TSTP Solution File: ITP001^1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP001^1 : TPTP v8.2.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : do_cvc5 %s %d
% Computer : n006.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 May 29 17:11:32 EDT 2024
% Result : Theorem 0.38s 0.59s
% Output : Proof 0.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.15 % Problem : ITP001^1 : TPTP v8.2.0. Bugfixed v7.5.0.
% 0.07/0.16 % Command : do_cvc5 %s %d
% 0.16/0.37 % Computer : n006.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Sun May 26 03:46:39 EDT 2024
% 0.16/0.38 % CPUTime :
% 0.38/0.56 %----Proving TH0
% 0.38/0.59 --- Run --ho-elim --full-saturate-quant at 10...
% 0.38/0.59 % SZS status Theorem for /export/starexec/sandbox2/tmp/tmp.ay6owFyd1p/cvc5---1.0.5_7190.smt2
% 0.38/0.59 % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.ay6owFyd1p/cvc5---1.0.5_7190.smt2
% 0.38/0.59 (assume a0 (forall ((A_27a tptp.d) (A_27b tptp.d) (V0f_2E0 tptp.u) (V1g_2E0 tptp.u)) (=> (forall ((V2x_2E0 tptp.u)) (= (@ (@ tptp.s A_27b) (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) A_27b)) V0f_2E0)) (@ (@ tptp.s A_27a) V2x_2E0))) (@ (@ tptp.s A_27b) (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) A_27b)) V1g_2E0)) (@ (@ tptp.s A_27a) V2x_2E0))))) (= (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) A_27b)) V0f_2E0) (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) A_27b)) V1g_2E0)))))
% 0.38/0.59 (assume a1 (forall ((A_27a tptp.d) (V0x_2E0 tptp.u)) (= (@ (@ tptp.s A_27a) (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) A_27a)) tptp.combin_i_2E0)) (@ (@ tptp.s A_27a) V0x_2E0))) (@ (@ tptp.s A_27a) V0x_2E0))))
% 0.38/0.59 (assume a2 (forall ((A_27a tptp.d) (A_27b tptp.d) (V0x_2E0 tptp.u) (V1y_2E0 tptp.u)) (= (@ (@ tptp.s A_27a) (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27b) A_27a)) (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) (@ (@ tptp.tyop_2Emin_2Efun A_27b) A_27a))) tptp.combin_k_2E0)) (@ (@ tptp.s A_27a) V0x_2E0)))) (@ (@ tptp.s A_27b) V1y_2E0))) (@ (@ tptp.s A_27a) V0x_2E0))))
% 0.38/0.59 (assume a3 (forall ((A_27a tptp.d) (A_27b tptp.d) (A_27c tptp.d) (V0f_2E0 tptp.u) (V1g_2E0 tptp.u) (V2x_2E0 tptp.u)) (= (@ (@ tptp.s A_27c) (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) A_27c)) (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun (@ (@ tptp.tyop_2Emin_2Efun A_27a) A_27b)) (@ (@ tptp.tyop_2Emin_2Efun A_27a) A_27c))) (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun (@ (@ tptp.tyop_2Emin_2Efun A_27a) (@ (@ tptp.tyop_2Emin_2Efun A_27b) A_27c))) (@ (@ tptp.tyop_2Emin_2Efun (@ (@ tptp.tyop_2Emin_2Efun A_27a) A_27b)) (@ (@ tptp.tyop_2Emin_2Efun A_27a) A_27c)))) tptp.combin_s_2E0)) (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) (@ (@ tptp.tyop_2Emin_2Efun A_27b) A_27c))) V0f_2E0)))) (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) A_27b)) V1g_2E0)))) (@ (@ tptp.s A_27a) V2x_2E0))) (@ (@ tptp.s A_27c) (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27b) A_27c)) (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) (@ (@ tptp.tyop_2Emin_2Efun A_27b) A_27c))) V0f_2E0)) (@ (@ tptp.s A_27a) V2x_2E0)))) (@ (@ tptp.s A_27b) (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) A_27b)) V1g_2E0)) (@ (@ tptp.s A_27a) V2x_2E0))))))))
% 0.38/0.59 (assume a4 (forall ((V0 Bool) (V1 Bool)) (= (@ (@ tptp.mono_2Ec_2Ebool_2E_2F_5C V0) V1) (and V0 V1))))
% 0.38/0.59 (assume a5 (forall ((V0 Bool) (V1 Bool)) (= (@ (@ tptp.mono_2Ec_2Ebool_2E_5C_2F V0) V1) (or V0 V1))))
% 0.38/0.59 (assume a6 (forall ((V0 Bool)) (= (@ tptp.mono_2Ec_2Ebool_2E_7E V0) (not V0))))
% 0.38/0.59 (assume a7 (forall ((V0 Bool) (V1 Bool)) (= (@ (@ tptp.mono_2Ec_2Emin_2E_3D_3D_3E V0) V1) (=> V0 V1))))
% 0.38/0.59 (assume a8 (forall ((A_27a tptp.d) (V0_2E0 tptp.u) (V1_2E0 tptp.u)) (= (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ (@ tptp.c_2Emin_2E_3D_2E2 (@ (@ tptp.s A_27a) V0_2E0)) (@ (@ tptp.s A_27a) V1_2E0)))) (= (@ (@ tptp.s A_27a) V0_2E0) (@ (@ tptp.s A_27a) V1_2E0)))))
% 0.38/0.59 (assume a9 (forall ((A_27a tptp.d) (V0f_2E0 tptp.u)) (= (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ tptp.c_2Ebool_2E_21_2E1 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool)) V0f_2E0)))) (forall ((V1x_2E0 tptp.u)) (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool)) V0f_2E0)) (@ (@ tptp.s A_27a) V1x_2E0))))))))
% 0.38/0.59 (assume a10 (forall ((A_27a tptp.d) (V0f_2E0 tptp.u)) (= (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ tptp.c_2Ebool_2E_3F_2E1 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool)) V0f_2E0)))) (exists ((V1x_2E0 tptp.u)) (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool)) V0f_2E0)) (@ (@ tptp.s A_27a) V1x_2E0))))))))
% 0.38/0.59 (assume a11 (forall ((V0_2E0 tptp.u)) (= (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ tptp.i_mono_2Etyop_2Emin_2Ebool (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) V0_2E0)))) (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) V0_2E0))))
% 0.38/0.59 (assume a12 (forall ((V0_2E0 tptp.u)) (= (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool) tptp.tyop_2Emin_2Ebool)) (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 (@ tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool) tptp.tyop_2Emin_2Ebool)) V0_2E0)))) (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool) tptp.tyop_2Emin_2Ebool)) V0_2E0))))
% 0.38/0.59 (assume a13 (forall ((V0_2E0 tptp.u)) (= (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool) (@ (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool) tptp.tyop_2Emin_2Ebool))) (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 (@ tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool) (@ (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool) tptp.tyop_2Emin_2Ebool))) V0_2E0)))) (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool) (@ (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool) tptp.tyop_2Emin_2Ebool))) V0_2E0))))
% 0.38/0.59 (assume a14 (forall ((V0 Bool)) (= (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ tptp.i_mono_2Etyop_2Emin_2Ebool V0))) V0)))
% 0.38/0.59 (assume a15 (forall ((V0 (-> Bool Bool))) (= (@ tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool) tptp.tyop_2Emin_2Ebool)) (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 V0))) V0)))
% 0.38/0.59 (assume a16 (forall ((V0 (-> Bool Bool Bool))) (= (@ tptp.j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool) (@ (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool) tptp.tyop_2Emin_2Ebool))) (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 V0))) V0)))
% 0.38/0.59 (assume a17 (forall ((A_27a tptp.d) (X0_2E0 tptp.u)) (= (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ tptp.c_2Ebool_2E_21_2E1 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool)) X0_2E0)))) (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool)) tptp.tyop_2Emin_2Ebool)) tptp.c_2Ebool_2E_21_2E0)) (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool)) X0_2E0)))))))
% 0.38/0.59 (assume a18 (forall ((A_27a tptp.d) (X0_2E0 tptp.u) (X1_2E0 tptp.u)) (= (= (@ (@ tptp.s A_27a) X0_2E0) (@ (@ tptp.s A_27a) X1_2E0)) (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool)) (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool))) tptp.c_2Emin_2E_3D_2E0)) (@ (@ tptp.s A_27a) X0_2E0)))) (@ (@ tptp.s A_27a) X1_2E0)))))))
% 0.38/0.59 (assume a19 (forall ((A_27a tptp.d) (X0_2E0 tptp.u)) (= (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ tptp.c_2Ebool_2E_3F_2E1 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool)) X0_2E0)))) (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool)) tptp.tyop_2Emin_2Ebool)) tptp.c_2Ebool_2E_3F_2E0)) (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool)) X0_2E0)))))))
% 0.38/0.59 (assume a20 (forall ((V0 (-> Bool Bool)) (V1 Bool)) (= (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ tptp.i_mono_2Etyop_2Emin_2Ebool (@ V0 V1))) (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool) tptp.tyop_2Emin_2Ebool)) (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 V0))) (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ tptp.i_mono_2Etyop_2Emin_2Ebool V1)))))))
% 0.38/0.59 (assume a21 (forall ((V0 (-> Bool Bool Bool)) (V1 Bool)) (= (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool) tptp.tyop_2Emin_2Ebool)) (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 (@ V0 V1))) (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool) tptp.tyop_2Emin_2Ebool)) (@ (@ tptp.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool) (@ (@ tptp.tyop_2Emin_2Efun tptp.tyop_2Emin_2Ebool) tptp.tyop_2Emin_2Ebool))) (@ tptp.i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 V0))) (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ tptp.i_mono_2Etyop_2Emin_2Ebool V1)))))))
% 0.38/0.59 (assume a22 (forall ((V0 (-> Bool Bool)) (V1 Bool)) (= (@ V0 V1) (@ V0 V1))))
% 0.38/0.59 (assume a23 (forall ((V0 (-> Bool Bool Bool)) (V1 Bool)) (= (@ V0 V1) (@ V0 V1))))
% 0.38/0.59 (assume a24 (= tptp.mono_2Ec_2Ebool_2ET (forall ((V0x Bool)) (= V0x V0x))))
% 0.38/0.59 (assume a25 (not tptp.mono_2Ec_2Ebool_2ET))
% 0.38/0.59 (assume a26 true)
% 0.38/0.59 (step t1 (cl (not (= (= tptp.mono_2Ec_2Ebool_2ET (forall ((V0x Bool)) (= V0x V0x))) tptp.mono_2Ec_2Ebool_2ET)) (not (= tptp.mono_2Ec_2Ebool_2ET (forall ((V0x Bool)) (= V0x V0x)))) tptp.mono_2Ec_2Ebool_2ET) :rule equiv_pos2)
% 0.38/0.59 (step t2 (cl (= tptp.mono_2Ec_2Ebool_2ET tptp.mono_2Ec_2Ebool_2ET)) :rule refl)
% 0.38/0.59 (anchor :step t3 :args ((V0x Bool) (:= V0x V0x)))
% 0.38/0.59 (step t3.t1 (cl (= V0x V0x)) :rule refl)
% 0.38/0.59 (step t3.t2 (cl (= (= V0x V0x) true)) :rule all_simplify)
% 0.38/0.59 (step t3 (cl (= (forall ((V0x Bool)) (= V0x V0x)) (forall ((V0x Bool)) true))) :rule bind)
% 0.38/0.59 (step t4 (cl (= (forall ((V0x Bool)) true) true)) :rule all_simplify)
% 0.38/0.59 (step t5 (cl (= (forall ((V0x Bool)) (= V0x V0x)) true)) :rule trans :premises (t3 t4))
% 0.38/0.59 (step t6 (cl (= (= tptp.mono_2Ec_2Ebool_2ET (forall ((V0x Bool)) (= V0x V0x))) (= tptp.mono_2Ec_2Ebool_2ET true))) :rule cong :premises (t2 t5))
% 0.38/0.59 (step t7 (cl (= (= tptp.mono_2Ec_2Ebool_2ET true) tptp.mono_2Ec_2Ebool_2ET)) :rule all_simplify)
% 0.38/0.59 (step t8 (cl (= (= tptp.mono_2Ec_2Ebool_2ET (forall ((V0x Bool)) (= V0x V0x))) tptp.mono_2Ec_2Ebool_2ET)) :rule trans :premises (t6 t7))
% 0.38/0.59 (step t9 (cl tptp.mono_2Ec_2Ebool_2ET) :rule resolution :premises (t1 t8 a24))
% 0.38/0.59 (step t10 (cl) :rule resolution :premises (t9 a25))
% 0.38/0.59
% 0.38/0.59 % SZS output end Proof for /export/starexec/sandbox2/tmp/tmp.ay6owFyd1p/cvc5---1.0.5_7190.smt2
% 0.38/0.59 % cvc5---1.0.5 exiting
% 0.38/0.59 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------