%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LDA001-1 : TPTP v9.2.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n022.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 : Tue May 5 04:46:52 PM UTC 2026
% Result : Unsatisfiable 1.27s 1.72s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of clauses : 22 ( 22 unt; 0 nHn; 15 RR)
% Number of literals : 22 ( 21 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 11 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a1,axiom,
f(X1,f(X2,X3)) = f(f(X1,X2),f(X1,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1) ).
cnf(clause_4,axiom,
u = f(n2,n2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_4) ).
cnf(clause_3,axiom,
n3 = f(n2,n1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3) ).
cnf(clause_2,axiom,
n2 = f(n1,n1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2) ).
cnf(prove_equation,negated_conjecture,
f(f(n3,n2),u) != f(f(u,u),u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equation) ).
cnf(c_0_5,axiom,
f(X1,f(X2,X3)) = f(f(X1,X2),f(X1,X3)),
a1 ).
cnf(c_0_6,axiom,
u = f(n2,n2),
clause_4 ).
cnf(c_0_7,axiom,
n3 = f(n2,n1),
clause_3 ).
cnf(c_0_8,plain,
f(f(n2,X1),u) = f(n2,f(X1,n2)),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_9,plain,
f(f(n2,X1),n3) = f(n2,f(X1,n1)),
inference(spm,[status(thm)],[c_0_5,c_0_7]) ).
cnf(c_0_10,axiom,
n2 = f(n1,n1),
clause_2 ).
cnf(c_0_11,negated_conjecture,
f(f(n3,n2),u) != f(f(u,u),u),
prove_equation ).
cnf(c_0_12,plain,
f(u,u) = f(n2,u),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_6]),c_0_6]) ).
cnf(c_0_13,plain,
f(n3,n3) = u,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_7]),c_0_10]),c_0_6]) ).
cnf(c_0_14,plain,
f(f(n1,X1),n2) = f(n1,f(X1,n1)),
inference(spm,[status(thm)],[c_0_5,c_0_10]) ).
cnf(c_0_15,negated_conjecture,
f(f(n3,n2),u) != f(n2,f(u,n2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_12]),c_0_8]) ).
cnf(c_0_16,plain,
f(f(n3,X1),u) = f(n3,f(X1,n3)),
inference(spm,[status(thm)],[c_0_5,c_0_13]) ).
cnf(c_0_17,plain,
f(n1,n2) = u,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_10]),c_0_6]),c_0_10]) ).
cnf(c_0_18,negated_conjecture,
f(n3,f(n2,n3)) != f(n2,f(u,n2)),
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,plain,
f(n3,f(n2,X1)) = f(n2,f(n1,X1)),
inference(spm,[status(thm)],[c_0_5,c_0_7]) ).
cnf(c_0_20,plain,
f(n1,n3) = f(u,n2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_17]),c_0_7]) ).
cnf(c_0_21,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19]),c_0_20])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LDA001-1 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n022.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 23:19:51 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.27/1.72 % Version : CSE_E---1.7
% 1.27/1.72 % Problem : theBenchmark.p
% 1.27/1.72 % SZS status Unsatisfiable for theBenchmark.p
% 1.27/1.72 % SZS output start CNFRefutation
% See solution above
% 1.27/1.72 % Total time : 1.373s
%------------------------------------------------------------------------------