%------------------------------------------------------------------------------ % 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 : 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 08:24:30 AM UTC 2026 % Result : Theorem 0.37s 0.57s % Output : Proof 0.37s % 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 % 0.16/0.34 % 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 03:47:03 EDT 2026 % 0.16/0.34 % CPUTime : % 0.30/0.50 %----Proving TH0 % 0.37/0.57 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.37/0.57 % SZS status Theorem % 0.37/0.57 % SZS output start Proof % 0.37/0.57 ( % 0.37/0.57 (declare-sort tptp.del 0) % 0.37/0.57 (declare-sort $$unsorted 0) % 0.37/0.57 (declare-const tptp.c_2Ebool_2E_21 (-> tptp.del $$unsorted)) % 0.37/0.57 (declare-const tptp.c_2Emin_2E_3D (-> tptp.del $$unsorted)) % 0.37/0.57 (declare-const tptp.c_2Ebool_2E_7E $$unsorted) % 0.37/0.57 (declare-const tptp.inj__o (-> Bool $$unsorted)) % 0.37/0.57 (declare-const tptp.p (-> $$unsorted Bool)) % 0.37/0.57 (declare-const tptp.bool tptp.del) % 0.37/0.57 (declare-const tptp.c_2Ebool_2EF $$unsorted) % 0.37/0.57 (declare-const tptp.mem (-> $$unsorted tptp.del Bool)) % 0.37/0.57 (declare-const tptp.c_2Emin_2E_3D_3D_3E $$unsorted) % 0.37/0.57 (declare-const tptp.ap (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.57 (declare-const tptp.c_2Ebool_2E_2F_5C $$unsorted) % 0.37/0.57 (declare-const tptp.arr (-> tptp.del tptp.del tptp.del)) % 0.37/0.57 (declare-const tptp.c_2Ebool_2ET $$unsorted) % 0.37/0.57 (declare-const tptp.lam (-> tptp.del (-> $$unsorted $$unsorted) $$unsorted)) % 0.37/0.57 (declare-const tptp.c_2Ecardinal_2Ecardleq (-> tptp.del tptp.del $$unsorted)) % 0.37/0.57 (declare-const tptp.c_2Ebool_2E_5C_2F $$unsorted) % 0.37/0.57 (define @t1 () (@var "X" Bool)) % 0.37/0.57 (define @t2 () (_ tptp.inj__o @t1)) % 0.37/0.57 (define @t3 () (@list @t1)) % 0.37/0.57 (define @t4 () (@var "X" $$unsorted)) % 0.37/0.57 (define @t5 () (_ tptp.mem @t4)) % 0.37/0.57 (define @t6 () (@list @t4)) % 0.37/0.57 (define @t7 () (@var "B" tptp.del)) % 0.37/0.57 (define @t8 () (@var "F" $$unsorted)) % 0.37/0.57 (define @t9 () (_ (_ tptp.ap @t8) @t4)) % 0.37/0.57 (define @t10 () (@var "A" tptp.del)) % 0.37/0.57 (define @t11 () (_ @t5 @t10)) % 0.37/0.57 (define @t12 () (_ tptp.arr @t10)) % 0.37/0.57 (define @t13 () (_ @t12 @t7)) % 0.37/0.57 (define @t14 () (_ (_ tptp.mem @t8) @t13)) % 0.37/0.57 (define @t15 () (@list @t10 @t7 @t8)) % 0.37/0.57 (define @t16 () (@var "F" (-> $$unsorted $$unsorted))) % 0.37/0.57 (define @t17 () (_ (_ tptp.lam @t10) @t16)) % 0.37/0.57 (define @t18 () (_ @t16 @t4)) % 0.37/0.57 (define @t19 () (@var "G" $$unsorted)) % 0.37/0.57 (define @t20 () (@var "A_27b" tptp.del)) % 0.37/0.57 (define @t21 () (_ (_ tptp.arr @t20) tptp.bool)) % 0.37/0.57 (define @t22 () (@var "A_27a" tptp.del)) % 0.37/0.57 (define @t23 () (_ tptp.arr @t22)) % 0.37/0.57 (define @t24 () (_ @t23 tptp.bool)) % 0.37/0.57 (define @t25 () (_ tptp.arr @t24)) % 0.37/0.57 (define @t26 () (_ (_ tptp.c_2Ecardinal_2Ecardleq @t22) @t20)) % 0.37/0.57 (define @t27 () (_ tptp.arr tptp.bool)) % 0.37/0.57 (define @t28 () (_ @t27 tptp.bool)) % 0.37/0.57 (define @t29 () (_ @t27 @t28)) % 0.37/0.57 (define @t30 () (@var "R" $$unsorted)) % 0.37/0.57 (define @t31 () (_ tptp.p @t30)) % 0.37/0.57 (define @t32 () (@var "Q" $$unsorted)) % 0.37/0.57 (define @t33 () (_ tptp.p @t32)) % 0.37/0.57 (define @t34 () (_ (_ tptp.mem @t30) tptp.bool)) % 0.37/0.57 (define @t35 () (@list @t30)) % 0.37/0.57 (define @t36 () (_ tptp.mem @t32)) % 0.37/0.57 (define @t37 () (_ @t36 tptp.bool)) % 0.37/0.57 (define @t38 () (@list @t32)) % 0.37/0.57 (define @t39 () (@list @t22)) % 0.37/0.57 (define @t40 () (@var "Y" $$unsorted)) % 0.37/0.57 (define @t41 () (@var "V0t" $$unsorted)) % 0.37/0.57 (define @t42 () (_ tptp.p @t41)) % 0.37/0.57 (define @t43 () (=> false @t42)) % 0.37/0.57 (define @t44 () (_ (_ tptp.mem @t41) tptp.bool)) % 0.37/0.57 (define @t45 () (@list @t41)) % 0.37/0.57 (define @t46 () (@var "V1x" $$unsorted)) % 0.37/0.57 (define @t47 () (not @t42)) % 0.37/0.57 (define @t48 () (not true)) % 0.37/0.57 (define @t49 () (forall @t45 (=> @t44 (= (not @t47) @t42)))) % 0.37/0.57 (define @t50 () (@var "V0x" $$unsorted)) % 0.37/0.57 (define @t51 () (@var "V0s" $$unsorted)) % 0.37/0.57 (define @t52 () (@var "V1t" $$unsorted)) % 0.37/0.57 (define @t53 () (_ tptp.p (_ (_ tptp.ap (_ (_ tptp.ap @t26) @t51)) @t52))) % 0.37/0.57 (define @t54 () (_ (_ tptp.mem @t52) @t21)) % 0.37/0.57 (define @t55 () (@list @t52)) % 0.37/0.57 (define @t56 () (_ (_ tptp.mem @t51) @t24)) % 0.37/0.57 (define @t57 () (@list @t22 @t20 @t51)) % 0.37/0.57 (define @t58 () (@var "V0A" $$unsorted)) % 0.37/0.57 (define @t59 () (_ tptp.p @t58)) % 0.37/0.57 (define @t60 () (not @t59)) % 0.37/0.57 (define @t61 () (=> @t60 false)) % 0.37/0.57 (define @t62 () (_ (_ tptp.mem @t58) tptp.bool)) % 0.37/0.57 (define @t63 () (@list @t58)) % 0.37/0.57 (define @t64 () (@var "V1B" $$unsorted)) % 0.37/0.57 (define @t65 () (_ tptp.p @t64)) % 0.37/0.57 (define @t66 () (=> (not @t65) false)) % 0.37/0.57 (define @t67 () (=> @t59 false)) % 0.37/0.57 (define @t68 () (_ (_ tptp.mem @t64) tptp.bool)) % 0.37/0.57 (define @t69 () (@list @t64)) % 0.37/0.57 (define @t70 () (@var "V0p" $$unsorted)) % 0.37/0.57 (define @t71 () (_ tptp.p @t70)) % 0.37/0.57 (define @t72 () (not @t71)) % 0.37/0.57 (define @t73 () (@var "V1q" $$unsorted)) % 0.37/0.57 (define @t74 () (_ tptp.p @t73)) % 0.37/0.57 (define @t75 () (not @t74)) % 0.37/0.57 (define @t76 () (@var "V2r" $$unsorted)) % 0.37/0.57 (define @t77 () (_ tptp.p @t76)) % 0.37/0.57 (define @t78 () (not @t77)) % 0.37/0.57 (define @t79 () (_ (_ tptp.mem @t73) tptp.bool)) % 0.37/0.57 (define @t80 () (@list @t73)) % 0.37/0.57 (define @t81 () (_ (_ tptp.mem @t70) tptp.bool)) % 0.37/0.57 (define @t82 () (@list @t70)) % 0.37/0.57 (define @t83 () (not @t53)) % 0.37/0.57 (define @t84 () (=> @t54 (= @t83 @t83))) % 0.37/0.57 (define @t85 () (forall @t55 @t84)) % 0.37/0.57 (define @t86 () (=> @t56 @t85)) % 0.37/0.57 (define @t87 () (forall @t57 @t86)) % 0.37/0.57 (define @t88 () (not @t87)) % 0.37/0.57 (assume @p1 (forall @t3 (= (_ tptp.p @t2) @t1))) % 0.37/0.57 (assume @p2 (forall @t3 (_ (_ tptp.mem @t2) tptp.bool))) % 0.37/0.57 (assume @p3 (forall @t6 (=> (_ @t5 tptp.bool) (= @t4 (_ tptp.inj__o (_ tptp.p @t4)))))) % 0.37/0.57 (assume @p4 (forall @t15 (=> @t14 (forall @t6 (=> @t11 (_ (_ tptp.mem @t9) @t7)))))) % 0.37/0.57 (assume @p5 (forall (@list @t10 @t7 @t16) (=> (forall @t6 (=> @t11 (_ (_ tptp.mem @t18) @t7))) (_ (_ tptp.mem @t17) @t13)))) % 0.37/0.57 (assume @p6 (forall @t15 (=> @t14 (forall (@list @t19) (=> (_ (_ tptp.mem @t19) @t13) (=> (forall @t6 (=> @t11 (= @t9 (_ (_ tptp.ap @t19) @t4)))) (= @t8 @t19))))))) % 0.37/0.57 (assume @p7 (forall (@list @t10 @t16 @t4) (=> @t11 (= (_ (_ tptp.ap @t17) @t4) @t18)))) % 0.37/0.57 (assume @p8 (_ (_ tptp.mem tptp.c_2Ebool_2ET) tptp.bool)) % 0.37/0.57 (assume @p9 (_ tptp.p tptp.c_2Ebool_2ET)) % 0.37/0.57 (assume @p10 (forall (@list @t22 @t20) (_ (_ tptp.mem @t26) (_ @t25 (_ (_ tptp.arr @t21) tptp.bool))))) % 0.37/0.57 (assume @p11 (_ (_ tptp.mem tptp.c_2Ebool_2EF) tptp.bool)) % 0.37/0.57 (assume @p12 (not (_ tptp.p tptp.c_2Ebool_2EF))) % 0.37/0.57 (assume @p13 (_ (_ tptp.mem tptp.c_2Emin_2E_3D_3D_3E) @t29)) % 0.37/0.57 (assume @p14 (forall @t38 (=> @t37 (forall @t35 (=> @t34 (= (_ tptp.p (_ (_ tptp.ap (_ (_ tptp.ap tptp.c_2Emin_2E_3D_3D_3E) @t32)) @t30)) (=> @t33 @t31))))))) % 0.37/0.57 (assume @p15 (_ (_ tptp.mem tptp.c_2Ebool_2E_5C_2F) @t29)) % 0.37/0.57 (assume @p16 (forall @t38 (=> @t37 (forall @t35 (=> @t34 (= (_ tptp.p (_ (_ tptp.ap (_ (_ tptp.ap tptp.c_2Ebool_2E_5C_2F) @t32)) @t30)) (or @t33 @t31))))))) % 0.37/0.57 (assume @p17 (_ (_ tptp.mem tptp.c_2Ebool_2E_2F_5C) @t29)) % 0.37/0.57 (assume @p18 (forall @t38 (=> @t37 (forall @t35 (=> @t34 (= (_ tptp.p (_ (_ tptp.ap (_ (_ tptp.ap tptp.c_2Ebool_2E_2F_5C) @t32)) @t30)) (and @t33 @t31))))))) % 0.37/0.57 (assume @p19 (_ (_ tptp.mem tptp.c_2Ebool_2E_7E) @t28)) % 0.37/0.57 (assume @p20 (forall @t38 (=> @t37 (= (_ tptp.p (_ (_ tptp.ap tptp.c_2Ebool_2E_7E) @t32)) (not @t33))))) % 0.37/0.57 (assume @p21 (forall @t39 (_ (_ tptp.mem (_ tptp.c_2Emin_2E_3D @t22)) (_ @t23 @t24)))) % 0.37/0.57 (assume @p22 (forall (@list @t10 @t4) (=> @t11 (forall (@list @t40) (=> (_ (_ tptp.mem @t40) @t10) (= (_ tptp.p (_ (_ tptp.ap (_ (_ tptp.ap (_ tptp.c_2Emin_2E_3D @t10)) @t4)) @t40)) (= @t4 @t40))))))) % 0.37/0.57 (assume @p23 (forall @t39 (_ (_ tptp.mem (_ tptp.c_2Ebool_2E_21 @t22)) (_ @t25 tptp.bool)))) % 0.37/0.57 (assume @p24 (forall (@list @t10 @t32) (=> (_ @t36 (_ @t12 tptp.bool)) (= (_ tptp.p (_ (_ tptp.ap (_ tptp.c_2Ebool_2E_21 @t10)) @t32)) (forall @t6 (=> @t11 (_ tptp.p (_ (_ tptp.ap @t32) @t4)))))))) % 0.37/0.57 (assume @p25 true) % 0.37/0.57 (assume @p26 (forall @t45 (=> @t44 @t43))) % 0.37/0.57 (assume @p27 (forall (@list @t22 @t41) (=> @t44 (= (forall (@list @t46) (=> (_ (_ tptp.mem @t46) @t22) @t42)) @t42)))) % 0.37/0.57 (assume @p28 (forall @t45 (=> @t44 (and (= (=> true @t42) @t42) (= (=> @t42 true) true) (= @t43 true) (= (=> @t42 @t42) true) (= (=> @t42 false) @t47))))) % 0.37/0.57 (assume @p29 (and @t49 (= @t48 false) (= (not false) true))) % 0.37/0.57 (assume @p30 (forall (@list @t22 @t50) (=> (_ (_ tptp.mem @t50) @t22) (= (= @t50 @t50) true)))) % 0.37/0.57 (assume @p31 (forall @t45 (=> @t44 (and (= (= true @t42) @t42) (= (= @t42 true) @t42) (= (= false @t42) @t47) (= (= @t42 false) @t47))))) % 0.37/0.57 (assume @p32 (forall @t57 (=> @t56 (forall @t55 (=> @t54 (or @t53 (_ tptp.p (_ (_ tptp.ap (_ (_ tptp.ap (_ (_ tptp.c_2Ecardinal_2Ecardleq @t20) @t22)) @t52)) @t51)))))))) % 0.37/0.57 (assume @p33 @t49) % 0.37/0.57 (assume @p34 (forall @t63 (=> @t62 (=> @t59 @t61)))) % 0.37/0.57 (assume @p35 (forall @t63 (=> @t62 (forall @t69 (=> @t68 (= (=> (not (or @t59 @t65)) false) (=> @t67 @t66))))))) % 0.37/0.57 (assume @p36 (forall @t63 (=> @t62 (forall @t69 (=> @t68 (= (=> (not (or @t60 @t65)) false) (=> @t59 @t66))))))) % 0.37/0.57 (assume @p37 (forall @t63 (=> @t62 (=> @t61 (=> @t67 false))))) % 0.37/0.57 (assume @p38 (forall @t82 (=> @t81 (forall @t80 (=> @t79 (forall (@list @t76) (=> (_ (_ tptp.mem @t76) tptp.bool) (= (= @t71 (= @t74 @t77)) (and (or @t71 @t74 @t77) (or @t71 @t78 @t75) (or @t74 @t78 @t72) (or @t77 @t75 @t72)))))))))) % 0.37/0.57 (assume @p39 (forall @t82 (=> @t81 (forall @t80 (=> @t79 (= (= @t71 @t75) (and (or @t71 @t74) (or @t75 @t72)))))))) % 0.37/0.58 (assume @p40 @t88) % 0.37/0.58 (step @p41 :rule evaluate :args (@t48)) % 0.37/0.58 (step @p42 :rule quant-unused-vars :args ((= (forall @t57 true) true))) % 0.37/0.58 (step @p43 :rule bool-impl-true1 :args (@t56)) % 0.37/0.58 (step @p44 :rule quant-unused-vars :args ((= (forall @t55 true) true))) % 0.37/0.58 (step @p45 :rule bool-impl-true1 :args (@t54)) % 0.37/0.58 (step @p46 :rule eq-refl :args (@t83)) % 0.37/0.58 (step @p47 :rule refl :args (@t54)) % 0.37/0.58 (step @p48 :rule cong :premises (@p47 @p46) :args (@t84)) % 0.37/0.58 (step @p49 :rule trans :premises (@p48 @p45)) % 0.37/0.58 (step @p50 :rule cong :premises (@p49) :args (@t85)) % 0.37/0.58 (step @p51 :rule trans :premises (@p50 @p44)) % 0.37/0.58 (step @p52 :rule refl :args (@t56)) % 0.37/0.58 (step @p53 :rule cong :premises (@p52 @p51) :args (@t86)) % 0.37/0.58 (step @p54 :rule trans :premises (@p53 @p43)) % 0.37/0.58 (step @p55 :rule cong :premises (@p54) :args (@t87)) % 0.37/0.58 (step @p56 :rule trans :premises (@p55 @p42)) % 0.37/0.58 (step @p57 :rule cong :premises (@p56) :args (@t88)) % 0.37/0.58 (step @p58 :rule trans :premises (@p57 @p41)) % 0.37/0.58 (step @p59 false :rule eq_resolve :premises (@p40 @p58)) % 0.37/0.58 ) % 0.37/0.58 % SZS output end Proof % 0.37/0.58 % cvc5 exiting %------------------------------------------------------------------------------