0.36/0.58 (assume @p36 (forall @t56 (=> @t55 (forall @t62 (=> @t61 (= (=> (not (or @t52 @t58)) false) (=> @t60 @t59))))))) % 0.36/0.58 (assume @p37 (forall @t56 (=> @t55 (forall @t62 (=> @t61 (= (=> (not (or @t53 @t58)) false) (=> @t52 @t59))))))) % 0.36/0.58 (assume @p38 (forall @t56 (=> @t55 (=> @t54 (=> @t60 false))))) % 0.36/0.58 (assume @p39 (forall @t75 (=> @t74 (forall @t73 (=> @t72 (forall (@list @t69) (=> (tptp.mem @t69 tptp.bool) (= (= @t64 (= @t67 @t70)) (and (or @t64 @t67 @t70) (or @t64 @t71 @t68) (or @t67 @t71 @t65) (or @t70 @t68 @t65)))))))))) % 0.36/0.58 (assume @p40 (forall @t75 (=> @t74 (forall @t73 (=> @t72 (= (= @t64 @t68) (and (or @t64 @t67) (or @t68 @t65)))))))) % 0.36/0.58 (assume @p41 @t85) % 0.36/0.58 (step @p42 :rule evaluate :args (@t41)) % 0.36/0.58 (step @p43 :rule quant-unused-vars :args ((= (forall @t31 true) true))) % 0.36/0.58 (step @p44 :rule bool-impl-true1 :args (@t30)) % 0.36/0.58 (step @p45 :rule quant-unused-vars :args ((= (forall @t29 true) true))) % 0.36/0.58 (step @p46 :rule bool-impl-true1 :args (@t28)) % 0.36/0.58 (step @p47 :rule quant-unused-vars :args ((= (forall @t50 true) true))) % 0.36/0.58 (step @p48 :rule bool-impl-true1 :args (@t49)) % 0.36/0.58 (step @p49 :rule quant-unused-vars :args ((= (forall @t48 true) true))) % 0.36/0.58 (step @p50 :rule bool-impl-true1 :args (@t47)) % 0.36/0.58 (step @p51 :rule eq-refl :args (@t76)) % 0.36/0.58 (step @p52 :rule refl :args (@t47)) % 0.36/0.58 (step @p53 :rule cong :premises (@p52 @p51) :args (@t77)) % 0.36/0.58 (step @p54 :rule trans :premises (@p53 @p50)) % 0.36/0.58 (step @p55 :rule cong :premises (@p54) :args (@t78)) % 0.36/0.58 (step @p56 :rule trans :premises (@p55 @p49)) % 0.36/0.58 (step @p57 :rule refl :args (@t49)) % 0.36/0.58 (step @p58 :rule cong :premises (@p57 @p56) :args (@t79)) % 0.36/0.58 (step @p59 :rule trans :premises (@p58 @p48)) % 0.36/0.58 (step @p60 :rule cong :premises (@p59) :args (@t80)) % 0.36/0.58 (step @p61 :rule trans :premises (@p60 @p47)) % 0.36/0.58 (step @p62 :rule refl :args (@t28)) % 0.36/0.58 (step @p63 :rule cong :premises (@p62 @p61) :args (@t81)) % 0.36/0.58 (step @p64 :rule trans :premises (@p63 @p46)) % 0.36/0.58 (step @p65 :rule cong :premises (@p64) :args (@t82)) % 0.36/0.58 (step @p66 :rule trans :premises (@p65 @p45)) % 0.36/0.58 (step @p67 :rule refl :args (@t30)) % 0.36/0.58 (step @p68 :rule cong :premises (@p67 @p66) :args (@t83)) % 0.36/0.58 (step @p69 :rule trans :premises (@p68 @p44)) % 0.36/0.58 (step @p70 :rule cong :premises (@p69) :args (@t84)) % 0.36/0.58 (step @p71 :rule trans :premises (@p70 @p43)) % 0.36/0.58 (step @p72 :rule cong :premises (@p71) :args (@t85)) % 0.36/0.58 (step @p73 :rule trans :premises (@p72 @p42)) % 0.36/0.58 (step @p74 false :rule eq_resolve :premises (@p41 @p73)) % 0.36/0.58 ) % 0.36/0.58 % SZS output end Proof % 0.36/0.58 % cvc5 exiting %------------------------------------------------------------------------------