%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : CAT004-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 06:55:55 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 12
% Syntax : Number of formulae : 97 ( 71 unt; 0 def)
% Number of atoms : 156 ( 155 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 131 ( 72 ~; 59 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 5 ( 2 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 : 61 ( 0 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(domain_of_codomain_is_codomain,axiom,
! [VAR_0] : domain(codomain(VAR_0)) = codomain(VAR_0),
file('theBenchmark.p',domain_of_codomain_is_codomain) ).
cnf(c_2,plain,
domain(codomain(A)) = codomain(A),
inference(clausify,[status(thm)],[domain_of_codomain_is_codomain]) ).
fof(codomain_composition,axiom,
! [VAR_0] : compose(VAR_0,codomain(VAR_0)) = VAR_0,
file('theBenchmark.p',codomain_composition) ).
cnf(c_4,plain,
compose(A,codomain(A)) = A,
inference(clausify,[status(thm)],[codomain_composition]) ).
fof(codomain_domain1,axiom,
! [VAR_0,VAR_1] :
( domain(compose(VAR_0,VAR_1)) = domain(VAR_0)
| codomain(VAR_0) != domain(VAR_1) ),
file('theBenchmark.p',codomain_domain1) ).
cnf(c_5,plain,
( domain(compose(A,B)) = domain(A)
| codomain(A) != domain(B) ),
inference(clausify,[status(thm)],[codomain_domain1]) ).
fof(codomain_domain2,axiom,
! [VAR_0,VAR_1] :
( codomain(compose(VAR_0,VAR_1)) = codomain(VAR_1)
| codomain(VAR_0) != domain(VAR_1) ),
file('theBenchmark.p',codomain_domain2) ).
cnf(c_6,plain,
( codomain(compose(A,B)) = codomain(B)
| codomain(A) != domain(B) ),
inference(clausify,[status(thm)],[codomain_domain2]) ).
fof(star_property,axiom,
! [VAR_0,VAR_1,VAR_2] :
( compose(VAR_0,compose(VAR_1,VAR_2)) = compose(compose(VAR_0,VAR_1),VAR_2)
| codomain(VAR_1) != domain(VAR_2)
| codomain(VAR_0) != domain(VAR_1) ),
file('theBenchmark.p',star_property) ).
cnf(c_7,plain,
( compose(A,compose(B,C)) = compose(compose(A,B),C)
| codomain(B) != domain(C)
| codomain(A) != domain(B) ),
inference(clausify,[status(thm)],[star_property]) ).
cnf(c_8,plain,
( compose(compose(A,B),C) = compose(A,compose(B,C))
| codomain(B) != domain(C)
| codomain(A) != domain(B) ),
inference(copy,[status(thm)],[c_7]) ).
fof(epimorphism1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_0 = VAR_2
| compose(a,VAR_2) != VAR_1
| codomain(a) != domain(VAR_2)
| compose(a,VAR_0) != VAR_1
| codomain(a) != domain(VAR_0) ),
file('theBenchmark.p',epimorphism1) ).
cnf(c_9,plain,
( A = C
| compose(a,C) != B
| codomain(a) != domain(C)
| compose(a,A) != B
| codomain(a) != domain(A) ),
inference(clausify,[status(thm)],[epimorphism1]) ).
cnf(c_113,plain,
( A = C
| compose(a,C) != B
| codomain(a) != domain(C)
| compose(a,A) != B
| domain(A) != codomain(a) ),
inference(copy,[status(thm)],[c_9]) ).
cnf(c_10,plain,
( A = C
| compose(a,C) != B
| domain(C) != codomain(a)
| compose(a,A) != B
| domain(A) != codomain(a) ),
inference(copy,[status(thm)],[c_113]) ).
fof(epimorphism2,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_0 = VAR_2
| compose(b,VAR_2) != VAR_1
| codomain(b) != domain(VAR_2)
| compose(b,VAR_0) != VAR_1
| codomain(b) != domain(VAR_0) ),
file('theBenchmark.p',epimorphism2) ).
cnf(c_11,plain,
( A = C
| compose(b,C) != B
| codomain(b) != domain(C)
| compose(b,A) != B
| codomain(b) != domain(A) ),
inference(clausify,[status(thm)],[epimorphism2]) ).
cnf(c_114,plain,
( A = C
| compose(b,C) != B
| codomain(b) != domain(C)
| compose(b,A) != B
| domain(A) != codomain(b) ),
inference(copy,[status(thm)],[c_11]) ).
cnf(c_12,plain,
( A = C
| compose(b,C) != B
| domain(C) != codomain(b)
| compose(b,A) != B
| domain(A) != codomain(b) ),
inference(copy,[status(thm)],[c_114]) ).
fof(codomain_of_a_equals_domain_of_b,axiom,
codomain(a) = domain(b),
file('theBenchmark.p',codomain_of_a_equals_domain_of_b) ).
cnf(c_13,plain,
codomain(a) = domain(b),
inference(clausify,[status(thm)],[codomain_of_a_equals_domain_of_b]) ).
cnf(c_14,plain,
domain(b) = codomain(a),
inference(copy,[status(thm)],[c_13]) ).
fof(codomain_of_ab_equals_domain_of_h,axiom,
codomain(compose(a,b)) = domain(h),
file('theBenchmark.p',codomain_of_ab_equals_domain_of_h) ).
cnf(c_15,plain,
codomain(compose(a,b)) = domain(h),
inference(clausify,[status(thm)],[codomain_of_ab_equals_domain_of_h]) ).
cnf(c_16,plain,
domain(h) = codomain(compose(a,b)),
inference(copy,[status(thm)],[c_15]) ).
fof(codomain_of_ab_equals_domain_of_g,axiom,
codomain(compose(a,b)) = domain(g),
file('theBenchmark.p',codomain_of_ab_equals_domain_of_g) ).
cnf(c_17,plain,
codomain(compose(a,b)) = domain(g),
inference(clausify,[status(thm)],[codomain_of_ab_equals_domain_of_g]) ).
cnf(c_18,plain,
domain(g) = codomain(compose(a,b)),
inference(copy,[status(thm)],[c_17]) ).
fof(ab_h_equals_ab_g,axiom,
compose(compose(a,b),h) = compose(compose(a,b),g),
file('theBenchmark.p',ab_h_equals_ab_g) ).
cnf(c_19,plain,
compose(compose(a,b),h) = compose(compose(a,b),g),
inference(clausify,[status(thm)],[ab_h_equals_ab_g]) ).
fof(prove_h_equals_g,axiom,
h != g,
file('theBenchmark.p',prove_h_equals_g) ).
cnf(c_20,plain,
h != g,
inference(clausify,[status(thm)],[prove_h_equals_g]) ).
cnf(c_115,plain,
codomain(a) = domain(b),
inference(copy,[status(thm)],[c_14]) ).
cnf(c_39,plain,
codomain(compose(a,b)) = codomain(b),
inference(resolve,[status(thm)],[c_6,c_115]) ).
cnf(c_48,plain,
domain(g) = codomain(b),
inference(paramod,[status(thm)],[c_39,c_18]) ).
cnf(c_49,plain,
domain(h) = codomain(b),
inference(paramod,[status(thm)],[c_39,c_16]) ).
cnf(c_116,plain,
codomain(a) = domain(b),
inference(copy,[status(thm)],[c_14]) ).
cnf(c_117,plain,
( compose(compose(a,b),A) = compose(a,compose(b,A))
| codomain(b) != domain(A) ),
inference(resolve,[status(thm)],[c_8,c_116]) ).
cnf(c_118,plain,
codomain(b) = domain(g),
inference(copy,[status(thm)],[c_48]) ).
cnf(c_54,plain,
compose(compose(a,b),g) = compose(a,compose(b,g)),
inference(resolve,[status(thm)],[c_117,c_118]) ).
cnf(c_119,plain,
codomain(b) = domain(g),
inference(copy,[status(thm)],[c_48]) ).
cnf(c_120,plain,
( compose(compose(b,g),A) = compose(b,compose(g,A))
| codomain(g) != domain(A) ),
inference(resolve,[status(thm)],[c_8,c_119]) ).
cnf(c_121,plain,
codomain(A) = domain(codomain(A)),
inference(copy,[status(thm)],[c_2]) ).
cnf(c_122,plain,
compose(compose(b,g),codomain(g)) = compose(b,compose(g,codomain(g))),
inference(resolve,[status(thm)],[c_120,c_121]) ).
cnf(c_55,plain,
compose(compose(b,g),codomain(g)) = compose(b,g),
inference(paramod,[status(thm)],[c_4,c_122]) ).
cnf(c_123,plain,
codomain(b) = domain(g),
inference(copy,[status(thm)],[c_48]) ).
cnf(c_56,plain,
codomain(compose(b,g)) = codomain(g),
inference(resolve,[status(thm)],[c_6,c_123]) ).
cnf(c_124,plain,
codomain(b) = domain(g),
inference(copy,[status(thm)],[c_48]) ).
cnf(c_125,plain,
domain(compose(b,g)) = domain(b),
inference(resolve,[status(thm)],[c_5,c_124]) ).
cnf(c_57,plain,
domain(compose(b,g)) = codomain(a),
inference(paramod,[status(thm)],[c_14,c_125]) ).
cnf(c_65,plain,
compose(compose(a,b),h) = compose(a,compose(b,g)),
inference(paramod,[status(thm)],[c_54,c_19]) ).
cnf(c_126,plain,
codomain(a) = domain(b),
inference(copy,[status(thm)],[c_14]) ).
cnf(c_127,plain,
( compose(compose(a,b),A) = compose(a,compose(b,A))
| codomain(b) != domain(A) ),
inference(resolve,[status(thm)],[c_8,c_126]) ).
cnf(c_128,plain,
codomain(b) = domain(h),
inference(copy,[status(thm)],[c_49]) ).
cnf(c_129,plain,
compose(compose(a,b),h) = compose(a,compose(b,h)),
inference(resolve,[status(thm)],[c_127,c_128]) ).
cnf(c_130,plain,
compose(a,compose(b,g)) = compose(a,compose(b,h)),
inference(paramod,[status(thm)],[c_65,c_129]) ).
cnf(c_67,plain,
compose(a,compose(b,h)) = compose(a,compose(b,g)),
inference(copy,[status(thm)],[c_130]) ).
cnf(c_131,plain,
codomain(b) = domain(h),
inference(copy,[status(thm)],[c_49]) ).
cnf(c_132,plain,
( compose(compose(b,h),A) = compose(b,compose(h,A))
| codomain(h) != domain(A) ),
inference(resolve,[status(thm)],[c_8,c_131]) ).
cnf(c_133,plain,
codomain(A) = domain(codomain(A)),
inference(copy,[status(thm)],[c_2]) ).
cnf(c_134,plain,
compose(compose(b,h),codomain(h)) = compose(b,compose(h,codomain(h))),
inference(resolve,[status(thm)],[c_132,c_133]) ).
cnf(c_68,plain,
compose(compose(b,h),codomain(h)) = compose(b,h),
inference(paramod,[status(thm)],[c_4,c_134]) ).
cnf(c_135,plain,
codomain(b) = domain(h),
inference(copy,[status(thm)],[c_49]) ).
cnf(c_69,plain,
codomain(compose(b,h)) = codomain(h),
inference(resolve,[status(thm)],[c_6,c_135]) ).
cnf(c_136,plain,
codomain(b) = domain(h),
inference(copy,[status(thm)],[c_49]) ).
cnf(c_137,plain,
domain(compose(b,h)) = domain(b),
inference(resolve,[status(thm)],[c_5,c_136]) ).
cnf(c_70,plain,
domain(compose(b,h)) = codomain(a),
inference(paramod,[status(thm)],[c_14,c_137]) ).
cnf(c_138,plain,
( g = B
| compose(b,B) != A
| domain(B) != codomain(b)
| compose(b,g) != A ),
inference(resolve,[status(thm)],[c_12,c_48]) ).
cnf(c_139,plain,
( g = h
| compose(b,h) != A
| compose(b,g) != A ),
inference(resolve,[status(thm)],[c_138,c_49]) ).
cnf(c_140,plain,
A = compose(A,codomain(A)),
inference(copy,[status(thm)],[c_4]) ).
cnf(c_141,plain,
( g = h
| compose(b,g) != compose(compose(b,h),codomain(compose(b,h))) ),
inference(resolve,[status(thm)],[c_139,c_140]) ).
cnf(c_142,plain,
g != h,
inference(copy,[status(thm)],[c_20]) ).
cnf(c_143,plain,
compose(b,g) != compose(compose(b,h),codomain(compose(b,h))),
inference(resolve,[status(thm)],[c_141,c_142]) ).
cnf(c_144,plain,
compose(b,g) != compose(compose(b,h),codomain(h)),
inference(paramod,[status(thm)],[c_69,c_143]) ).
cnf(c_145,plain,
compose(b,g) != compose(b,h),
inference(paramod,[status(thm)],[c_68,c_144]) ).
cnf(c_71,plain,
compose(b,h) != compose(b,g),
inference(copy,[status(thm)],[c_145]) ).
cnf(c_146,plain,
codomain(a) = domain(compose(b,g)),
inference(copy,[status(thm)],[c_57]) ).
cnf(c_147,plain,
( compose(compose(a,compose(b,g)),A) = compose(a,compose(compose(b,g),A))
| codomain(compose(b,g)) != domain(A) ),
inference(resolve,[status(thm)],[c_8,c_146]) ).
cnf(c_148,plain,
codomain(A) = domain(codomain(A)),
inference(copy,[status(thm)],[c_2]) ).
cnf(c_149,plain,
compose(compose(a,compose(b,g)),codomain(compose(b,g))) = compose(a,compose(compose(b,g),codomain(compose(b,g)))),
inference(resolve,[status(thm)],[c_147,c_148]) ).
cnf(c_150,plain,
compose(compose(a,compose(b,g)),codomain(g)) = compose(a,compose(compose(b,g),codomain(compose(b,g)))),
inference(paramod,[status(thm)],[c_56,c_149]) ).
cnf(c_151,plain,
compose(compose(a,compose(b,g)),codomain(g)) = compose(a,compose(compose(b,g),codomain(g))),
inference(paramod,[status(thm)],[c_56,c_150]) ).
cnf(c_98,plain,
compose(compose(a,compose(b,g)),codomain(g)) = compose(a,compose(b,g)),
inference(paramod,[status(thm)],[c_55,c_151]) ).
cnf(c_152,plain,
codomain(a) = domain(compose(b,g)),
inference(copy,[status(thm)],[c_57]) ).
cnf(c_153,plain,
codomain(compose(a,compose(b,g))) = codomain(compose(b,g)),
inference(resolve,[status(thm)],[c_6,c_152]) ).
cnf(c_99,plain,
codomain(compose(a,compose(b,g))) = codomain(g),
inference(paramod,[status(thm)],[c_56,c_153]) ).
cnf(c_154,plain,
( compose(b,g) = B
| compose(a,B) != A
| domain(B) != codomain(a)
| compose(a,compose(b,g)) != A ),
inference(resolve,[status(thm)],[c_10,c_57]) ).
cnf(c_155,plain,
( compose(b,g) = compose(b,h)
| compose(a,compose(b,h)) != A
| compose(a,compose(b,g)) != A ),
inference(resolve,[status(thm)],[c_154,c_70]) ).
cnf(c_156,plain,
A = compose(A,codomain(A)),
inference(copy,[status(thm)],[c_4]) ).
cnf(c_157,plain,
( compose(b,g) = compose(b,h)
| compose(a,compose(b,g)) != compose(compose(a,compose(b,h)),codomain(compose(a,compose(b,h)))) ),
inference(resolve,[status(thm)],[c_155,c_156]) ).
cnf(c_158,plain,
compose(b,g) != compose(b,h),
inference(copy,[status(thm)],[c_71]) ).
cnf(c_159,plain,
compose(a,compose(b,g)) != compose(compose(a,compose(b,h)),codomain(compose(a,compose(b,h)))),
inference(resolve,[status(thm)],[c_157,c_158]) ).
cnf(c_160,plain,
compose(a,compose(b,g)) != compose(compose(a,compose(b,g)),codomain(compose(a,compose(b,h)))),
inference(paramod,[status(thm)],[c_67,c_159]) ).
cnf(c_161,plain,
compose(a,compose(b,g)) != compose(compose(a,compose(b,g)),codomain(compose(a,compose(b,g)))),
inference(paramod,[status(thm)],[c_67,c_160]) ).
cnf(c_162,plain,
compose(a,compose(b,g)) != compose(compose(a,compose(b,g)),codomain(g)),
inference(paramod,[status(thm)],[c_99,c_161]) ).
cnf(c_163,plain,
compose(a,compose(b,g)) != compose(a,compose(b,g)),
inference(paramod,[status(thm)],[c_98,c_162]) ).
cnf(c_112,plain,
$false,
inference(copy,[status(thm)],[c_163]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : CAT004-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n001.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Sat Sep 26 22:54:28 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 2869014 was started by sandbox on n001,
% 0.09/0.35 % Sat Sep 26 22:54:28 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.35
% 0.09/0.35 % From the command line: assign(max_seconds, 300).
% 0.12/0.38
% 0.12/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.38
% 0.12/0.38 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.12/0.38 % Length of proof is 34.
% 0.12/0.38 % Level of proof is 7.
% 0.12/0.38 % Maximum clause weight is 23.000.
% 0.12/0.38 % Given clauses 28.
% 0.12/0.38
% 0.12/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------