%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET041-3 : TPTP v9.2.1. Released v1.0.0.
% 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 : n009.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 05:06:59 PM UTC 2026
% Result : Unsatisfiable 1.36s 1.75s
% Output : CNFRefutation 1.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of clauses : 16 ( 9 unt; 0 nHn; 10 RR)
% Number of literals : 27 ( 6 equ; 13 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 19 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(apply_for_composition1,axiom,
( subset(apply(X3,apply(X1,X2)),apply(compose(X3,X1),X2))
| ~ function(X1)
| ~ member(X2,domain_of(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apply_for_composition1) ).
cnf(member_of_domain,hypothesis,
member(a,domain_of(a_function)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_domain) ).
cnf(a_function,hypothesis,
function(a_function),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_function) ).
cnf(two_sets_equal,axiom,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',two_sets_equal) ).
cnf(apply_for_composition2,axiom,
( subset(apply(compose(X2,X1),X3),apply(X2,apply(X1,X3)))
| ~ function(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apply_for_composition2) ).
cnf(prove_apply_for_composition3,negated_conjecture,
apply(another_function,apply(a_function,a)) != apply(compose(another_function,a_function),a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_apply_for_composition3) ).
cnf(c_0_6,axiom,
( subset(apply(X3,apply(X1,X2)),apply(compose(X3,X1),X2))
| ~ function(X1)
| ~ member(X2,domain_of(X1)) ),
apply_for_composition1 ).
cnf(c_0_7,hypothesis,
member(a,domain_of(a_function)),
member_of_domain ).
cnf(c_0_8,hypothesis,
function(a_function),
a_function ).
cnf(c_0_9,axiom,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
two_sets_equal ).
cnf(c_0_10,hypothesis,
subset(apply(X1,apply(a_function,a)),apply(compose(X1,a_function),a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_7]),c_0_8])]) ).
cnf(c_0_11,hypothesis,
( apply(compose(X1,a_function),a) = apply(X1,apply(a_function,a))
| ~ subset(apply(compose(X1,a_function),a),apply(X1,apply(a_function,a))) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_12,axiom,
( subset(apply(compose(X2,X1),X3),apply(X2,apply(X1,X3)))
| ~ function(X1) ),
apply_for_composition2 ).
cnf(c_0_13,negated_conjecture,
apply(another_function,apply(a_function,a)) != apply(compose(another_function,a_function),a),
prove_apply_for_composition3 ).
cnf(c_0_14,hypothesis,
apply(compose(X1,a_function),a) = apply(X1,apply(a_function,a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_8])]) ).
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 : SET041-3 : TPTP v9.2.1. Released v1.0.0.
% 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
% 0.15/0.33 % Computer : n009.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 : Tue May 5 02:06:11 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.36/1.75 % Version : CSE_E---1.7
% 1.36/1.75 % Problem : theBenchmark.p
% 1.36/1.75 % SZS status Unsatisfiable for theBenchmark.p
% 1.36/1.75 % SZS output start CNFRefutation
% See solution above
% 1.36/1.75 % Total time : 1.373s
%------------------------------------------------------------------------------