%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : CAT009-1 : TPTP v9.2.1. Released v1.0.0.
% 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 : n012.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 04:11:40 PM UTC 2026
% Result : Unsatisfiable 1.15s 1.63s
% Output : CNFRefutation 1.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of clauses : 29 ( 16 unt; 0 nHn; 23 RR)
% Number of literals : 50 ( 5 equ; 23 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 38 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(closure_of_composition,axiom,
( product(X1,X2,compose(X1,X2))
| ~ defined(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',closure_of_composition) ).
cnf(ba_defined,hypothesis,
defined(b,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ba_defined) ).
cnf(associative_property2,axiom,
( defined(X2,X4)
| ~ product(X1,X2,X3)
| ~ defined(X3,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',associative_property2) ).
cnf(product_on_domain,axiom,
product(X1,domain(X1),X1),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',product_on_domain) ).
cnf(mapping_from_x_to_its_domain,axiom,
defined(X1,domain(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',mapping_from_x_to_its_domain) ).
cnf(identity2,axiom,
( product(X1,X2,X1)
| ~ defined(X1,X2)
| ~ identity_map(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',identity2) ).
cnf(domain_is_an_identity_map,axiom,
identity_map(domain(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',domain_is_an_identity_map) ).
cnf(composition_is_well_defined,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',composition_is_well_defined) ).
cnf(identity1,axiom,
( product(X1,X2,X2)
| ~ defined(X1,X2)
| ~ identity_map(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',identity1) ).
cnf(prove_domain_of_ba_equals_domain_of_a,negated_conjecture,
domain(compose(b,a)) != domain(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_domain_of_ba_equals_domain_of_a) ).
cnf(c_0_10,axiom,
( product(X1,X2,compose(X1,X2))
| ~ defined(X1,X2) ),
closure_of_composition ).
cnf(c_0_11,hypothesis,
defined(b,a),
ba_defined ).
cnf(c_0_12,axiom,
( defined(X2,X4)
| ~ product(X1,X2,X3)
| ~ defined(X3,X4) ),
associative_property2 ).
cnf(c_0_13,hypothesis,
product(b,a,compose(b,a)),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,axiom,
product(X1,domain(X1),X1),
product_on_domain ).
cnf(c_0_15,hypothesis,
( defined(a,X1)
| ~ defined(compose(b,a),X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,axiom,
defined(X1,domain(X1)),
mapping_from_x_to_its_domain ).
cnf(c_0_17,plain,
( defined(domain(X1),X2)
| ~ defined(X1,X2) ),
inference(spm,[status(thm)],[c_0_12,c_0_14]) ).
cnf(c_0_18,hypothesis,
defined(a,domain(compose(b,a))),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,axiom,
( product(X1,X2,X1)
| ~ defined(X1,X2)
| ~ identity_map(X2) ),
identity2 ).
cnf(c_0_20,hypothesis,
defined(domain(a),domain(compose(b,a))),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,axiom,
identity_map(domain(X1)),
domain_is_an_identity_map ).
cnf(c_0_22,axiom,
( X3 = X4
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
composition_is_well_defined ).
cnf(c_0_23,hypothesis,
product(domain(a),domain(compose(b,a)),domain(a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]) ).
cnf(c_0_24,axiom,
( product(X1,X2,X2)
| ~ defined(X1,X2)
| ~ identity_map(X1) ),
identity1 ).
cnf(c_0_25,hypothesis,
( X1 = domain(a)
| ~ product(domain(a),domain(compose(b,a)),X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,hypothesis,
product(domain(a),domain(compose(b,a)),domain(compose(b,a))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_20]),c_0_21])]) ).
cnf(c_0_27,negated_conjecture,
domain(compose(b,a)) != domain(a),
prove_domain_of_ba_equals_domain_of_a ).
cnf(c_0_28,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : CAT009-1 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.06 % 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
% 0.06/0.24 % Computer : n012.cluster.edu
% 0.06/0.24 % Model : x86_64 x86_64
% 0.06/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.24 % Memory : 8042.1875MB
% 0.06/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.24 % CPULimit : 300
% 0.06/0.24 % WCLimit : 300
% 0.06/0.24 % DateTime : Tue May 5 10:46:31 EDT 2026
% 0.06/0.24 % CPUTime :
% 0.06/0.25 % start to proof: theBenchmark
% 1.15/1.63 % Version : CSE_E---1.7
% 1.15/1.63 % Problem : theBenchmark.p
% 1.15/1.63 % SZS status Unsatisfiable for theBenchmark.p
% 1.15/1.63 % SZS output start CNFRefutation
% See solution above
% 1.15/1.63 % Total time : 1.361s
%------------------------------------------------------------------------------