TSTP Solution File: ITP010^1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP010^1 : TPTP v8.2.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : do_cvc5 %s %d
% Computer : n010.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 17:11:44 EDT 2024
% Result : Theorem 0.22s 0.55s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ITP010^1 : TPTP v8.2.0. Bugfixed v7.5.0.
% 0.07/0.14 % Command : do_cvc5 %s %d
% 0.15/0.35 % Computer : n010.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sun May 26 03:40:09 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.22/0.52 %----Proving TH0
% 0.22/0.55 --- Run --ho-elim --full-saturate-quant at 10...
% 0.22/0.55 % SZS status Theorem for /export/starexec/sandbox/tmp/tmp.5qoox4ZhXN/cvc5---1.0.5_4175.smt2
% 0.22/0.55 % SZS output start Proof for /export/starexec/sandbox/tmp/tmp.5qoox4ZhXN/cvc5---1.0.5_4175.smt2
% 0.22/0.55 (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)))))
% 0.22/0.55 (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))))
% 0.22/0.55 (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))))
% 0.22/0.55 (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))))))))
% 0.22/0.55 (assume a4 (forall ((V0 Bool) (V1 Bool)) (= (@ (@ tptp.mono_2Ec_2Ebool_2E_2F_5C V0) V1) (and V0 V1))))
% 0.22/0.55 (assume a5 (forall ((V0 Bool) (V1 Bool)) (= (@ (@ tptp.mono_2Ec_2Ebool_2E_5C_2F V0) V1) (or V0 V1))))
% 0.22/0.55 (assume a6 (forall ((V0 Bool)) (= (@ tptp.mono_2Ec_2Ebool_2E_7E V0) (not V0))))
% 0.22/0.55 (assume a7 (forall ((V0 Bool) (V1 Bool)) (= (@ (@ tptp.mono_2Ec_2Emin_2E_3D_3D_3E V0) V1) (=> V0 V1))))
% 0.22/0.55 (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)))))
% 0.22/0.55 (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))))))))
% 0.22/0.55 (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))))))))
% 0.22/0.55 (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))))
% 0.22/0.55 (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))))
% 0.22/0.55 (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))))
% 0.22/0.55 (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)))
% 0.22/0.55 (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)))
% 0.22/0.55 (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)))
% 0.22/0.55 (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)))))))
% 0.22/0.55 (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)))))))
% 0.22/0.55 (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)))))))
% 0.22/0.55 (assume a20 (forall ((A_27a tptp.d) (A_27b tptp.d) (X0_2E0 tptp.u) (X1_2E0 tptp.u)) (= (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ (@ tptp.c_2Ecardinal_2Ecardleq_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool)) X0_2E0)) (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27b) tptp.tyop_2Emin_2Ebool)) X1_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_27b) tptp.tyop_2Emin_2Ebool)) 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_2Efun (@ (@ tptp.tyop_2Emin_2Efun A_27b) tptp.tyop_2Emin_2Ebool)) tptp.tyop_2Emin_2Ebool))) tptp.c_2Ecardinal_2Ecardleq_2E0)) (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool)) X0_2E0)))) (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27b) tptp.tyop_2Emin_2Ebool)) X1_2E0)))))))
% 0.22/0.55 (assume a21 (forall ((A_27a tptp.d) (A_27b tptp.d) (X0_2E0 tptp.u) (X1_2E0 tptp.u)) (= (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ (@ tptp.c_2Ecardinal_2Ecardleq_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27b) tptp.tyop_2Emin_2Ebool)) X0_2E0)) (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool)) X1_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.app_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun (@ (@ tptp.tyop_2Emin_2Efun A_27b) tptp.tyop_2Emin_2Ebool)) (@ (@ tptp.tyop_2Emin_2Efun (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool)) tptp.tyop_2Emin_2Ebool))) tptp.c_2Ecardinal_2Ecardleq_2E0)) (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27b) tptp.tyop_2Emin_2Ebool)) X0_2E0)))) (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool)) X1_2E0)))))))
% 0.22/0.55 (assume a22 (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)))))))
% 0.22/0.55 (assume a23 (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)))))))
% 0.22/0.55 (assume a24 (forall ((V0 (-> Bool Bool)) (V1 Bool)) (= (@ V0 V1) (@ V0 V1))))
% 0.22/0.55 (assume a25 (forall ((V0 (-> Bool Bool Bool)) (V1 Bool)) (= (@ V0 V1) (@ V0 V1))))
% 0.22/0.55 (assume a26 tptp.mono_2Ec_2Ebool_2ET)
% 0.22/0.55 (assume a27 (forall ((V0t Bool)) (=> tptp.mono_2Ec_2Ebool_2EF V0t)))
% 0.22/0.55 (assume a28 (forall ((A_27a tptp.d) (V0t Bool)) (= (forall ((V1x_2E0 tptp.u)) V0t) V0t)))
% 0.22/0.55 (assume a29 (forall ((V0t Bool)) (and (= (=> tptp.mono_2Ec_2Ebool_2ET V0t) V0t) (= (=> V0t tptp.mono_2Ec_2Ebool_2ET) tptp.mono_2Ec_2Ebool_2ET) (= (=> tptp.mono_2Ec_2Ebool_2EF V0t) tptp.mono_2Ec_2Ebool_2ET) (= (=> V0t V0t) tptp.mono_2Ec_2Ebool_2ET) (= (=> V0t tptp.mono_2Ec_2Ebool_2EF) (not V0t)))))
% 0.22/0.55 (assume a30 (and (forall ((V0t Bool)) (= (not (not V0t)) V0t)) (= (not tptp.mono_2Ec_2Ebool_2ET) tptp.mono_2Ec_2Ebool_2EF) (= (not tptp.mono_2Ec_2Ebool_2EF) tptp.mono_2Ec_2Ebool_2ET)))
% 0.22/0.55 (assume a31 (forall ((A_27a tptp.d) (V0x_2E0 tptp.u)) (= (= (@ (@ tptp.s A_27a) V0x_2E0) (@ (@ tptp.s A_27a) V0x_2E0)) tptp.mono_2Ec_2Ebool_2ET)))
% 0.22/0.55 (assume a32 (forall ((V0t Bool)) (and (= (= tptp.mono_2Ec_2Ebool_2ET V0t) V0t) (= (= V0t tptp.mono_2Ec_2Ebool_2ET) V0t) (= (= tptp.mono_2Ec_2Ebool_2EF V0t) (not V0t)) (= (= V0t tptp.mono_2Ec_2Ebool_2EF) (not V0t)))))
% 0.22/0.55 (assume a33 (forall ((A_27a tptp.d) (A_27b tptp.d) (V0s_2E0 tptp.u) (V1t_2E0 tptp.u)) (or (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ (@ tptp.c_2Ecardinal_2Ecardleq_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool)) V0s_2E0)) (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27b) tptp.tyop_2Emin_2Ebool)) V1t_2E0)))) (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ (@ tptp.c_2Ecardinal_2Ecardleq_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27b) tptp.tyop_2Emin_2Ebool)) V1t_2E0)) (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool)) V0s_2E0)))))))
% 0.22/0.55 (assume a34 (forall ((V0t Bool)) (= (not (not V0t)) V0t)))
% 0.22/0.55 (assume a35 (forall ((V0A Bool)) (=> V0A (=> (not V0A) tptp.mono_2Ec_2Ebool_2EF))))
% 0.22/0.55 (assume a36 (forall ((V0B Bool) (V1A Bool)) (= (=> (not (or V1A V0B)) tptp.mono_2Ec_2Ebool_2EF) (=> (=> V1A tptp.mono_2Ec_2Ebool_2EF) (=> (not V0B) tptp.mono_2Ec_2Ebool_2EF)))))
% 0.22/0.55 (assume a37 (forall ((V0B Bool) (V1A Bool)) (= (=> (not (or (not V1A) V0B)) tptp.mono_2Ec_2Ebool_2EF) (=> V1A (=> (not V0B) tptp.mono_2Ec_2Ebool_2EF)))))
% 0.22/0.55 (assume a38 (forall ((V0A Bool)) (=> (=> (not V0A) tptp.mono_2Ec_2Ebool_2EF) (=> (=> V0A tptp.mono_2Ec_2Ebool_2EF) tptp.mono_2Ec_2Ebool_2EF))))
% 0.22/0.55 (assume a39 (forall ((V0r Bool) (V1q Bool) (V2p Bool)) (= (= V2p (= V1q V0r)) (and (or V2p V1q V0r) (or V2p (not V0r) (not V1q)) (or V1q (not V0r) (not V2p)) (or V0r (not V1q) (not V2p))))))
% 0.22/0.55 (assume a40 (forall ((V0q Bool) (V1p Bool)) (= (= V1p (not V0q)) (and (or V1p V0q) (or (not V0q) (not V1p))))))
% 0.22/0.55 (assume a41 (not (forall ((A_27a tptp.d) (A_27b tptp.d) (V0s_2E0 tptp.u) (V1t_2E0 tptp.u)) (= (not (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ (@ tptp.c_2Ecardinal_2Ecardleq_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool)) V0s_2E0)) (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27b) tptp.tyop_2Emin_2Ebool)) V1t_2E0))))) (not (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ (@ tptp.c_2Ecardinal_2Ecardleq_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool)) V0s_2E0)) (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27b) tptp.tyop_2Emin_2Ebool)) V1t_2E0)))))))))
% 0.22/0.55 (assume a42 true)
% 0.22/0.55 (step t1 (cl (not (= (not (forall ((A_27a tptp.d) (A_27b tptp.d) (V0s_2E0 tptp.u) (V1t_2E0 tptp.u)) (= (not (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ (@ tptp.c_2Ecardinal_2Ecardleq_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool)) V0s_2E0)) (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27b) tptp.tyop_2Emin_2Ebool)) V1t_2E0))))) (not (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ (@ tptp.c_2Ecardinal_2Ecardleq_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool)) V0s_2E0)) (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27b) tptp.tyop_2Emin_2Ebool)) V1t_2E0)))))))) false)) (not (not (forall ((A_27a tptp.d) (A_27b tptp.d) (V0s_2E0 tptp.u) (V1t_2E0 tptp.u)) (= (not (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ (@ tptp.c_2Ecardinal_2Ecardleq_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool)) V0s_2E0)) (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27b) tptp.tyop_2Emin_2Ebool)) V1t_2E0))))) (not (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ (@ tptp.c_2Ecardinal_2Ecardleq_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool)) V0s_2E0)) (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27b) tptp.tyop_2Emin_2Ebool)) V1t_2E0))))))))) false) :rule equiv_pos2)
% 0.22/0.55 (anchor :step t2 :args ((A_27a tptp.d) (:= A_27a A_27a) (A_27b tptp.d) (:= A_27b A_27b) (V0s_2E0 tptp.u) (:= V0s_2E0 V0s_2E0) (V1t_2E0 tptp.u) (:= V1t_2E0 V1t_2E0)))
% 0.22/0.55 (step t2.t1 (cl (= A_27a A_27a)) :rule refl)
% 0.22/0.55 (step t2.t2 (cl (= A_27b A_27b)) :rule refl)
% 0.22/0.55 (step t2.t3 (cl (= V0s_2E0 V0s_2E0)) :rule refl)
% 0.22/0.55 (step t2.t4 (cl (= V1t_2E0 V1t_2E0)) :rule refl)
% 0.22/0.55 (step t2.t5 (cl (= (= (not (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ (@ tptp.c_2Ecardinal_2Ecardleq_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool)) V0s_2E0)) (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27b) tptp.tyop_2Emin_2Ebool)) V1t_2E0))))) (not (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ (@ tptp.c_2Ecardinal_2Ecardleq_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool)) V0s_2E0)) (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27b) tptp.tyop_2Emin_2Ebool)) V1t_2E0)))))) true)) :rule all_simplify)
% 0.22/0.55 (step t2 (cl (= (forall ((A_27a tptp.d) (A_27b tptp.d) (V0s_2E0 tptp.u) (V1t_2E0 tptp.u)) (= (not (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ (@ tptp.c_2Ecardinal_2Ecardleq_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool)) V0s_2E0)) (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27b) tptp.tyop_2Emin_2Ebool)) V1t_2E0))))) (not (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ (@ tptp.c_2Ecardinal_2Ecardleq_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool)) V0s_2E0)) (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27b) tptp.tyop_2Emin_2Ebool)) V1t_2E0))))))) (forall ((A_27a tptp.d) (A_27b tptp.d) (V0s_2E0 tptp.u) (V1t_2E0 tptp.u)) true))) :rule bind)
% 0.22/0.55 (step t3 (cl (= (forall ((A_27a tptp.d) (A_27b tptp.d) (V0s_2E0 tptp.u) (V1t_2E0 tptp.u)) true) true)) :rule all_simplify)
% 0.22/0.55 (step t4 (cl (= (forall ((A_27a tptp.d) (A_27b tptp.d) (V0s_2E0 tptp.u) (V1t_2E0 tptp.u)) (= (not (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ (@ tptp.c_2Ecardinal_2Ecardleq_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool)) V0s_2E0)) (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27b) tptp.tyop_2Emin_2Ebool)) V1t_2E0))))) (not (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ (@ tptp.c_2Ecardinal_2Ecardleq_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool)) V0s_2E0)) (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27b) tptp.tyop_2Emin_2Ebool)) V1t_2E0))))))) true)) :rule trans :premises (t2 t3))
% 0.22/0.55 (step t5 (cl (= (not (forall ((A_27a tptp.d) (A_27b tptp.d) (V0s_2E0 tptp.u) (V1t_2E0 tptp.u)) (= (not (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ (@ tptp.c_2Ecardinal_2Ecardleq_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool)) V0s_2E0)) (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27b) tptp.tyop_2Emin_2Ebool)) V1t_2E0))))) (not (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ (@ tptp.c_2Ecardinal_2Ecardleq_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool)) V0s_2E0)) (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27b) tptp.tyop_2Emin_2Ebool)) V1t_2E0)))))))) (not true))) :rule cong :premises (t4))
% 0.22/0.55 (step t6 (cl (= (not true) false)) :rule all_simplify)
% 0.22/0.55 (step t7 (cl (= (not (forall ((A_27a tptp.d) (A_27b tptp.d) (V0s_2E0 tptp.u) (V1t_2E0 tptp.u)) (= (not (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ (@ tptp.c_2Ecardinal_2Ecardleq_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool)) V0s_2E0)) (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27b) tptp.tyop_2Emin_2Ebool)) V1t_2E0))))) (not (@ tptp.j_mono_2Etyop_2Emin_2Ebool (@ (@ tptp.s tptp.tyop_2Emin_2Ebool) (@ (@ tptp.c_2Ecardinal_2Ecardleq_2E2 (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27a) tptp.tyop_2Emin_2Ebool)) V0s_2E0)) (@ (@ tptp.s (@ (@ tptp.tyop_2Emin_2Efun A_27b) tptp.tyop_2Emin_2Ebool)) V1t_2E0)))))))) false)) :rule trans :premises (t5 t6))
% 0.22/0.55 (step t8 (cl false) :rule resolution :premises (t1 t7 a41))
% 0.22/0.55 (step t9 (cl (not false)) :rule false)
% 0.22/0.55 (step t10 (cl) :rule resolution :premises (t8 t9))
% 0.22/0.55
% 0.22/0.55 % SZS output end Proof for /export/starexec/sandbox/tmp/tmp.5qoox4ZhXN/cvc5---1.0.5_4175.smt2
% 0.22/0.55 % cvc5---1.0.5 exiting
% 0.22/0.56 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------