%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : COL066-3 : TPTP v9.2.1. Bugfixed v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n031.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 04:12:14 PM UTC 2026
% Result : Unsatisfiable 1.31s 1.74s
% Output : CNFRefutation 1.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of clauses : 16 ( 16 unt; 0 nHn; 7 RR)
% Number of literals : 16 ( 15 equ; 6 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 23 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_p_combinator,negated_conjecture,
apply(apply(apply(apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x),y),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p_combinator) ).
cnf(w_definition,axiom,
apply(apply(w,X1),X2) = apply(apply(X1,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',w_definition) ).
cnf(b_definition,axiom,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_definition) ).
cnf(q_definition,axiom,
apply(apply(apply(q,X1),X2),X3) = apply(X2,apply(X1,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',q_definition) ).
cnf(c_0_4,negated_conjecture,
apply(apply(apply(apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x),y),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
prove_p_combinator ).
cnf(c_0_5,axiom,
apply(apply(w,X1),X2) = apply(apply(X1,X2),X2),
w_definition ).
cnf(c_0_6,negated_conjecture,
apply(apply(apply(w,apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x)),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
inference(rw,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_7,axiom,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
b_definition ).
cnf(c_0_8,axiom,
apply(apply(apply(q,X1),X2),X3) = apply(X2,apply(X1,X3)),
q_definition ).
cnf(c_0_9,negated_conjecture,
apply(apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
inference(rw,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_10,plain,
apply(apply(w,apply(q,X1)),X2) = apply(X2,apply(X1,X2)),
inference(spm,[status(thm)],[c_0_5,c_0_8]) ).
cnf(c_0_11,negated_conjecture,
apply(apply(apply(w,apply(apply(q,x),apply(apply(q,q),apply(q,x)))),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_12,plain,
apply(apply(w,apply(apply(q,X1),X2)),X3) = apply(apply(X2,apply(X1,X3)),X3),
inference(spm,[status(thm)],[c_0_5,c_0_8]) ).
cnf(c_0_13,negated_conjecture,
apply(apply(apply(w,q),apply(x,y)),z) != apply(apply(x,y),apply(apply(x,y),z)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_12]),c_0_8]),c_0_8]),c_0_5]) ).
cnf(c_0_14,plain,
apply(apply(apply(w,q),X1),X2) = apply(X1,apply(X1,X2)),
inference(spm,[status(thm)],[c_0_8,c_0_5]) ).
cnf(c_0_15,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COL066-3 : TPTP v9.2.1. Bugfixed v1.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n031.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 16:18:38 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.31/1.74 % Version : CSE_E---1.7
% 1.31/1.74 % Problem : theBenchmark.p
% 1.31/1.74 % SZS status Unsatisfiable for theBenchmark.p
% 1.31/1.74 % SZS output start CNFRefutation
% See solution above
% 1.31/1.74 % Total time : 1.370s
%------------------------------------------------------------------------------