%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU014+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 08:44:54 AM UTC 2026
% Result : Theorem 2.54s 0.73s
% Output : CNFRefutation 2.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 71 ( 21 unt; 0 def)
% Number of atoms : 261 ( 59 equ)
% Maximal formula atoms : 23 ( 3 avg)
% Number of connectives : 319 ( 129 ~; 133 |; 40 &)
% ( 1 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 75 ( 0 sgn 29 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d8_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
<=> ! [B,C] :
( ( apply(A,B) = apply(A,C)
& in(C,relation_dom(A))
& in(B,relation_dom(A)) )
=> B = C ) ) ),
file('theBenchmark.p',d8_funct_1) ).
fof(dt_k5_relat_1,axiom,
! [A,B] :
( ( relation(B)
& relation(A) )
=> relation(relation_composition(A,B)) ),
file('theBenchmark.p',dt_k5_relat_1) ).
fof(fc1_funct_1,axiom,
! [A,B] :
( ( function(B)
& relation(B)
& function(A)
& relation(A) )
=> ( function(relation_composition(A,B))
& relation(relation_composition(A,B)) ) ),
file('theBenchmark.p',fc1_funct_1) ).
fof(t23_funct_1,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( in(A,relation_dom(B))
=> apply(relation_composition(B,C),A) = apply(C,apply(B,A)) ) ) ),
file('theBenchmark.p',t23_funct_1) ).
fof(t46_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( subset(relation_rng(A),relation_dom(B))
=> relation_dom(relation_composition(A,B)) = relation_dom(A) ) ) ),
file('theBenchmark.p',t46_relat_1) ).
fof(t47_funct_1,conjecture,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B] :
( ( function(B)
& relation(B) )
=> ( ( subset(relation_rng(B),relation_dom(A))
& one_to_one(relation_composition(B,A)) )
=> one_to_one(B) ) ) ),
file('theBenchmark.p',t47_funct_1) ).
fof(t47_funct_1_neg,negated_conjecture,
~ ! [A] :
( ( function(A)
& relation(A) )
=> ! [B] :
( ( function(B)
& relation(B) )
=> ( ( subset(relation_rng(B),relation_dom(A))
& one_to_one(relation_composition(B,A)) )
=> one_to_one(B) ) ) ),
inference(assume_negation,[status(cth)],[t47_funct_1]) ).
fof(nnf_36,plain,
? [A] :
( ? [B] :
( ~ one_to_one(B)
& subset(relation_rng(B),relation_dom(A))
& one_to_one(relation_composition(B,A))
& function(B)
& relation(B) )
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[t47_funct_1_neg]) ).
fof(sk_t47_funct_1_neg,plain,
( ~ one_to_one(sK0)
& subset(relation_rng(sK0),relation_dom(sK1))
& one_to_one(relation_composition(sK0,sK1))
& function(sK0)
& relation(sK0)
& function(sK1)
& relation(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0]),skolemize(A,sK1),skolemize(B,sK0)],[nnf_36]) ).
cnf(c_37,negated_conjecture,
~ one_to_one(sK0),
inference(split_conjunct,[status(thm)],[sk_t47_funct_1_neg]) ).
cnf(c_38,negated_conjecture,
subset(relation_rng(sK0),relation_dom(sK1)),
inference(split_conjunct,[status(thm)],[sk_t47_funct_1_neg]) ).
cnf(c_39,negated_conjecture,
one_to_one(relation_composition(sK0,sK1)),
inference(split_conjunct,[status(thm)],[sk_t47_funct_1_neg]) ).
cnf(c_40,negated_conjecture,
function(sK0),
inference(split_conjunct,[status(thm)],[sk_t47_funct_1_neg]) ).
cnf(c_41,negated_conjecture,
relation(sK0),
inference(split_conjunct,[status(thm)],[sk_t47_funct_1_neg]) ).
cnf(c_42,negated_conjecture,
function(sK1),
inference(split_conjunct,[status(thm)],[sk_t47_funct_1_neg]) ).
cnf(c_43,negated_conjecture,
relation(sK1),
inference(split_conjunct,[status(thm)],[sk_t47_funct_1_neg]) ).
cnf(c_49,plain,
( relation_dom(relation_composition(A,B)) = relation_dom(A)
| ~ subset(relation_rng(A),relation_dom(B))
| ~ relation(B)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t46_relat_1]) ).
cnf(c_53,plain,
( apply(relation_composition(A,B),C) = apply(B,apply(A,C))
| ~ in(C,relation_dom(A))
| ~ function(B)
| ~ relation(B)
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t23_funct_1]) ).
cnf(c_80,plain,
( function(relation_composition(A,B))
| ~ function(B)
| ~ relation(B)
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[fc1_funct_1]) ).
cnf(c_85,plain,
( relation(relation_composition(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(clausify,[status(thm)],[dt_k5_relat_1]) ).
fof(nnf_4,plain,
! [A] :
( ( ( ? [B,C] :
( C != B
& apply(A,C) = apply(A,B)
& in(C,relation_dom(A))
& in(B,relation_dom(A)) )
| one_to_one(A) )
& ( ! [X0,X1] :
( X1 = X0
| apply(A,X1) != apply(A,X0)
| ~ in(X1,relation_dom(A))
| ~ in(X0,relation_dom(A)) )
| ~ one_to_one(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d8_funct_1]) ).
fof(sk_d8_funct_1_sk,plain,
! [A] :
( ( ( ( sK2(A) != sK3(A)
& apply(A,sK2(A)) = apply(A,sK3(A))
& in(sK2(A),relation_dom(A))
& in(sK3(A),relation_dom(A)) )
| one_to_one(A) )
& ( ! [X0,X1] :
( X1 = X0
| apply(A,X1) != apply(A,X0)
| ~ in(X1,relation_dom(A))
| ~ in(X0,relation_dom(A)) )
| ~ one_to_one(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK2]),skolemize(B,sK3(A)),skolemize(C,sK2(A))],[nnf_4]) ).
fof(sk_d8_funct_1,plain,
( ! [VAR_0] :
( sK2(VAR_0) != sK3(VAR_0)
| one_to_one(VAR_0)
| ~ function(VAR_0)
| ~ relation(VAR_0) )
& ! [VAR_0] :
( apply(VAR_0,sK2(VAR_0)) = apply(VAR_0,sK3(VAR_0))
| one_to_one(VAR_0)
| ~ function(VAR_0)
| ~ relation(VAR_0) )
& ! [VAR_0] :
( in(sK2(VAR_0),relation_dom(VAR_0))
| one_to_one(VAR_0)
| ~ function(VAR_0)
| ~ relation(VAR_0) )
& ! [VAR_0] :
( in(sK3(VAR_0),relation_dom(VAR_0))
| one_to_one(VAR_0)
| ~ function(VAR_0)
| ~ relation(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( VAR_2 = VAR_1
| apply(VAR_0,VAR_2) != apply(VAR_0,VAR_1)
| ~ in(VAR_2,relation_dom(VAR_0))
| ~ in(VAR_1,relation_dom(VAR_0))
| ~ one_to_one(VAR_0)
| ~ function(VAR_0)
| ~ relation(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_d8_funct_1_sk]) ).
cnf(c_86,plain,
( sK2(A) != sK3(A)
| one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(split_conjunct,[status(thm)],[sk_d8_funct_1]) ).
cnf(c_87,plain,
( apply(A,sK2(A)) = apply(A,sK3(A))
| one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(split_conjunct,[status(thm)],[sk_d8_funct_1]) ).
cnf(c_88,plain,
( in(sK2(A),relation_dom(A))
| one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(split_conjunct,[status(thm)],[sk_d8_funct_1]) ).
cnf(c_89,plain,
( in(sK3(A),relation_dom(A))
| one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(split_conjunct,[status(thm)],[sk_d8_funct_1]) ).
cnf(c_90,plain,
( C = B
| apply(A,C) != apply(A,B)
| ~ in(C,relation_dom(A))
| ~ in(B,relation_dom(A))
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(split_conjunct,[status(thm)],[sk_d8_funct_1]) ).
cnf(c_2273,negated_conjecture,
( relation_dom(relation_composition(sK0,sK1)) = relation_dom(sK0)
| ~ relation(sK1)
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_49,c_38]) ).
cnf(c_2274,negated_conjecture,
( relation_dom(relation_composition(sK0,sK1)) = relation_dom(sK0)
| ~ relation(sK1) ),
inference(resolve,[status(thm)],[c_41,c_2273]) ).
cnf(c_100,negated_conjecture,
relation_dom(relation_composition(sK0,sK1)) = relation_dom(sK0),
inference(resolve,[status(thm)],[c_43,c_2274]) ).
cnf(c_2275,negated_conjecture,
( function(relation_composition(sK0,A))
| ~ function(A)
| ~ relation(A)
| ~ function(sK0) ),
inference(resolve,[status(thm)],[c_80,c_41]) ).
cnf(c_2276,negated_conjecture,
( function(relation_composition(sK0,A))
| ~ function(A)
| ~ relation(A) ),
inference(resolve,[status(thm)],[c_2275,c_40]) ).
cnf(c_2277,negated_conjecture,
( function(relation_composition(sK0,sK1))
| ~ function(sK1) ),
inference(resolve,[status(thm)],[c_2276,c_43]) ).
cnf(c_146,negated_conjecture,
function(relation_composition(sK0,sK1)),
inference(resolve,[status(thm)],[c_2277,c_42]) ).
cnf(c_2278,negated_conjecture,
( relation(relation_composition(sK0,A))
| ~ relation(A) ),
inference(resolve,[status(thm)],[c_85,c_41]) ).
cnf(c_196,negated_conjecture,
relation(relation_composition(sK0,sK1)),
inference(resolve,[status(thm)],[c_2278,c_43]) ).
cnf(c_2279,negated_conjecture,
( sK2(sK0) != sK3(sK0)
| one_to_one(sK0)
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_86,c_40]) ).
cnf(c_2280,negated_conjecture,
( sK2(sK0) != sK3(sK0)
| one_to_one(sK0) ),
inference(resolve,[status(thm)],[c_41,c_2279]) ).
cnf(c_200,negated_conjecture,
sK2(sK0) != sK3(sK0),
inference(resolve,[status(thm)],[c_37,c_2280]) ).
cnf(c_2281,negated_conjecture,
( apply(sK0,sK2(sK0)) = apply(sK0,sK3(sK0))
| one_to_one(sK0)
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_87,c_40]) ).
cnf(c_2282,negated_conjecture,
( apply(sK0,sK2(sK0)) = apply(sK0,sK3(sK0))
| one_to_one(sK0) ),
inference(resolve,[status(thm)],[c_41,c_2281]) ).
cnf(c_203,negated_conjecture,
apply(sK0,sK2(sK0)) = apply(sK0,sK3(sK0)),
inference(resolve,[status(thm)],[c_37,c_2282]) ).
cnf(c_2283,negated_conjecture,
( in(sK2(sK0),relation_dom(sK0))
| one_to_one(sK0)
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_88,c_40]) ).
cnf(c_2284,negated_conjecture,
( in(sK2(sK0),relation_dom(sK0))
| one_to_one(sK0) ),
inference(resolve,[status(thm)],[c_41,c_2283]) ).
cnf(c_206,negated_conjecture,
in(sK2(sK0),relation_dom(sK0)),
inference(resolve,[status(thm)],[c_37,c_2284]) ).
cnf(c_2285,negated_conjecture,
( in(sK3(sK0),relation_dom(sK0))
| one_to_one(sK0)
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_89,c_40]) ).
cnf(c_2286,negated_conjecture,
( in(sK3(sK0),relation_dom(sK0))
| one_to_one(sK0) ),
inference(resolve,[status(thm)],[c_41,c_2285]) ).
cnf(c_209,negated_conjecture,
in(sK3(sK0),relation_dom(sK0)),
inference(resolve,[status(thm)],[c_37,c_2286]) ).
cnf(c_2287,plain,
( B = A
| apply(relation_composition(sK0,sK1),B) != apply(relation_composition(sK0,sK1),A)
| ~ in(B,relation_dom(relation_composition(sK0,sK1)))
| ~ in(A,relation_dom(sK0))
| ~ one_to_one(relation_composition(sK0,sK1))
| ~ function(relation_composition(sK0,sK1))
| ~ relation(relation_composition(sK0,sK1)) ),
inference(paramod,[status(thm)],[c_100,c_90]) ).
cnf(c_2288,plain,
( B = A
| apply(relation_composition(sK0,sK1),B) != apply(relation_composition(sK0,sK1),A)
| ~ in(B,relation_dom(sK0))
| ~ in(A,relation_dom(sK0))
| ~ one_to_one(relation_composition(sK0,sK1))
| ~ function(relation_composition(sK0,sK1))
| ~ relation(relation_composition(sK0,sK1)) ),
inference(paramod,[status(thm)],[c_100,c_2287]) ).
cnf(c_2289,plain,
( B = A
| apply(relation_composition(sK0,sK1),B) != apply(relation_composition(sK0,sK1),A)
| ~ in(B,relation_dom(sK0))
| ~ in(A,relation_dom(sK0))
| ~ one_to_one(relation_composition(sK0,sK1))
| ~ function(relation_composition(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_196,c_2288]) ).
cnf(c_2290,plain,
( B = A
| apply(relation_composition(sK0,sK1),B) != apply(relation_composition(sK0,sK1),A)
| ~ in(B,relation_dom(sK0))
| ~ in(A,relation_dom(sK0))
| ~ one_to_one(relation_composition(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_146,c_2289]) ).
cnf(c_217,negated_conjecture,
( B = A
| apply(relation_composition(sK0,sK1),B) != apply(relation_composition(sK0,sK1),A)
| ~ in(B,relation_dom(sK0))
| ~ in(A,relation_dom(sK0)) ),
inference(resolve,[status(thm)],[c_39,c_2290]) ).
cnf(c_2291,negated_conjecture,
( apply(relation_composition(sK0,A),B) = apply(A,apply(sK0,B))
| ~ in(B,relation_dom(sK0))
| ~ function(A)
| ~ relation(A)
| ~ function(sK0) ),
inference(resolve,[status(thm)],[c_53,c_41]) ).
cnf(c_2292,negated_conjecture,
( apply(relation_composition(sK0,A),B) = apply(A,apply(sK0,B))
| ~ in(B,relation_dom(sK0))
| ~ function(A)
| ~ relation(A) ),
inference(resolve,[status(thm)],[c_2291,c_40]) ).
cnf(c_2293,negated_conjecture,
( apply(relation_composition(sK0,sK1),A) = apply(sK1,apply(sK0,A))
| ~ in(A,relation_dom(sK0))
| ~ function(sK1) ),
inference(resolve,[status(thm)],[c_2292,c_43]) ).
cnf(c_2294,negated_conjecture,
( apply(relation_composition(sK0,sK1),A) = apply(sK1,apply(sK0,A))
| ~ in(A,relation_dom(sK0)) ),
inference(resolve,[status(thm)],[c_2293,c_42]) ).
cnf(c_2295,negated_conjecture,
apply(relation_composition(sK0,sK1),sK2(sK0)) = apply(sK1,apply(sK0,sK2(sK0))),
inference(resolve,[status(thm)],[c_2294,c_206]) ).
cnf(c_1785,negated_conjecture,
apply(relation_composition(sK0,sK1),sK2(sK0)) = apply(sK1,apply(sK0,sK3(sK0))),
inference(paramod,[status(thm)],[c_203,c_2295]) ).
cnf(c_2296,negated_conjecture,
( apply(relation_composition(sK0,A),B) = apply(A,apply(sK0,B))
| ~ in(B,relation_dom(sK0))
| ~ function(A)
| ~ relation(A)
| ~ function(sK0) ),
inference(resolve,[status(thm)],[c_53,c_41]) ).
cnf(c_2297,negated_conjecture,
( apply(relation_composition(sK0,A),B) = apply(A,apply(sK0,B))
| ~ in(B,relation_dom(sK0))
| ~ function(A)
| ~ relation(A) ),
inference(resolve,[status(thm)],[c_2296,c_40]) ).
cnf(c_2298,negated_conjecture,
( apply(relation_composition(sK0,sK1),A) = apply(sK1,apply(sK0,A))
| ~ in(A,relation_dom(sK0))
| ~ function(sK1) ),
inference(resolve,[status(thm)],[c_2297,c_43]) ).
cnf(c_2299,negated_conjecture,
( apply(relation_composition(sK0,sK1),A) = apply(sK1,apply(sK0,A))
| ~ in(A,relation_dom(sK0)) ),
inference(resolve,[status(thm)],[c_2298,c_42]) ).
cnf(c_1803,negated_conjecture,
apply(relation_composition(sK0,sK1),sK3(sK0)) = apply(sK1,apply(sK0,sK3(sK0))),
inference(resolve,[status(thm)],[c_2299,c_209]) ).
cnf(c_2300,plain,
( A = sK3(sK0)
| apply(relation_composition(sK0,sK1),A) != apply(relation_composition(sK0,sK1),sK3(sK0))
| ~ in(A,relation_dom(sK0)) ),
inference(resolve,[status(thm)],[c_217,c_209]) ).
cnf(c_2301,plain,
( sK2(sK0) = sK3(sK0)
| apply(relation_composition(sK0,sK1),sK2(sK0)) != apply(relation_composition(sK0,sK1),sK3(sK0)) ),
inference(resolve,[status(thm)],[c_2300,c_206]) ).
cnf(c_2302,plain,
apply(relation_composition(sK0,sK1),sK2(sK0)) != apply(relation_composition(sK0,sK1),sK3(sK0)),
inference(resolve,[status(thm)],[c_2301,c_200]) ).
cnf(c_2303,plain,
apply(sK1,apply(sK0,sK3(sK0))) != apply(relation_composition(sK0,sK1),sK3(sK0)),
inference(paramod,[status(thm)],[c_1785,c_2302]) ).
cnf(c_2304,plain,
apply(sK1,apply(sK0,sK3(sK0))) != apply(sK1,apply(sK0,sK3(sK0))),
inference(paramod,[status(thm)],[c_1803,c_2303]) ).
cnf(c_2272,plain,
$false,
inference(copy,[status(thm)],[c_2304]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU014+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n002.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 08:33:52 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 1264135 was started by sandbox on n002,
% 0.10/0.37 % Sat Sep 26 08:33:52 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 2.54/0.73
% 2.54/0.73 % SZS status Theorem for theBenchmark
% 2.54/0.73
% 2.54/0.73 % Proof 1 at 0.24 (+ 0.10) seconds.
% 2.54/0.73 % Length of proof is 33.
% 2.54/0.73 % Level of proof is 4.
% 2.54/0.73 % Maximum clause weight is 43.000.
% 2.54/0.73 % Given clauses 303.
% 2.54/0.73
% 2.54/0.73 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------