%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL026-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 07:57:47 AM UTC 2026
% Result : Unsatisfiable 13.35s 2.70s
% Output : CNFRefutation 13.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 6
% Syntax : Number of formulae : 75 ( 75 unt; 0 def)
% Number of atoms : 75 ( 74 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 : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-4 aty)
% Number of variables : 176 ( 44 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(c0_2,axiom,
! [VAR_0,VAR_1] : is_a_theorem(implies(VAR_0,implies(VAR_1,VAR_0))) = true,
file('theBenchmark.p',c0_2) ).
cnf(c_3,plain,
is_a_theorem(implies(A,implies(B,A))) = true,
inference(clausify,[status(thm)],[c0_2]) ).
fof(c0_5,axiom,
! [VAR_0] : is_a_theorem(implies(implies(implies(VAR_0,falsehood),falsehood),VAR_0)) = true,
file('theBenchmark.p',c0_5) ).
cnf(c_4,plain,
is_a_theorem(implies(implies(implies(A,falsehood),falsehood),A)) = true,
inference(clausify,[status(thm)],[c0_5]) ).
fof(c0_6,axiom,
! [VAR_0,VAR_1,VAR_2] : is_a_theorem(implies(implies(VAR_0,implies(VAR_1,VAR_2)),implies(implies(VAR_0,VAR_1),implies(VAR_0,VAR_2)))) = true,
file('theBenchmark.p',c0_6) ).
cnf(c_5,plain,
is_a_theorem(implies(implies(A,implies(B,C)),implies(implies(A,B),implies(A,C)))) = true,
inference(clausify,[status(thm)],[c0_6]) ).
fof(prove_c0_3,axiom,
is_a_theorem(implies(implies(implies(a,b),a),a)) != true,
file('theBenchmark.p',prove_c0_3) ).
cnf(c_6,plain,
is_a_theorem(implies(implies(implies(a,b),a),a)) != true,
inference(clausify,[status(thm)],[prove_c0_3]) ).
cnf(c_2581,plain,
ifeq(true,true,ifeq(is_a_theorem(A),true,is_a_theorem(implies(B,A)),true),true) = true,
inference(paramod,[status(thm)],[c_3,c_2]) ).
cnf(c_7,plain,
ifeq(is_a_theorem(A),true,is_a_theorem(implies(B,A)),true) = true,
inference(paramod,[status(thm)],[c_1,c_2581]) ).
cnf(c_2582,plain,
ifeq(is_a_theorem(implies(implies(A,implies(B,A)),C)),true,ifeq(true,true,is_a_theorem(C),true),true) = true,
inference(paramod,[status(thm)],[c_3,c_2]) ).
cnf(c_8,plain,
ifeq(is_a_theorem(implies(implies(A,implies(B,A)),C)),true,is_a_theorem(C),true) = true,
inference(paramod,[status(thm)],[c_1,c_2582]) ).
cnf(c_2583,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(A,implies(B,C))),true,is_a_theorem(implies(implies(A,B),implies(A,C))),true),true) = true,
inference(paramod,[status(thm)],[c_5,c_2]) ).
cnf(c_13,plain,
ifeq(is_a_theorem(implies(A,implies(B,C))),true,is_a_theorem(implies(implies(A,B),implies(A,C))),true) = true,
inference(paramod,[status(thm)],[c_1,c_2583]) ).
cnf(c_2584,plain,
ifeq(true,true,is_a_theorem(implies(A,implies(B,implies(C,B)))),true) = true,
inference(paramod,[status(thm)],[c_3,c_7]) ).
cnf(c_16,plain,
is_a_theorem(implies(A,implies(B,implies(C,B)))) = true,
inference(paramod,[status(thm)],[c_1,c_2584]) ).
cnf(c_2585,plain,
ifeq(true,true,is_a_theorem(implies(A,implies(implies(implies(B,falsehood),falsehood),B))),true) = true,
inference(paramod,[status(thm)],[c_4,c_7]) ).
cnf(c_18,plain,
is_a_theorem(implies(A,implies(implies(implies(B,falsehood),falsehood),B))) = true,
inference(paramod,[status(thm)],[c_1,c_2585]) ).
cnf(c_2586,plain,
ifeq(true,true,is_a_theorem(implies(A,implies(implies(B,implies(C,D)),implies(implies(B,C),implies(B,D))))),true) = true,
inference(paramod,[status(thm)],[c_5,c_7]) ).
cnf(c_20,plain,
is_a_theorem(implies(A,implies(implies(B,implies(C,D)),implies(implies(B,C),implies(B,D))))) = true,
inference(paramod,[status(thm)],[c_1,c_2586]) ).
cnf(c_2587,plain,
ifeq(is_a_theorem(implies(implies(A,implies(B,implies(C,B))),D)),true,ifeq(true,true,is_a_theorem(D),true),true) = true,
inference(paramod,[status(thm)],[c_16,c_2]) ).
cnf(c_21,plain,
ifeq(is_a_theorem(implies(implies(A,implies(B,implies(C,B))),D)),true,is_a_theorem(D),true) = true,
inference(paramod,[status(thm)],[c_1,c_2587]) ).
cnf(c_2588,plain,
ifeq(true,true,is_a_theorem(implies(implies(A,B),implies(A,A))),true) = true,
inference(paramod,[status(thm)],[c_5,c_8]) ).
cnf(c_29,plain,
is_a_theorem(implies(implies(A,B),implies(A,A))) = true,
inference(paramod,[status(thm)],[c_1,c_2588]) ).
cnf(c_2589,plain,
ifeq(true,true,is_a_theorem(implies(A,A)),true) = true,
inference(paramod,[status(thm)],[c_29,c_8]) ).
cnf(c_33,plain,
is_a_theorem(implies(A,A)) = true,
inference(paramod,[status(thm)],[c_1,c_2589]) ).
cnf(c_2590,plain,
ifeq(is_a_theorem(implies(implies(A,A),B)),true,ifeq(true,true,is_a_theorem(B),true),true) = true,
inference(paramod,[status(thm)],[c_33,c_2]) ).
cnf(c_35,plain,
ifeq(is_a_theorem(implies(implies(A,A),B)),true,is_a_theorem(B),true) = true,
inference(paramod,[status(thm)],[c_1,c_2590]) ).
cnf(c_2591,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(A,B),A),implies(implies(A,B),B))),true) = true,
inference(paramod,[status(thm)],[c_5,c_35]) ).
cnf(c_41,plain,
is_a_theorem(implies(implies(implies(A,B),A),implies(implies(A,B),B))) = true,
inference(paramod,[status(thm)],[c_1,c_2591]) ).
cnf(c_2592,plain,
ifeq(is_a_theorem(implies(implies(implies(implies(A,B),A),implies(implies(A,B),B)),C)),true,ifeq(true,true,is_a_theorem(C),true),true) = true,
inference(paramod,[status(thm)],[c_41,c_2]) ).
cnf(c_44,plain,
ifeq(is_a_theorem(implies(implies(implies(implies(A,B),A),implies(implies(A,B),B)),C)),true,is_a_theorem(C),true) = true,
inference(paramod,[status(thm)],[c_1,c_2592]) ).
cnf(c_2593,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(A,implies(B,C)),implies(A,B)),implies(implies(A,implies(B,C)),implies(A,C)))),true) = true,
inference(paramod,[status(thm)],[c_5,c_13]) ).
cnf(c_60,plain,
is_a_theorem(implies(implies(implies(A,implies(B,C)),implies(A,B)),implies(implies(A,implies(B,C)),implies(A,C)))) = true,
inference(paramod,[status(thm)],[c_1,c_2593]) ).
cnf(c_2594,plain,
ifeq(true,true,is_a_theorem(implies(implies(A,implies(implies(B,falsehood),falsehood)),implies(A,B))),true) = true,
inference(paramod,[status(thm)],[c_18,c_13]) ).
cnf(c_64,plain,
is_a_theorem(implies(implies(A,implies(implies(B,falsehood),falsehood)),implies(A,B))) = true,
inference(paramod,[status(thm)],[c_1,c_2594]) ).
cnf(c_2595,plain,
ifeq(true,true,is_a_theorem(implies(falsehood,A)),true) = true,
inference(paramod,[status(thm)],[c_64,c_8]) ).
cnf(c_165,plain,
is_a_theorem(implies(falsehood,A)) = true,
inference(paramod,[status(thm)],[c_1,c_2595]) ).
cnf(c_2596,plain,
ifeq(true,true,is_a_theorem(implies(A,implies(falsehood,B))),true) = true,
inference(paramod,[status(thm)],[c_165,c_7]) ).
cnf(c_173,plain,
is_a_theorem(implies(A,implies(falsehood,B))) = true,
inference(paramod,[status(thm)],[c_1,c_2596]) ).
cnf(c_2597,plain,
ifeq(true,true,is_a_theorem(implies(implies(A,falsehood),implies(A,B))),true) = true,
inference(paramod,[status(thm)],[c_173,c_13]) ).
cnf(c_178,plain,
is_a_theorem(implies(implies(A,falsehood),implies(A,B))) = true,
inference(paramod,[status(thm)],[c_1,c_2597]) ).
cnf(c_2598,plain,
ifeq(is_a_theorem(implies(implies(implies(A,falsehood),implies(A,B)),C)),true,ifeq(true,true,is_a_theorem(C),true),true) = true,
inference(paramod,[status(thm)],[c_178,c_2]) ).
cnf(c_182,plain,
ifeq(is_a_theorem(implies(implies(implies(A,falsehood),implies(A,B)),C)),true,is_a_theorem(C),true) = true,
inference(paramod,[status(thm)],[c_1,c_2598]) ).
cnf(c_2599,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(A,falsehood),A),A)),true) = true,
inference(paramod,[status(thm)],[c_64,c_44]) ).
cnf(c_228,plain,
is_a_theorem(implies(implies(implies(A,falsehood),A),A)) = true,
inference(paramod,[status(thm)],[c_1,c_2599]) ).
cnf(c_2600,plain,
ifeq(true,true,is_a_theorem(implies(A,implies(implies(implies(B,falsehood),B),B))),true) = true,
inference(paramod,[status(thm)],[c_228,c_7]) ).
cnf(c_231,plain,
is_a_theorem(implies(A,implies(implies(implies(B,falsehood),B),B))) = true,
inference(paramod,[status(thm)],[c_1,c_2600]) ).
cnf(c_2601,plain,
ifeq(true,true,is_a_theorem(implies(implies(A,implies(implies(B,falsehood),B)),implies(A,B))),true) = true,
inference(paramod,[status(thm)],[c_231,c_13]) ).
cnf(c_364,plain,
is_a_theorem(implies(implies(A,implies(implies(B,falsehood),B)),implies(A,B))) = true,
inference(paramod,[status(thm)],[c_1,c_2601]) ).
cnf(c_2602,plain,
ifeq(true,true,is_a_theorem(implies(implies(A,implies(implies(B,A),C)),implies(A,C))),true) = true,
inference(paramod,[status(thm)],[c_60,c_21]) ).
cnf(c_665,plain,
is_a_theorem(implies(implies(A,implies(implies(B,A),C)),implies(A,C))) = true,
inference(paramod,[status(thm)],[c_1,c_2602]) ).
cnf(c_2603,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(A,implies(implies(B,falsehood),B))),true,is_a_theorem(implies(A,B)),true),true) = true,
inference(paramod,[status(thm)],[c_364,c_2]) ).
cnf(c_721,plain,
ifeq(is_a_theorem(implies(A,implies(implies(B,falsehood),B))),true,is_a_theorem(implies(A,B)),true) = true,
inference(paramod,[status(thm)],[c_1,c_2603]) ).
cnf(c_2604,plain,
ifeq(true,true,ifeq(is_a_theorem(implies(A,implies(implies(B,A),C))),true,is_a_theorem(implies(A,C)),true),true) = true,
inference(paramod,[status(thm)],[c_665,c_2]) ).
cnf(c_908,plain,
ifeq(is_a_theorem(implies(A,implies(implies(B,A),C))),true,is_a_theorem(implies(A,C)),true) = true,
inference(paramod,[status(thm)],[c_1,c_2604]) ).
cnf(c_2605,plain,
ifeq(true,true,is_a_theorem(implies(implies(A,B),implies(implies(C,A),implies(C,B)))),true) = true,
inference(paramod,[status(thm)],[c_20,c_908]) ).
cnf(c_923,plain,
is_a_theorem(implies(implies(A,B),implies(implies(C,A),implies(C,B)))) = true,
inference(paramod,[status(thm)],[c_1,c_2605]) ).
cnf(c_2606,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(A,B),implies(C,A)),implies(implies(A,B),implies(C,B)))),true) = true,
inference(paramod,[status(thm)],[c_923,c_13]) ).
cnf(c_1097,plain,
is_a_theorem(implies(implies(implies(A,B),implies(C,A)),implies(implies(A,B),implies(C,B)))) = true,
inference(paramod,[status(thm)],[c_1,c_2606]) ).
cnf(c_2607,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(A,B),C),implies(B,C))),true) = true,
inference(paramod,[status(thm)],[c_1097,c_21]) ).
cnf(c_2201,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(B,C))) = true,
inference(paramod,[status(thm)],[c_1,c_2607]) ).
cnf(c_2608,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_2201,c_2]) ).
cnf(c_2216,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_2608]) ).
cnf(c_2609,plain,
ifeq(true,true,is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))),true) = true,
inference(paramod,[status(thm)],[c_1097,c_2216]) ).
cnf(c_2242,plain,
is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(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,B),C),implies(implies(A,falsehood),C))),true) = true,
inference(paramod,[status(thm)],[c_2242,c_182]) ).
cnf(c_2439,plain,
is_a_theorem(implies(implies(implies(A,B),C),implies(implies(A,falsehood),C))) = true,
inference(paramod,[status(thm)],[c_1,c_2610]) ).
cnf(c_2611,plain,
ifeq(true,true,is_a_theorem(implies(implies(implies(A,B),A),A)),true) = true,
inference(paramod,[status(thm)],[c_2439,c_721]) ).
cnf(c_2579,plain,
is_a_theorem(implies(implies(implies(A,B),A),A)) = true,
inference(paramod,[status(thm)],[c_1,c_2611]) ).
cnf(c_2580,plain,
$false,
inference(resolve,[status(thm)],[c_2579,c_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL026-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n011.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Fri Sep 25 21:44:29 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.46 % Process 2977777 was started by sandbox2 on n011,
% 0.19/0.46 % Fri Sep 25 21:44:29 2026
% 0.19/0.46 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.46
% 0.19/0.46 % From the command line: assign(max_seconds, 300).
% 13.35/2.70
% 13.35/2.70 % Assigning unary symbol is_a_theorem kb_weight 0 and highest precedence (8).
% 13.35/2.70
% 13.35/2.70 % SZS status Unsatisfiable for theBenchmark
% 13.35/2.70
% 13.35/2.70 % Proof 1 at 1.34 (+ 0.63) seconds.
% 13.35/2.70 % Length of proof is 38.
% 13.35/2.70 % Level of proof is 13.
% 13.35/2.70 % Maximum clause weight is 68.000.
% 13.35/2.70 % Given clauses 275.
% 13.35/2.70
% 13.35/2.70 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------