%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : CAT004-2 : 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 : 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 04:11:38 PM UTC 2026
% Result : Unsatisfiable 1.16s 1.92s
% Output : CNFRefutation 1.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of clauses : 37 ( 18 unt; 0 nHn; 37 RR)
% Number of literals : 79 ( 78 equ; 46 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 39 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(codomain_domain2,axiom,
( codomain(compose(X1,X2)) = codomain(X2)
| codomain(X1) != domain(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT002-0.ax',codomain_domain2) ).
cnf(codomain_of_a_equals_domain_of_b,hypothesis,
codomain(a) = domain(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_of_a_equals_domain_of_b) ).
cnf(codomain_of_ab_equals_domain_of_h,hypothesis,
codomain(compose(a,b)) = domain(h),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_of_ab_equals_domain_of_h) ).
cnf(epimorphism2,hypothesis,
( X1 = X3
| codomain(b) != domain(X1)
| compose(b,X1) != X2
| codomain(b) != domain(X3)
| compose(b,X3) != X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',epimorphism2) ).
cnf(codomain_domain1,axiom,
( domain(compose(X1,X2)) = domain(X1)
| codomain(X1) != domain(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT002-0.ax',codomain_domain1) ).
cnf(star_property,axiom,
( compose(X1,compose(X2,X3)) = compose(compose(X1,X2),X3)
| codomain(X1) != domain(X2)
| codomain(X2) != domain(X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT002-0.ax',star_property) ).
cnf(epimorphism1,hypothesis,
( X1 = X3
| codomain(a) != domain(X1)
| compose(a,X1) != X2
| codomain(a) != domain(X3)
| compose(a,X3) != X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',epimorphism1) ).
cnf(codomain_of_ab_equals_domain_of_g,hypothesis,
codomain(compose(a,b)) = domain(g),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_of_ab_equals_domain_of_g) ).
cnf(prove_h_equals_g,negated_conjecture,
h != g,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_h_equals_g) ).
cnf(ab_h_equals_ab_g,hypothesis,
compose(compose(a,b),h) = compose(compose(a,b),g),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ab_h_equals_ab_g) ).
cnf(c_0_10,axiom,
( codomain(compose(X1,X2)) = codomain(X2)
| codomain(X1) != domain(X2) ),
codomain_domain2 ).
cnf(c_0_11,hypothesis,
codomain(a) = domain(b),
codomain_of_a_equals_domain_of_b ).
cnf(c_0_12,hypothesis,
( codomain(compose(a,X1)) = codomain(X1)
| domain(b) != domain(X1) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_13,hypothesis,
codomain(compose(a,b)) = domain(h),
codomain_of_ab_equals_domain_of_h ).
cnf(c_0_14,hypothesis,
( X1 = X3
| codomain(b) != domain(X1)
| compose(b,X1) != X2
| codomain(b) != domain(X3)
| compose(b,X3) != X2 ),
epimorphism2 ).
cnf(c_0_15,axiom,
( domain(compose(X1,X2)) = domain(X1)
| codomain(X1) != domain(X2) ),
codomain_domain1 ).
cnf(c_0_16,hypothesis,
codomain(b) = domain(h),
inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_12]),c_0_13]) ).
cnf(c_0_17,hypothesis,
( X1 = X2
| compose(b,X1) != compose(b,X2)
| codomain(b) != domain(X2)
| codomain(b) != domain(X1) ),
inference(er,[status(thm)],[c_0_14]) ).
cnf(c_0_18,axiom,
( compose(X1,compose(X2,X3)) = compose(compose(X1,X2),X3)
| codomain(X1) != domain(X2)
| codomain(X2) != domain(X3) ),
star_property ).
cnf(c_0_19,hypothesis,
( X1 = X3
| codomain(a) != domain(X1)
| compose(a,X1) != X2
| codomain(a) != domain(X3)
| compose(a,X3) != X2 ),
epimorphism1 ).
cnf(c_0_20,hypothesis,
( domain(compose(b,X1)) = domain(b)
| domain(h) != domain(X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,hypothesis,
codomain(compose(a,b)) = domain(g),
codomain_of_ab_equals_domain_of_g ).
cnf(c_0_22,hypothesis,
( X1 = X2
| compose(b,X1) != compose(b,X2)
| domain(h) != domain(X2)
| domain(h) != domain(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_16]),c_0_16]) ).
cnf(c_0_23,hypothesis,
( compose(compose(X1,b),X2) = compose(X1,compose(b,X2))
| domain(h) != domain(X2)
| codomain(X1) != domain(b) ),
inference(spm,[status(thm)],[c_0_18,c_0_16]) ).
cnf(c_0_24,hypothesis,
( X1 = X2
| compose(a,X1) != compose(a,X2)
| domain(b) != domain(X2)
| domain(b) != domain(X1) ),
inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_11]),c_0_11])]) ).
cnf(c_0_25,hypothesis,
domain(compose(b,h)) = domain(b),
inference(er,[status(thm)],[c_0_20]) ).
cnf(c_0_26,hypothesis,
domain(g) = domain(h),
inference(rw,[status(thm)],[c_0_21,c_0_13]) ).
cnf(c_0_27,hypothesis,
( X1 = h
| compose(b,X1) != compose(b,h)
| domain(h) != domain(X1) ),
inference(er,[status(thm)],[c_0_22]) ).
cnf(c_0_28,negated_conjecture,
h != g,
prove_h_equals_g ).
cnf(c_0_29,hypothesis,
( compose(compose(a,b),X1) = compose(a,compose(b,X1))
| domain(h) != domain(X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_11]) ).
cnf(c_0_30,hypothesis,
( X1 = compose(b,h)
| compose(a,X1) != compose(a,compose(b,h))
| domain(b) != domain(X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_31,hypothesis,
domain(compose(b,g)) = domain(b),
inference(spm,[status(thm)],[c_0_20,c_0_26]) ).
cnf(c_0_32,hypothesis,
compose(b,g) != compose(b,h),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_26]),c_0_28]) ).
cnf(c_0_33,hypothesis,
compose(compose(a,b),h) = compose(compose(a,b),g),
ab_h_equals_ab_g ).
cnf(c_0_34,hypothesis,
compose(compose(a,b),h) = compose(a,compose(b,h)),
inference(er,[status(thm)],[c_0_29]) ).
cnf(c_0_35,hypothesis,
compose(a,compose(b,g)) != compose(a,compose(b,h)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).
cnf(c_0_36,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_26]),c_0_33]),c_0_34]),c_0_35]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.22 % Problem : CAT004-2 : TPTP v9.2.1. Released v1.0.0.
% 0.02/0.22 % 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
% 0.11/0.46 % Computer : n004.cluster.edu
% 0.11/0.46 % Model : x86_64 x86_64
% 0.11/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.46 % Memory : 8042.1875MB
% 0.11/0.46 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.46 % CPULimit : 300
% 0.11/0.46 % WCLimit : 300
% 0.11/0.46 % DateTime : Tue May 5 10:47:02 EDT 2026
% 0.11/0.46 % CPUTime :
% 0.11/0.47 % start to proof: theBenchmark
% 1.16/1.92 % Version : CSE_E---1.7
% 1.16/1.92 % Problem : theBenchmark.p
% 1.16/1.92 % SZS status Unsatisfiable for theBenchmark.p
% 1.16/1.92 % SZS output start CNFRefutation
% See solution above
% 1.16/1.92 % Total time : 1.414s
%------------------------------------------------------------------------------