%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : CAT003-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 06:55:54 AM UTC 2026
% Result : Unsatisfiable 0.13s 10.46s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 42 ( 28 unt; 0 def)
% Number of atoms : 74 ( 73 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 67 ( 35 ~; 32 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 3 ( 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 : 30 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(endomorphism,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_0 = VAR_2
| compose(compose(a,b),VAR_2) != VAR_1
| codomain(compose(a,b)) != domain(VAR_2)
| compose(compose(a,b),VAR_0) != VAR_1
| codomain(compose(a,b)) != domain(VAR_0) ),
file('theBenchmark.p',endomorphism) ).
cnf(c_9,plain,
( A = C
| compose(compose(a,b),C) != B
| codomain(compose(a,b)) != domain(C)
| compose(compose(a,b),A) != B
| codomain(compose(a,b)) != domain(A) ),
inference(clausify,[status(thm)],[endomorphism]) ).
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_10,plain,
codomain(a) = domain(b),
inference(clausify,[status(thm)],[codomain_of_a_equals_domain_of_b]) ).
cnf(c_11,plain,
domain(b) = codomain(a),
inference(copy,[status(thm)],[c_10]) ).
fof(codomain_of_b_equals_domain_of_h,axiom,
codomain(b) = domain(h),
file('theBenchmark.p',codomain_of_b_equals_domain_of_h) ).
cnf(c_12,plain,
codomain(b) = domain(h),
inference(clausify,[status(thm)],[codomain_of_b_equals_domain_of_h]) ).
cnf(c_13,plain,
domain(h) = codomain(b),
inference(copy,[status(thm)],[c_12]) ).
fof(codomain_of_b_equals_domain_of_g,axiom,
codomain(b) = domain(g),
file('theBenchmark.p',codomain_of_b_equals_domain_of_g) ).
cnf(c_14,plain,
codomain(b) = domain(g),
inference(clausify,[status(thm)],[codomain_of_b_equals_domain_of_g]) ).
cnf(c_15,plain,
domain(g) = codomain(b),
inference(copy,[status(thm)],[c_14]) ).
fof(bh_equals_bg,axiom,
compose(b,h) = compose(b,g),
file('theBenchmark.p',bh_equals_bg) ).
cnf(c_16,plain,
compose(b,h) = compose(b,g),
inference(clausify,[status(thm)],[bh_equals_bg]) ).
fof(prove_g_equals_h,axiom,
g != h,
file('theBenchmark.p',prove_g_equals_h) ).
cnf(c_17,plain,
g != h,
inference(clausify,[status(thm)],[prove_g_equals_h]) ).
cnf(c_18,plain,
h != g,
inference(copy,[status(thm)],[c_17]) ).
cnf(c_47,plain,
codomain(a) = domain(b),
inference(copy,[status(thm)],[c_11]) ).
cnf(c_26,plain,
codomain(compose(a,b)) = codomain(b),
inference(resolve,[status(thm)],[c_6,c_47]) ).
cnf(c_48,plain,
( A = C
| compose(compose(a,b),C) != B
| codomain(compose(a,b)) != domain(C)
| compose(compose(a,b),A) != B
| codomain(b) != domain(A) ),
inference(paramod,[status(thm)],[c_26,c_9]) ).
cnf(c_29,plain,
( A = C
| compose(compose(a,b),C) != B
| codomain(b) != domain(C)
| compose(compose(a,b),A) != B
| codomain(b) != domain(A) ),
inference(paramod,[status(thm)],[c_26,c_48]) ).
cnf(c_49,plain,
codomain(a) = domain(b),
inference(copy,[status(thm)],[c_11]) ).
cnf(c_50,plain,
( compose(compose(a,b),A) = compose(a,compose(b,A))
| codomain(b) != domain(A) ),
inference(resolve,[status(thm)],[c_8,c_49]) ).
cnf(c_51,plain,
codomain(b) = domain(h),
inference(copy,[status(thm)],[c_13]) ).
cnf(c_52,plain,
compose(compose(a,b),h) = compose(a,compose(b,h)),
inference(resolve,[status(thm)],[c_50,c_51]) ).
cnf(c_31,plain,
compose(compose(a,b),h) = compose(a,compose(b,g)),
inference(paramod,[status(thm)],[c_16,c_52]) ).
cnf(c_53,plain,
codomain(a) = domain(b),
inference(copy,[status(thm)],[c_11]) ).
cnf(c_54,plain,
( compose(compose(a,b),A) = compose(a,compose(b,A))
| codomain(b) != domain(A) ),
inference(resolve,[status(thm)],[c_8,c_53]) ).
cnf(c_55,plain,
codomain(b) = domain(g),
inference(copy,[status(thm)],[c_15]) ).
cnf(c_36,plain,
compose(compose(a,b),g) = compose(a,compose(b,g)),
inference(resolve,[status(thm)],[c_54,c_55]) ).
cnf(c_56,plain,
codomain(b) = domain(g),
inference(copy,[status(thm)],[c_15]) ).
cnf(c_57,plain,
( g = B
| compose(compose(a,b),B) != A
| codomain(b) != domain(B)
| compose(compose(a,b),g) != A ),
inference(resolve,[status(thm)],[c_29,c_56]) ).
cnf(c_58,plain,
( g = A
| compose(compose(a,b),A) != compose(a,compose(b,g))
| codomain(b) != domain(A) ),
inference(resolve,[status(thm)],[c_57,c_36]) ).
cnf(c_59,plain,
codomain(b) = domain(h),
inference(copy,[status(thm)],[c_13]) ).
cnf(c_60,plain,
( g = h
| compose(compose(a,b),h) != compose(a,compose(b,g)) ),
inference(resolve,[status(thm)],[c_58,c_59]) ).
cnf(c_61,plain,
g = h,
inference(resolve,[status(thm)],[c_60,c_31]) ).
cnf(c_62,plain,
h = g,
inference(copy,[status(thm)],[c_61]) ).
cnf(c_46,plain,
$false,
inference(resolve,[status(thm)],[c_18,c_62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT003-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/10.41 % Computer : n010.cluster.edu
% 0.13/10.41 % Model : x86_64 x86_64
% 0.13/10.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/10.41 % Memory : 8046.5625MB
% 0.13/10.41 % OS : Linux 6.8.0-71-generic
% 0.13/10.42 % CPULimit : 300
% 0.13/10.42 % WCLimit : 300
% 0.13/10.42 % DateTime : Sat Sep 26 22:48:47 UTC 2026
% 0.13/10.42 % CPUTime :
% 0.13/10.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/10.42 % Process 217419 was started by sandbox2 on n010,
% 0.13/10.42 % Sat Sep 26 22:48:47 2026
% 0.13/10.42 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/10.43
% 0.13/10.43 % From the command line: assign(max_seconds, 300).
% 0.13/10.46
% 0.13/10.46 % SZS status Unsatisfiable for theBenchmark
% 0.13/10.46
% 0.13/10.46 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.13/10.46 % Length of proof is 18.
% 0.13/10.46 % Level of proof is 4.
% 0.13/10.46 % Maximum clause weight is 50.000.
% 0.13/10.46 % Given clauses 36.
% 0.13/10.46
% 0.13/10.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------