%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : COL035-1 : 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 : n020.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 04:12:05 PM UTC 2026
% Result : Unsatisfiable 1.30s 1.73s
% Output : CNFRefutation 1.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of clauses : 14 ( 14 unt; 0 nHn; 6 RR)
% Number of literals : 14 ( 13 equ; 5 neg)
% Maximal clause size : 1 ( 1 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 : 25 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(q_definition,axiom,
apply(apply(apply(q,X1),X2),X3) = apply(X2,apply(X1,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',q_definition) ).
cnf(l_definition,axiom,
apply(apply(l,X1),X2) = apply(X1,apply(X2,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l_definition) ).
cnf(prove_fixed_point,negated_conjecture,
apply(X1,f(X1)) != apply(f(X1),apply(X1,f(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_fixed_point) ).
cnf(w_definition,axiom,
apply(apply(w,X1),X2) = apply(apply(X1,X2),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',w_definition) ).
cnf(c_0_4,axiom,
apply(apply(apply(q,X1),X2),X3) = apply(X2,apply(X1,X3)),
q_definition ).
cnf(c_0_5,axiom,
apply(apply(l,X1),X2) = apply(X1,apply(X2,X2)),
l_definition ).
cnf(c_0_6,negated_conjecture,
apply(X1,f(X1)) != apply(f(X1),apply(X1,f(X1))),
prove_fixed_point ).
cnf(c_0_7,plain,
apply(apply(apply(apply(l,q),X1),X2),X3) = apply(X2,apply(apply(X1,X1),X3)),
inference(spm,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_8,axiom,
apply(apply(w,X1),X2) = apply(apply(X1,X2),X2),
w_definition ).
cnf(c_0_9,negated_conjecture,
apply(apply(w,apply(apply(l,q),X1)),f(apply(X1,X1))) != apply(apply(X1,X1),f(apply(X1,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_7]),c_0_8]) ).
cnf(c_0_10,negated_conjecture,
apply(apply(w,apply(q,apply(X1,X1))),f(apply(X1,X1))) != apply(apply(X1,X1),f(apply(X1,X1))),
inference(spm,[status(thm)],[c_0_9,c_0_5]) ).
cnf(c_0_11,plain,
apply(apply(l,apply(apply(q,X1),X2)),X3) = apply(X2,apply(X1,apply(X3,X3))),
inference(spm,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_12,negated_conjecture,
apply(apply(apply(l,apply(apply(q,q),w)),X1),f(apply(X1,X1))) != apply(apply(X1,X1),f(apply(X1,X1))),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_13,negated_conjecture,
$false,
inference(er,[status(thm)],[c_0_12]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COL035-1 : 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
% 0.16/0.33 % Computer : n020.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 16:14:20 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 1.30/1.73 % Version : CSE_E---1.7
% 1.30/1.73 % Problem : theBenchmark.p
% 1.30/1.73 % SZS status Unsatisfiable for theBenchmark.p
% 1.30/1.73 % SZS output start CNFRefutation
% See solution above
% 1.30/1.73 % Total time : 1.368s
%------------------------------------------------------------------------------