%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : COL074-3 : TPTP v9.2.1. Released 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 04:12:15 PM UTC 2026
% Result : Unsatisfiable 1.24s 1.72s
% Output : CNFRefutation 1.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of clauses : 17 ( 14 unt; 3 nHn; 10 RR)
% Number of literals : 20 ( 19 equ; 2 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 11 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(self_referential,axiom,
s = apply(eq,pair(apply(k,s),apply(k,projection2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',self_referential) ).
cnf(k_projection2,axiom,
apply(k,projection2) = k_projection2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_projection2) ).
cnf(extensionality1,axiom,
( X1 = X2
| apply(eq,pair(X1,X2)) = projection2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality1) ).
cnf(k_definition,negated_conjecture,
apply(apply(k,X1),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_definition) ).
cnf(equality,axiom,
apply(eq,pair(X1,X1)) = projection1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equality) ).
cnf(different_projections,axiom,
projection1 != projection2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',different_projections) ).
cnf(c_0_6,axiom,
s = apply(eq,pair(apply(k,s),apply(k,projection2))),
self_referential ).
cnf(c_0_7,axiom,
apply(k,projection2) = k_projection2,
k_projection2 ).
cnf(c_0_8,axiom,
( X1 = X2
| apply(eq,pair(X1,X2)) = projection2 ),
extensionality1 ).
cnf(c_0_9,plain,
apply(eq,pair(apply(k,s),k_projection2)) = s,
inference(rw,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_10,negated_conjecture,
apply(apply(k,X1),X2) = X1,
k_definition ).
cnf(c_0_11,plain,
( apply(k,s) = k_projection2
| s = projection2 ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_12,negated_conjecture,
apply(k_projection2,X1) = projection2,
inference(spm,[status(thm)],[c_0_10,c_0_7]) ).
cnf(c_0_13,negated_conjecture,
s = projection2,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12])]) ).
cnf(c_0_14,axiom,
apply(eq,pair(X1,X1)) = projection1,
equality ).
cnf(c_0_15,axiom,
projection1 != projection2,
different_projections ).
cnf(c_0_16,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_13]),c_0_7]),c_0_14]),c_0_13]),c_0_15]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COL074-3 : TPTP v9.2.1. Released 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 16:18:23 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.24/1.72 % Version : CSE_E---1.7
% 1.24/1.72 % Problem : theBenchmark.p
% 1.24/1.72 % SZS status Unsatisfiable for theBenchmark.p
% 1.24/1.72 % SZS output start CNFRefutation
% See solution above
% 1.24/1.72 % Total time : 1.371s
%------------------------------------------------------------------------------