%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL400-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:58:48 AM UTC 2026
% Result : Unsatisfiable 5.30s 1.13s
% Output : CNFRefutation 5.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 48
% Number of leaves : 6
% Syntax : Number of formulae : 95 ( 95 unt; 0 def)
% Number of atoms : 95 ( 94 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-4 aty)
% Number of variables : 266 ( 86 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ifeq_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : ifeq(VAR_0,VAR_0,VAR_1,VAR_2) = VAR_1,
file('theBenchmark.p',ifeq_axiom) ).
cnf(c_1,plain,
ifeq(A,A,B,C) = B,
inference(clausify,[status(thm)],[ifeq_axiom]) ).
fof(condensed_detachment,axiom,
! [VAR_0,VAR_1] : ifeq(is_a_theorem(implies(VAR_0,VAR_1)),true,ifeq(is_a_theorem(VAR_0),true,is_a_theorem(VAR_1),true),true) = true,
file('theBenchmark.p',condensed_detachment) ).
cnf(c_2,plain,
ifeq(is_a_theorem(implies(A,B)),true,ifeq(is_a_theorem(A),true,is_a_theorem(B),true),true) = true,
inference(clausify,[status(thm)],[condensed_detachment]) ).
fof(cn_1,axiom,
! [VAR_0,VAR_1,VAR_2] : is_a_theorem(implies(implies(VAR_0,VAR_1),implies(implies(VAR_1,VAR_2),implies(VAR_0,VAR_2)))) = true,
file('theBenchmark.p',cn_1) ).
cnf(c_3,plain,
is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))) = true,
inference(clausify,[status(thm)],[cn_1]) ).
fof(cn_2,axiom,
! [VAR_0] : is_a_theorem(implies(implies(not(VAR_0),VAR_0),VAR_0)) = true,
file('theBenchmark.p',cn_2) ).
cnf(c_4,plain,
is_a_theorem(implies(implies(not(A),A),A)) = true,
inference(clausify,[status(thm)],[cn_2]) ).
fof(cn_3,axiom,
! [VAR_0,VAR_1] : is_a_theorem(implies(VAR_0,implies(not(VAR_0),VAR_1))) = true,
file('theBenchmark.p',cn_3) ).
cnf(c_5,plain,
is_a_theorem(implies(A,implies(not(A),B))) = true,
inference(clausify,[status(thm)],[cn_3]) ).
fof(prove_cn_66,axiom,
is_a_theorem(implies(not(implies(x,y)),x)) != true,
file('theBenchmark.p',prove_cn_66) ).
cnf(c_6,plain,
is_a_theorem(implies(not(implies(x,y)),x)) != true,
inference(clausify,[status(thm)],[prove_cn_66]) ).
cnf(c_2591,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(A,B)),true,is_a_theorem(implies(implies(B,C),implies(A,C))),true),true) = true,
inference(paramod,[status(thm)],[c_3,c_2]) ).
cnf(c_7,plain,
ifeq(is_a_theorem(implies(A,B)),true,is_a_theorem(implies(implies(B,C),implies(A,C))),true) = true,
inference(paramod,[status(thm)],[c_1,c_2591]) ).
cnf(c_2592,plain,
ifeq(is_a_theorem(implies(implies(implies(A,B),implies(implies(B,C),implies(A,C))),D)),true,ifeq(true,true,is_a_theorem(D),true),true) = true,
inference(paramod,[status(thm)],[c_3,c_2]) ).
cnf(c_8,plain,
ifeq(is_a_theorem(implies(implies(implies(A,B),implies(implies(B,C),implies(A,C))),D)),true,is_a_theorem(D),true) = true,
inference(paramod,[status(thm)],[c_1,c_2592]) ).
cnf(c_2593,plain,
ifeq(is_a_theorem(implies(implies(implies(not(A),A),A),B)),true,ifeq(true,true,is_a_theorem(B),true),true) = true,
inference(paramod,[status(thm)],[c_4,c_2]) ).
cnf(c_11,plain,
ifeq(is_a_theorem(implies(implies(implies(not(A),A),A),B)),true,is_a_theorem(B),true) = true,
inference(paramod,[status(thm)],[c_1,c_2593]) ).
cnf(c_2594,plain,
ifeq(true,true,ifeq(is_a_theorem(A),true,is_a_theorem(implies(not(A),B)),true),true) = true,
inference(paramod,[status(thm)],[c_5,c_2]) ).
cnf(c_13,plain,
ifeq(is_a_theorem(A),true,is_a_theorem(implies(not(A),B)),true) = true,
inference(paramod,[status(thm)],[c_1,c_2594]) ).
cnf(c_2595,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(implies(A,B),implies(C,B)),D),implies(implies(C,A),D))),true) = true,
inference(paramod,[status(thm)],[c_3,c_7]) ).
cnf(c_16,plain,
is_a_theorem(implies(implies(implies(implies(A,B),implies(C,B)),D),implies(implies(C,A),D))) = true,
inference(paramod,[status(thm)],[c_1,c_2595]) ).
cnf(c_2596,plain,
ifeq(true,true,is_a_theorem(implies(implies(A,B),implies(implies(not(A),A),B))),true) = true,
inference(paramod,[status(thm)],[c_4,c_7]) ).
cnf(c_18,plain,
is_a_theorem(implies(implies(A,B),implies(implies(not(A),A),B))) = true,
inference(paramod,[status(thm)],[c_1,c_2596]) ).
cnf(c_2597,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(not(A),B),C),implies(A,C))),true) = true,
inference(paramod,[status(thm)],[c_5,c_7]) ).
cnf(c_19,plain,
is_a_theorem(implies(implies(implies(not(A),B),C),implies(A,C))) = true,
inference(paramod,[status(thm)],[c_1,c_2597]) ).
cnf(c_2598,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(implies(implies(A,B),implies(C,B)),D)),true,is_a_theorem(implies(implies(C,A),D)),true),true) = true,
inference(paramod,[status(thm)],[c_16,c_2]) ).
cnf(c_40,plain,
ifeq(is_a_theorem(implies(implies(implies(A,B),implies(C,B)),D)),true,is_a_theorem(implies(implies(C,A),D)),true) = true,
inference(paramod,[status(thm)],[c_1,c_2598]) ).
cnf(c_2599,plain,
ifeq(is_a_theorem(implies(implies(implies(A,B),implies(implies(not(A),A),B)),C)),true,ifeq(true,true,is_a_theorem(C),true),true) = true,
inference(paramod,[status(thm)],[c_18,c_2]) ).
cnf(c_47,plain,
ifeq(is_a_theorem(implies(implies(implies(A,B),implies(implies(not(A),A),B)),C)),true,is_a_theorem(C),true) = true,
inference(paramod,[status(thm)],[c_1,c_2599]) ).
cnf(c_2600,plain,
ifeq(true,true,is_a_theorem(implies(implies(not(implies(A,B)),implies(A,B)),implies(implies(B,C),implies(A,C)))),true) = true,
inference(paramod,[status(thm)],[c_18,c_8]) ).
cnf(c_49,plain,
is_a_theorem(implies(implies(not(implies(A,B)),implies(A,B)),implies(implies(B,C),implies(A,C)))) = true,
inference(paramod,[status(thm)],[c_1,c_2600]) ).
cnf(c_2601,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(implies(not(A),B),C)),true,is_a_theorem(implies(A,C)),true),true) = true,
inference(paramod,[status(thm)],[c_19,c_2]) ).
cnf(c_61,plain,
ifeq(is_a_theorem(implies(implies(not(A),B),C)),true,is_a_theorem(implies(A,C)),true) = true,
inference(paramod,[status(thm)],[c_1,c_2601]) ).
cnf(c_2602,plain,
ifeq(true,true,is_a_theorem(implies(A,A)),true) = true,
inference(paramod,[status(thm)],[c_19,c_11]) ).
cnf(c_66,plain,
is_a_theorem(implies(A,A)) = true,
inference(paramod,[status(thm)],[c_1,c_2602]) ).
cnf(c_2603,plain,
ifeq(true,true,is_a_theorem(implies(not(implies(A,A)),B)),true) = true,
inference(paramod,[status(thm)],[c_66,c_13]) ).
cnf(c_79,plain,
is_a_theorem(implies(not(implies(A,A)),B)) = true,
inference(paramod,[status(thm)],[c_1,c_2603]) ).
cnf(c_2604,plain,
ifeq(true,true,is_a_theorem(implies(implies(A,B),implies(not(implies(C,C)),B))),true) = true,
inference(paramod,[status(thm)],[c_79,c_7]) ).
cnf(c_82,plain,
is_a_theorem(implies(implies(A,B),implies(not(implies(C,C)),B))) = true,
inference(paramod,[status(thm)],[c_1,c_2604]) ).
cnf(c_2605,plain,
ifeq(true,true,is_a_theorem(implies(A,implies(not(implies(B,B)),C))),true) = true,
inference(paramod,[status(thm)],[c_82,c_61]) ).
cnf(c_119,plain,
is_a_theorem(implies(A,implies(not(implies(B,B)),C))) = true,
inference(paramod,[status(thm)],[c_1,c_2605]) ).
cnf(c_2606,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(not(implies(A,A)),B),C),implies(D,C))),true) = true,
inference(paramod,[status(thm)],[c_119,c_7]) ).
cnf(c_122,plain,
is_a_theorem(implies(implies(implies(not(implies(A,A)),B),C),implies(D,C))) = true,
inference(paramod,[status(thm)],[c_1,c_2606]) ).
cnf(c_2607,plain,
ifeq(true,true,is_a_theorem(implies(implies(A,not(B)),implies(B,implies(A,C)))),true) = true,
inference(paramod,[status(thm)],[c_19,c_40]) ).
cnf(c_131,plain,
is_a_theorem(implies(implies(A,not(B)),implies(B,implies(A,C)))) = true,
inference(paramod,[status(thm)],[c_1,c_2607]) ).
cnf(c_2608,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(A,implies(B,C)),D),implies(implies(B,not(A)),D))),true) = true,
inference(paramod,[status(thm)],[c_131,c_7]) ).
cnf(c_135,plain,
is_a_theorem(implies(implies(implies(A,implies(B,C)),D),implies(implies(B,not(A)),D))) = true,
inference(paramod,[status(thm)],[c_1,c_2608]) ).
cnf(c_2609,plain,
ifeq(true,true,is_a_theorem(implies(A,implies(B,implies(not(A),C)))),true) = true,
inference(paramod,[status(thm)],[c_131,c_61]) ).
cnf(c_138,plain,
is_a_theorem(implies(A,implies(B,implies(not(A),C)))) = true,
inference(paramod,[status(thm)],[c_1,c_2609]) ).
cnf(c_2610,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(A,implies(not(B),C)),D),implies(B,D))),true) = true,
inference(paramod,[status(thm)],[c_138,c_7]) ).
cnf(c_146,plain,
is_a_theorem(implies(implies(implies(A,implies(not(B),C)),D),implies(B,D))) = true,
inference(paramod,[status(thm)],[c_1,c_2610]) ).
cnf(c_2611,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(not(implies(A,B)),implies(A,B))),true,is_a_theorem(implies(implies(B,C),implies(A,C))),true),true) = true,
inference(paramod,[status(thm)],[c_49,c_2]) ).
cnf(c_241,plain,
ifeq(is_a_theorem(implies(not(implies(A,B)),implies(A,B))),true,is_a_theorem(implies(implies(B,C),implies(A,C))),true) = true,
inference(paramod,[status(thm)],[c_1,c_2611]) ).
cnf(c_2612,plain,
ifeq(true,true,is_a_theorem(implies(A,implies(B,B))),true) = true,
inference(paramod,[status(thm)],[c_122,c_11]) ).
cnf(c_354,plain,
is_a_theorem(implies(A,implies(B,B))) = true,
inference(paramod,[status(thm)],[c_1,c_2612]) ).
cnf(c_2613,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(A,A),B),implies(C,B))),true) = true,
inference(paramod,[status(thm)],[c_354,c_7]) ).
cnf(c_360,plain,
is_a_theorem(implies(implies(implies(A,A),B),implies(C,B))) = true,
inference(paramod,[status(thm)],[c_1,c_2613]) ).
cnf(c_2614,plain,
ifeq(true,true,is_a_theorem(implies(A,implies(implies(not(B),B),B))),true) = true,
inference(paramod,[status(thm)],[c_360,c_47]) ).
cnf(c_393,plain,
is_a_theorem(implies(A,implies(implies(not(B),B),B))) = true,
inference(paramod,[status(thm)],[c_1,c_2614]) ).
cnf(c_2615,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(implies(not(A),A),A),B),implies(C,B))),true) = true,
inference(paramod,[status(thm)],[c_393,c_7]) ).
cnf(c_413,plain,
is_a_theorem(implies(implies(implies(implies(not(A),A),A),B),implies(C,B))) = true,
inference(paramod,[status(thm)],[c_1,c_2615]) ).
cnf(c_2616,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(implies(A,implies(B,C)),D)),true,is_a_theorem(implies(implies(B,not(A)),D)),true),true) = true,
inference(paramod,[status(thm)],[c_135,c_2]) ).
cnf(c_824,plain,
ifeq(is_a_theorem(implies(implies(A,implies(B,C)),D)),true,is_a_theorem(implies(implies(B,not(A)),D)),true) = true,
inference(paramod,[status(thm)],[c_1,c_2616]) ).
cnf(c_2617,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(implies(A,implies(not(B),C)),D)),true,is_a_theorem(implies(B,D)),true),true) = true,
inference(paramod,[status(thm)],[c_146,c_2]) ).
cnf(c_965,plain,
ifeq(is_a_theorem(implies(implies(A,implies(not(B),C)),D)),true,is_a_theorem(implies(B,D)),true) = true,
inference(paramod,[status(thm)],[c_1,c_2617]) ).
cnf(c_2618,plain,
ifeq(true,true,is_a_theorem(implies(implies(A,implies(not(B),B)),implies(C,implies(A,B)))),true) = true,
inference(paramod,[status(thm)],[c_413,c_40]) ).
cnf(c_1188,plain,
is_a_theorem(implies(implies(A,implies(not(B),B)),implies(C,implies(A,B)))) = true,
inference(paramod,[status(thm)],[c_1,c_2618]) ).
cnf(c_2619,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(A,implies(not(B),B))),true,is_a_theorem(implies(C,implies(A,B))),true),true) = true,
inference(paramod,[status(thm)],[c_1188,c_2]) ).
cnf(c_1195,plain,
ifeq(is_a_theorem(implies(A,implies(not(B),B))),true,is_a_theorem(implies(C,implies(A,B))),true) = true,
inference(paramod,[status(thm)],[c_1,c_2619]) ).
cnf(c_2620,plain,
ifeq(true,true,is_a_theorem(implies(implies(not(A),not(B)),implies(C,implies(B,A)))),true) = true,
inference(paramod,[status(thm)],[c_1188,c_824]) ).
cnf(c_1205,plain,
is_a_theorem(implies(implies(not(A),not(B)),implies(C,implies(B,A)))) = true,
inference(paramod,[status(thm)],[c_1,c_2620]) ).
cnf(c_2621,plain,
ifeq(true,true,is_a_theorem(implies(A,implies(B,implies(C,A)))),true) = true,
inference(paramod,[status(thm)],[c_1188,c_965]) ).
cnf(c_1206,plain,
is_a_theorem(implies(A,implies(B,implies(C,A)))) = true,
inference(paramod,[status(thm)],[c_1,c_2621]) ).
cnf(c_2622,plain,
ifeq(true,true,is_a_theorem(implies(A,implies(B,implies(C,B)))),true) = true,
inference(paramod,[status(thm)],[c_1206,c_1195]) ).
cnf(c_1348,plain,
is_a_theorem(implies(A,implies(B,implies(C,B)))) = true,
inference(paramod,[status(thm)],[c_1,c_2622]) ).
cnf(c_2623,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(A,B),C),implies(B,C))),true) = true,
inference(paramod,[status(thm)],[c_1348,c_241]) ).
cnf(c_1370,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(B,C))) = true,
inference(paramod,[status(thm)],[c_1,c_2623]) ).
cnf(c_2624,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(implies(A,B),C)),true,is_a_theorem(implies(B,C)),true),true) = true,
inference(paramod,[status(thm)],[c_1370,c_2]) ).
cnf(c_1428,plain,
ifeq(is_a_theorem(implies(implies(A,B),C)),true,is_a_theorem(implies(B,C)),true) = true,
inference(paramod,[status(thm)],[c_1,c_2624]) ).
cnf(c_2625,plain,
ifeq(true,true,is_a_theorem(implies(not(A),implies(B,implies(A,C)))),true) = true,
inference(paramod,[status(thm)],[c_1205,c_1428]) ).
cnf(c_1472,plain,
is_a_theorem(implies(not(A),implies(B,implies(A,C)))) = true,
inference(paramod,[status(thm)],[c_1,c_2625]) ).
cnf(c_2626,plain,
ifeq(true,true,is_a_theorem(implies(A,implies(not(B),implies(B,C)))),true) = true,
inference(paramod,[status(thm)],[c_1472,c_1195]) ).
cnf(c_1606,plain,
is_a_theorem(implies(A,implies(not(B),implies(B,C)))) = true,
inference(paramod,[status(thm)],[c_1,c_2626]) ).
cnf(c_2627,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(A,B),C),implies(not(A),C))),true) = true,
inference(paramod,[status(thm)],[c_1606,c_241]) ).
cnf(c_1625,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(not(A),C))) = true,
inference(paramod,[status(thm)],[c_1,c_2627]) ).
cnf(c_2628,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(implies(A,B),C)),true,is_a_theorem(implies(not(A),C)),true),true) = true,
inference(paramod,[status(thm)],[c_1625,c_2]) ).
cnf(c_2444,plain,
ifeq(is_a_theorem(implies(implies(A,B),C)),true,is_a_theorem(implies(not(A),C)),true) = true,
inference(paramod,[status(thm)],[c_1,c_2628]) ).
cnf(c_2629,plain,
ifeq(true,true,is_a_theorem(implies(not(implies(A,B)),implies(not(A),C))),true) = true,
inference(paramod,[status(thm)],[c_1625,c_2444]) ).
cnf(c_2511,plain,
is_a_theorem(implies(not(implies(A,B)),implies(not(A),C))) = true,
inference(paramod,[status(thm)],[c_1,c_2629]) ).
cnf(c_2630,plain,
ifeq(true,true,is_a_theorem(implies(A,implies(not(implies(B,C)),B))),true) = true,
inference(paramod,[status(thm)],[c_2511,c_1195]) ).
cnf(c_2527,plain,
is_a_theorem(implies(A,implies(not(implies(B,C)),B))) = true,
inference(paramod,[status(thm)],[c_1,c_2630]) ).
cnf(c_2631,plain,
ifeq(true,true,is_a_theorem(implies(not(implies(A,B)),A)),true) = true,
inference(paramod,[status(thm)],[c_2527,c_8]) ).
cnf(c_2589,plain,
is_a_theorem(implies(not(implies(A,B)),A)) = true,
inference(paramod,[status(thm)],[c_1,c_2631]) ).
cnf(c_2590,plain,
$false,
inference(resolve,[status(thm)],[c_2589,c_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL400-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n008.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 22:27:40 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.38 % Process 2090523 was started by sandbox2 on n008,
% 0.10/0.38 % Fri Sep 25 22:27:40 2026
% 0.10/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 5.30/1.13
% 5.30/1.13 % SZS status Unsatisfiable for theBenchmark
% 5.30/1.13
% 5.30/1.13 % Proof 1 at 0.53 (+ 0.20) seconds.
% 5.30/1.13 % Length of proof is 48.
% 5.30/1.13 % Level of proof is 24.
% 5.30/1.13 % Maximum clause weight is 81.000.
% 5.30/1.13 % Given clauses 338.
% 5.30/1.13
% 5.30/1.13 % SZS output start CNFRefutation for theBenchmark
% See solution above
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