%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : CAT009-3 : 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 : 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 04:11:40 PM UTC 2026
% Result : Unsatisfiable 1.36s 1.76s
% Output : CNFRefutation 1.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of clauses : 46 ( 22 unt; 0 nHn; 34 RR)
% Number of literals : 73 ( 40 equ; 29 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 47 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(composition_implies_domain,axiom,
( there_exists(domain(X1))
| ~ there_exists(compose(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT003-0.ax',composition_implies_domain) ).
cnf(compose_domain,axiom,
compose(X1,domain(X1)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/CAT003-0.ax',compose_domain) ).
cnf(domain_codomain_composition2,axiom,
( there_exists(compose(X1,X2))
| ~ there_exists(domain(X1))
| domain(X1) != codomain(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT003-0.ax',domain_codomain_composition2) ).
cnf(ab_exists,hypothesis,
there_exists(compose(a,b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ab_exists) ).
cnf(associativity_of_compose,axiom,
compose(X1,compose(X2,X3)) = compose(compose(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT003-0.ax',associativity_of_compose) ).
cnf(domain_codomain_composition1,axiom,
( domain(X1) = codomain(X2)
| ~ there_exists(compose(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT003-0.ax',domain_codomain_composition1) ).
cnf(compose_codomain,axiom,
compose(codomain(X1),X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/CAT003-0.ax',compose_codomain) ).
cnf(codomain_has_elements,axiom,
( there_exists(X1)
| ~ there_exists(codomain(X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT003-0.ax',codomain_has_elements) ).
cnf(prove_domain_of_ab_equals_domain_of_b,negated_conjecture,
domain(compose(a,b)) != domain(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_domain_of_ab_equals_domain_of_b) ).
cnf(c_0_9,axiom,
( there_exists(domain(X1))
| ~ there_exists(compose(X1,X2)) ),
composition_implies_domain ).
cnf(c_0_10,axiom,
compose(X1,domain(X1)) = X1,
compose_domain ).
cnf(c_0_11,axiom,
( there_exists(compose(X1,X2))
| ~ there_exists(domain(X1))
| domain(X1) != codomain(X2) ),
domain_codomain_composition2 ).
cnf(c_0_12,plain,
( there_exists(domain(X1))
| ~ there_exists(X1) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,plain,
( there_exists(compose(X1,X2))
| codomain(X2) != domain(X1)
| ~ there_exists(X1) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_14,hypothesis,
there_exists(compose(a,b)),
ab_exists ).
cnf(c_0_15,axiom,
compose(X1,compose(X2,X3)) = compose(compose(X1,X2),X3),
associativity_of_compose ).
cnf(c_0_16,axiom,
( domain(X1) = codomain(X2)
| ~ there_exists(compose(X1,X2)) ),
domain_codomain_composition1 ).
cnf(c_0_17,hypothesis,
( there_exists(compose(a,compose(b,X1)))
| codomain(X1) != domain(compose(a,b)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
cnf(c_0_18,plain,
compose(X1,compose(domain(X1),X2)) = compose(X1,X2),
inference(spm,[status(thm)],[c_0_15,c_0_10]) ).
cnf(c_0_19,hypothesis,
( codomain(compose(b,X1)) = domain(a)
| codomain(X1) != domain(compose(a,b)) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,plain,
compose(X1,compose(X2,domain(compose(X1,X2)))) = compose(X1,X2),
inference(spm,[status(thm)],[c_0_10,c_0_15]) ).
cnf(c_0_21,plain,
compose(X1,domain(domain(X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_10]),c_0_10]) ).
cnf(c_0_22,axiom,
compose(codomain(X1),X1) = X1,
compose_codomain ).
cnf(c_0_23,hypothesis,
codomain(b) = domain(a),
inference(spm,[status(thm)],[c_0_16,c_0_14]) ).
cnf(c_0_24,axiom,
( there_exists(X1)
| ~ there_exists(codomain(X1)) ),
codomain_has_elements ).
cnf(c_0_25,hypothesis,
there_exists(domain(a)),
inference(spm,[status(thm)],[c_0_9,c_0_14]) ).
cnf(c_0_26,hypothesis,
( codomain(compose(b,X1)) = domain(a)
| codomain(compose(domain(b),X1)) != domain(compose(a,b)) ),
inference(spm,[status(thm)],[c_0_19,c_0_18]) ).
cnf(c_0_27,plain,
compose(X1,compose(domain(domain(X1)),domain(X1))) = X1,
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_28,hypothesis,
compose(domain(a),b) = b,
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_29,hypothesis,
there_exists(b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_23]),c_0_25])]) ).
cnf(c_0_30,hypothesis,
( codomain(compose(b,compose(domain(domain(domain(b))),domain(domain(b))))) = domain(a)
| codomain(domain(b)) != domain(compose(a,b)) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,hypothesis,
compose(domain(a),compose(b,X1)) = compose(b,X1),
inference(spm,[status(thm)],[c_0_15,c_0_28]) ).
cnf(c_0_32,hypothesis,
domain(domain(a)) = domain(a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_28]),c_0_23]),c_0_29])]) ).
cnf(c_0_33,plain,
( codomain(X1) = domain(compose(X2,X3))
| ~ there_exists(compose(X2,compose(X3,X1))) ),
inference(spm,[status(thm)],[c_0_16,c_0_15]) ).
cnf(c_0_34,hypothesis,
( there_exists(compose(b,compose(domain(domain(domain(b))),domain(domain(b)))))
| codomain(domain(b)) != domain(compose(a,b)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_30]),c_0_25])]) ).
cnf(c_0_35,plain,
compose(X1,domain(domain(domain(X1)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_21]),c_0_10]) ).
cnf(c_0_36,plain,
( codomain(domain(domain(X1))) = domain(X1)
| ~ there_exists(X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_21]) ).
cnf(c_0_37,hypothesis,
( there_exists(compose(a,X1))
| codomain(X1) != domain(a) ),
inference(spm,[status(thm)],[c_0_11,c_0_25]) ).
cnf(c_0_38,hypothesis,
( codomain(compose(b,X1)) = domain(a)
| ~ there_exists(compose(b,X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_31]),c_0_32]) ).
cnf(c_0_39,hypothesis,
( codomain(domain(domain(b))) = domain(b)
| codomain(domain(b)) != domain(compose(a,b)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]) ).
cnf(c_0_40,plain,
( domain(domain(X1)) = domain(X1)
| ~ there_exists(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_36]),c_0_10]) ).
cnf(c_0_41,hypothesis,
( there_exists(compose(a,compose(b,X1)))
| ~ there_exists(compose(b,X1)) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_42,hypothesis,
( codomain(domain(b)) = domain(b)
| codomain(domain(b)) != domain(compose(a,b)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_29])]) ).
cnf(c_0_43,hypothesis,
( codomain(X1) = domain(compose(a,b))
| ~ there_exists(compose(b,X1)) ),
inference(spm,[status(thm)],[c_0_33,c_0_41]) ).
cnf(c_0_44,negated_conjecture,
domain(compose(a,b)) != domain(b),
prove_domain_of_ab_equals_domain_of_b ).
cnf(c_0_45,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_10]),c_0_29])]),c_0_44]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : CAT009-3 : TPTP v9.2.1. Released v1.0.0.
% 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
% 0.14/0.32 % Computer : n020.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 10:46:50 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.36/1.76 % Version : CSE_E---1.7
% 1.36/1.76 % Problem : theBenchmark.p
% 1.36/1.76 % SZS status Unsatisfiable for theBenchmark.p
% 1.36/1.76 % SZS output start CNFRefutation
% See solution above
% 1.36/1.77 % Total time : 1.370s
%------------------------------------------------------------------------------