%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL897+1 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n026.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 : Fri Sep 25 02:03:18 PM UTC 2026
% Result : Theorem 5.10s 1.15s
% Output : Proof 5.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 5
% Syntax : Number of formulae : 43 ( 43 unt; 0 def)
% Number of atoms : 43 ( 42 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 17 ( 17 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 60 ( 0 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [A,B] : qtd0(A,qtd2(A,B)) = qtd0(B,qtd2(B,A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_08) ).
fof(f7_nnf,plain,
! [A,B] : qtd0(A,qtd2(A,B)) = qtd0(B,qtd2(B,A)),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A,B] : qtd0(A,qtd2(A,B)) = qtd0(B,qtd2(B,A)),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
qtd0(X0,qtd2(X0,X1)) = qtd0(X1,qtd2(X1,X0)),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(t5,plain,
qtd0(X1,qtd2(X1,X2)) = qtd0(X2,qtd2(X2,X1)),
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t16,plain,
qtd0(X1,qtd2(X1,X2)) = qtd0(X2,qtd2(X2,X1)),
inference(orient,[status(thm)],[t5]) ).
fof(f1,axiom,
! [A,B] : qtd0(A,B) = qtd0(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_02) ).
fof(f1_nnf,plain,
! [A,B] : qtd0(A,B) = qtd0(B,A),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B] : qtd0(A,B) = qtd0(B,A),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
qtd0(X0,X1) = qtd0(X1,X0),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t4,plain,
qtd0(X1,X2) = qtd0(X2,X1),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t10,plain,
qtd0(X1,X2) = qtd0(X2,X1),
inference(orient,[status(thm)],[t4]) ).
fof(f0,axiom,
! [A,B,C] : qtd0(qtd0(A,B),C) = qtd0(A,qtd0(B,C)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_01) ).
fof(f0_nnf,plain,
! [A,B,C] : qtd0(qtd0(A,B),C) = qtd0(A,qtd0(B,C)),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B,C] : qtd0(qtd0(A,B),C) = qtd0(A,qtd0(B,C)),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
qtd0(qtd0(X0,X1),X2) = qtd0(X0,qtd0(X1,X2)),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t6,plain,
qtd0(qtd0(X1,X2),X3) = qtd0(X1,qtd0(X2,X3)),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t12,plain,
qtd0(qtd0(X1,X2),X3) = qtd0(X1,qtd0(X2,X3)),
inference(orient,[status(thm)],[t6]) ).
fof(f6,axiom,
! [A,B,C] : qtd2(qtd0(A,B),C) = qtd2(A,qtd2(B,C)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_07) ).
fof(f6_nnf,plain,
! [A,B,C] : qtd2(qtd0(A,B),C) = qtd2(A,qtd2(B,C)),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A,B,C] : qtd2(qtd0(A,B),C) = qtd2(A,qtd2(B,C)),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
qtd2(qtd0(X0,X1),X2) = qtd2(X0,qtd2(X1,X2)),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t7,plain,
qtd2(qtd0(X1,X2),X3) = qtd2(X1,qtd2(X2,X3)),
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t21,plain,
qtd2(qtd0(X1,X2),X3) = qtd2(X1,qtd2(X2,X3)),
inference(orient,[status(thm)],[t7]) ).
fof(f8,conjecture,
qtd0(qtd0(a,qtd2(a,b)),qtd2(qtd0(a,qtd2(a,b)),c)) = qtd0(a,qtd2(a,qtd0(b,qtd2(b,c)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_09) ).
fof(f8_neg,negated_conjecture,
qtd0(qtd0(a,qtd2(a,b)),qtd2(qtd0(a,qtd2(a,b)),c)) != qtd0(a,qtd2(a,qtd0(b,qtd2(b,c)))),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f8_nnf,plain,
qtd0(qtd0(a,qtd2(a,b)),qtd2(qtd0(a,qtd2(a,b)),c)) != qtd0(a,qtd2(a,qtd0(b,qtd2(b,c)))),
inference(nnf_transformation,[status(thm)],[f8_neg]) ).
fof(f8_sk,plain,
qtd0(qtd0(a,qtd2(a,b)),qtd2(qtd0(a,qtd2(a,b)),c)) != qtd0(a,qtd2(a,qtd0(b,qtd2(b,c)))),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
qtd0(qtd0(a,qtd2(a,b)),qtd2(qtd0(a,qtd2(a,b)),c)) != qtd0(a,qtd2(a,qtd0(b,qtd2(b,c)))),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(goal_0,negated_conjecture,
qtd0(qtd0(a,qtd2(a,b)),qtd2(qtd0(a,qtd2(a,b)),c)) != qtd0(a,qtd2(a,qtd0(b,qtd2(b,c)))),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(g0_0,plain,
qtd0(qtd0(b,qtd2(b,c)),qtd2(qtd0(b,qtd2(b,c)),a)) != qtd0(a,qtd2(a,qtd0(b,qtd2(b,c)))),
inference(rw,[status(thm)],[goal_0,t16]) ).
cnf(g0_1,plain,
qtd0(qtd0(b,qtd2(b,c)),qtd2(qtd0(qtd2(b,c),b),a)) != qtd0(a,qtd2(a,qtd0(b,qtd2(b,c)))),
inference(rw,[status(thm)],[g0_0,t10]) ).
cnf(g0_2,plain,
qtd0(b,qtd0(qtd2(b,c),qtd2(qtd0(qtd2(b,c),b),a))) != qtd0(a,qtd2(a,qtd0(b,qtd2(b,c)))),
inference(rw,[status(thm)],[g0_1,t12]) ).
cnf(g0_3,plain,
qtd0(b,qtd0(qtd2(b,c),qtd2(qtd2(b,c),qtd2(b,a)))) != qtd0(a,qtd2(a,qtd0(b,qtd2(b,c)))),
inference(rw,[status(thm)],[g0_2,t21]) ).
cnf(g0_4,plain,
qtd0(b,qtd0(qtd2(b,c),qtd2(qtd2(b,c),qtd2(b,a)))) != qtd0(qtd2(qtd0(a,qtd2(a,b)),c),qtd0(a,qtd2(a,b))),
inference(rw,[status(thm)],[g0_3,t10]) ).
cnf(g0_5,plain,
qtd0(b,qtd0(qtd2(b,c),qtd2(qtd2(b,c),qtd2(b,a)))) != qtd0(qtd2(qtd0(b,qtd2(b,a)),c),qtd0(a,qtd2(a,b))),
inference(rw,[status(thm)],[g0_4,t16]) ).
cnf(g0_6,plain,
qtd0(b,qtd0(qtd2(b,c),qtd2(qtd2(b,c),qtd2(b,a)))) != qtd0(qtd2(qtd0(qtd2(b,a),b),c),qtd0(a,qtd2(a,b))),
inference(rw,[status(thm)],[g0_5,t10]) ).
cnf(g0_7,plain,
qtd0(b,qtd0(qtd2(b,c),qtd2(qtd2(b,c),qtd2(b,a)))) != qtd0(qtd2(qtd0(qtd2(b,a),b),c),qtd0(b,qtd2(b,a))),
inference(rw,[status(thm)],[g0_6,t16]) ).
cnf(g0_8,plain,
qtd0(b,qtd0(qtd2(b,c),qtd2(qtd2(b,c),qtd2(b,a)))) != qtd0(qtd0(b,qtd2(b,a)),qtd2(qtd0(qtd2(b,a),b),c)),
inference(rw,[status(thm)],[g0_7,t10]) ).
cnf(g0_9,plain,
qtd0(b,qtd0(qtd2(b,c),qtd2(qtd2(b,c),qtd2(b,a)))) != qtd0(b,qtd0(qtd2(b,a),qtd2(qtd0(qtd2(b,a),b),c))),
inference(rw,[status(thm)],[g0_8,t12]) ).
cnf(g0_10,plain,
qtd0(b,qtd0(qtd2(b,c),qtd2(qtd2(b,c),qtd2(b,a)))) != qtd0(b,qtd0(qtd2(b,a),qtd2(qtd2(b,a),qtd2(b,c)))),
inference(rw,[status(thm)],[g0_9,t21]) ).
cnf(g0_11,plain,
qtd0(b,qtd0(qtd2(b,c),qtd2(qtd2(b,c),qtd2(b,a)))) != qtd0(b,qtd0(qtd2(b,c),qtd2(qtd2(b,c),qtd2(b,a)))),
inference(rw,[status(thm)],[g0_10,t16]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL897+1 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n026.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 00:42:24 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.10/1.15 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.10/1.15 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------