%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : CAT010-10 : TPTP v9.2.1. Released v7.3.0.
% 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 : n004.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 1.26s 1.72s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of clauses : 37 ( 37 unt; 0 nHn; 13 RR)
% Number of literals : 37 ( 36 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 : 10 ( 10 usr; 3 con; 0-4 aty)
% Number of variables : 48 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(domain_codomain_composition1,axiom,
ifeq2(there_exists(compose(X1,X2)),true,domain(X1),codomain(X2)) = codomain(X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_codomain_composition1) ).
cnf(ab_exists,hypothesis,
there_exists(compose(a,b)) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ab_exists) ).
cnf(ifeq_axiom_001,axiom,
ifeq2(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_001) ).
cnf(composition_implies_domain,axiom,
ifeq(there_exists(compose(X1,X2)),true,there_exists(domain(X1)),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_implies_domain) ).
cnf(ifeq_axiom_002,axiom,
ifeq(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_002) ).
cnf(compose_codomain,axiom,
compose(codomain(X1),X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_codomain) ).
cnf(codomain_has_elements,axiom,
ifeq(there_exists(codomain(X1)),true,there_exists(X1),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_has_elements) ).
cnf(compose_domain,axiom,
compose(X1,domain(X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_domain) ).
cnf(domain_codomain_composition2,axiom,
ifeq(there_exists(domain(X1)),true,ifeq3(domain(X1),codomain(X2),there_exists(compose(X1,X2)),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_codomain_composition2) ).
cnf(associativity_of_compose,axiom,
compose(X1,compose(X2,X3)) = compose(compose(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_compose) ).
cnf(ifeq_axiom,axiom,
ifeq3(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(prove_codomain_of_ab_equals_codomain_of_a,negated_conjecture,
codomain(compose(a,b)) != codomain(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_codomain_of_ab_equals_codomain_of_a) ).
cnf(c_0_12,axiom,
ifeq2(there_exists(compose(X1,X2)),true,domain(X1),codomain(X2)) = codomain(X2),
domain_codomain_composition1 ).
cnf(c_0_13,hypothesis,
there_exists(compose(a,b)) = true,
ab_exists ).
cnf(c_0_14,axiom,
ifeq2(X1,X1,X2,X3) = X2,
ifeq_axiom_001 ).
cnf(c_0_15,axiom,
ifeq(there_exists(compose(X1,X2)),true,there_exists(domain(X1)),true) = true,
composition_implies_domain ).
cnf(c_0_16,axiom,
ifeq(X1,X1,X2,X3) = X2,
ifeq_axiom_002 ).
cnf(c_0_17,hypothesis,
domain(a) = codomain(b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).
cnf(c_0_18,axiom,
compose(codomain(X1),X1) = X1,
compose_codomain ).
cnf(c_0_19,axiom,
ifeq(there_exists(codomain(X1)),true,there_exists(X1),true) = true,
codomain_has_elements ).
cnf(c_0_20,hypothesis,
there_exists(codomain(b)) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_13]),c_0_16]),c_0_17]) ).
cnf(c_0_21,plain,
ifeq2(there_exists(X1),true,domain(codomain(X1)),codomain(X1)) = codomain(X1),
inference(spm,[status(thm)],[c_0_12,c_0_18]) ).
cnf(c_0_22,hypothesis,
there_exists(b) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_16]) ).
cnf(c_0_23,axiom,
compose(X1,domain(X1)) = X1,
compose_domain ).
cnf(c_0_24,hypothesis,
domain(codomain(b)) = codomain(b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_14]) ).
cnf(c_0_25,axiom,
ifeq(there_exists(domain(X1)),true,ifeq3(domain(X1),codomain(X2),there_exists(compose(X1,X2)),true),true) = true,
domain_codomain_composition2 ).
cnf(c_0_26,hypothesis,
compose(codomain(b),codomain(b)) = codomain(b),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_27,axiom,
compose(X1,compose(X2,X3)) = compose(compose(X1,X2),X3),
associativity_of_compose ).
cnf(c_0_28,plain,
ifeq(there_exists(domain(X1)),true,ifeq3(domain(X1),codomain(domain(X1)),there_exists(X1),true),true) = true,
inference(spm,[status(thm)],[c_0_25,c_0_23]) ).
cnf(c_0_29,hypothesis,
codomain(codomain(b)) = codomain(b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_26]),c_0_20]),c_0_24]),c_0_14]) ).
cnf(c_0_30,axiom,
ifeq3(X1,X1,X2,X3) = X2,
ifeq_axiom ).
cnf(c_0_31,plain,
compose(codomain(X1),compose(X1,X2)) = compose(X1,X2),
inference(spm,[status(thm)],[c_0_27,c_0_18]) ).
cnf(c_0_32,hypothesis,
there_exists(a) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_17]),c_0_20]),c_0_29]),c_0_30]),c_0_16]) ).
cnf(c_0_33,plain,
ifeq2(there_exists(compose(X1,X2)),true,domain(codomain(X1)),codomain(compose(X1,X2))) = codomain(compose(X1,X2)),
inference(spm,[status(thm)],[c_0_12,c_0_31]) ).
cnf(c_0_34,hypothesis,
domain(codomain(a)) = codomain(a),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_32]),c_0_14]) ).
cnf(c_0_35,negated_conjecture,
codomain(compose(a,b)) != codomain(a),
prove_codomain_of_ab_equals_codomain_of_a ).
cnf(c_0_36,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_13]),c_0_34]),c_0_14]),c_0_35]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : CAT010-10 : TPTP v9.2.1. Released v7.3.0.
% 0.00/0.11 % 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
% 0.15/0.32 % Computer : n004.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 10:46:32 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 1.26/1.72 % Version : CSE_E---1.7
% 1.26/1.72 % Problem : theBenchmark.p
% 1.26/1.72 % SZS status Unsatisfiable for theBenchmark.p
% 1.26/1.72 % SZS output start CNFRefutation
% See solution above
% 1.26/1.72 % Total time : 1.370s
%------------------------------------------------------------------------------