%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : COL075-1 : 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 : n024.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 1.13s 1.62s
% Output : CNFRefutation 1.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of clauses : 9 ( 9 unt; 0 nHn; 3 RR)
% Number of literals : 9 ( 8 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 17 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(abstraction,axiom,
apply(apply(apply(abstraction,X1),X2),X3) = apply(apply(X1,apply(k,X3)),apply(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstraction) ).
cnf(k_definition,axiom,
apply(apply(k,X1),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_definition) ).
cnf(prove_diagonal_combinator,negated_conjecture,
apply(apply(X1,b(X1)),c(X1)) != apply(b(X1),b(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_diagonal_combinator) ).
cnf(c_0_3,axiom,
apply(apply(apply(abstraction,X1),X2),X3) = apply(apply(X1,apply(k,X3)),apply(X2,X3)),
abstraction ).
cnf(c_0_4,axiom,
apply(apply(k,X1),X2) = X1,
k_definition ).
cnf(c_0_5,plain,
apply(apply(apply(abstraction,X1),apply(k,X2)),X3) = apply(apply(X1,apply(k,X3)),X2),
inference(spm,[status(thm)],[c_0_3,c_0_4]) ).
cnf(c_0_6,negated_conjecture,
apply(apply(X1,b(X1)),c(X1)) != apply(b(X1),b(X1)),
prove_diagonal_combinator ).
cnf(c_0_7,plain,
apply(apply(apply(apply(abstraction,abstraction),k),X1),X2) = apply(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_3]),c_0_4]) ).
cnf(c_0_8,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_6,c_0_7]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : COL075-1 : TPTP v9.2.1. Released v1.2.0.
% 0.00/0.06 % 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
% 0.06/0.25 % Computer : n024.cluster.edu
% 0.06/0.25 % Model : x86_64 x86_64
% 0.06/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.25 % Memory : 8042.1875MB
% 0.06/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.25 % CPULimit : 300
% 0.06/0.25 % WCLimit : 300
% 0.06/0.25 % DateTime : Mon May 4 11:16:11 EDT 2026
% 0.06/0.25 % CPUTime :
% 0.06/0.25 % start to proof: theBenchmark
% 1.13/1.62 % Version : CSE_E---1.7
% 1.13/1.62 % Problem : theBenchmark.p
% 1.13/1.62 % SZS status Unsatisfiable for theBenchmark.p
% 1.13/1.62 % SZS output start CNFRefutation
% See solution above
% 1.13/1.62 % Total time : 1.361s
%------------------------------------------------------------------------------