%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : COL077-1 : TPTP v9.2.1. Released v1.2.0.
% 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 04:12:15 PM UTC 2026
% Result : Unsatisfiable 1.44s 1.79s
% Output : CNFRefutation 1.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of clauses : 16 ( 13 unt; 0 nHn; 7 RR)
% Number of literals : 19 ( 18 equ; 6 neg)
% Maximal clause size : 2 ( 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; 2 con; 0-2 aty)
% Number of variables : 25 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(abstraction,axiom,
apply(apply(apply(abstraction,X1),X2),X3) = apply(apply(X1,k(X3)),apply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/COL001-0.ax',abstraction) ).
cnf(k_definition,axiom,
apply(k(X1),X2) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/COL001-0.ax',k_definition) ).
cnf(extensionality2,axiom,
( X1 = X2
| apply(X1,n(X1,X2)) != apply(X2,n(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/COL001-0.ax',extensionality2) ).
cnf(identity_definition,axiom,
apply(identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_definition) ).
cnf(prove_TRC1a,negated_conjecture,
apply(apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),abstraction),abstraction) != identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_TRC1a) ).
cnf(c_0_5,axiom,
apply(apply(apply(abstraction,X1),X2),X3) = apply(apply(X1,k(X3)),apply(X2,X3)),
abstraction ).
cnf(c_0_6,axiom,
apply(k(X1),X2) = X1,
k_definition ).
cnf(c_0_7,axiom,
( X1 = X2
| apply(X1,n(X1,X2)) != apply(X2,n(X1,X2)) ),
extensionality2 ).
cnf(c_0_8,axiom,
apply(identity,X1) = X1,
identity_definition ).
cnf(c_0_9,plain,
apply(apply(apply(apply(abstraction,abstraction),X1),X2),X3) = apply(X2,apply(apply(X1,X2),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_5]),c_0_6]) ).
cnf(c_0_10,negated_conjecture,
apply(apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),abstraction),abstraction) != identity,
prove_TRC1a ).
cnf(c_0_11,plain,
( identity = X1
| apply(X1,n(identity,X1)) != n(identity,X1) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_12,plain,
apply(apply(apply(abstraction,apply(apply(abstraction,abstraction),X1)),X2),X3) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_9]),c_0_6]) ).
cnf(c_0_13,negated_conjecture,
apply(apply(abstraction,apply(apply(abstraction,abstraction),abstraction)),abstraction) != identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_5]),c_0_5]),c_0_6]) ).
cnf(c_0_14,plain,
apply(apply(abstraction,apply(apply(abstraction,abstraction),X1)),X2) = identity,
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
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 : COL077-1 : TPTP v9.2.1. Released v1.2.0.
% 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 : n020.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 16:16:20 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.44/1.79 % Version : CSE_E---1.7
% 1.44/1.79 % Problem : theBenchmark.p
% 1.44/1.79 % SZS status Unsatisfiable for theBenchmark.p
% 1.44/1.79 % SZS output start CNFRefutation
% See solution above
% 1.44/1.80 % Total time : 1.368s
%------------------------------------------------------------------------------