%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU008+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 : 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 08:44:53 AM UTC 2026
% Result : Theorem 243.31s 32.26s
% Output : CNFRefutation 243.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 42 ( 16 unt; 0 def)
% Number of atoms : 111 ( 38 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 116 ( 47 ~; 43 |; 14 &)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 69 ( 5 sgn 20 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d3_xboole_0,axiom,
! [A,B,C] :
( C = set_intersection2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
& in(D,A) ) ) ),
file('theBenchmark.p',d3_xboole_0) ).
fof(dt_k6_relat_1,axiom,
! [A] : relation(identity_relation(A)),
file('theBenchmark.p',dt_k6_relat_1) ).
fof(fc2_funct_1,axiom,
! [A] :
( function(identity_relation(A))
& relation(identity_relation(A)) ),
file('theBenchmark.p',fc2_funct_1) ).
fof(idempotence_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,A) = A,
file('theBenchmark.p',idempotence_k3_xboole_0) ).
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(t34_funct_1,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( B = identity_relation(A)
<=> ( ! [C] :
( in(C,A)
=> apply(B,C) = C )
& relation_dom(B) = A ) ) ),
file('theBenchmark.p',t34_funct_1) ).
fof(t38_funct_1,conjecture,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,set_intersection2(relation_dom(C),A))
=> apply(C,B) = apply(relation_composition(identity_relation(A),C),B) ) ),
file('theBenchmark.p',t38_funct_1) ).
fof(t38_funct_1_neg,negated_conjecture,
~ ! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,set_intersection2(relation_dom(C),A))
=> apply(C,B) = apply(relation_composition(identity_relation(A),C),B) ) ),
inference(assume_negation,[status(cth)],[t38_funct_1]) ).
cnf(c_50,plain,
( in(D,B)
| ~ in(D,C)
| set_intersection2(A,B) != C ),
inference(clausify,[status(thm)],[d3_xboole_0]) ).
cnf(c_56,plain,
relation(identity_relation(A)),
inference(clausify,[status(thm)],[dt_k6_relat_1]) ).
cnf(c_65,plain,
function(identity_relation(A)),
inference(clausify,[status(thm)],[fc2_funct_1]) ).
cnf(c_71,plain,
set_intersection2(A,A) = A,
inference(clausify,[status(thm)],[idempotence_k3_xboole_0]) ).
cnf(c_86,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_89,plain,
( relation_dom(A) = B
| identity_relation(B) != A
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t34_funct_1]) ).
cnf(c_90,plain,
( apply(A,C) = C
| ~ in(C,B)
| identity_relation(B) != A
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t34_funct_1]) ).
fof(nnf_40,plain,
? [A,B,C] :
( apply(relation_composition(identity_relation(A),C),B) != apply(C,B)
& in(B,set_intersection2(relation_dom(C),A))
& function(C)
& relation(C) ),
inference(fof_nnf,[status(thm)],[t38_funct_1_neg]) ).
fof(sk_t38_funct_1_neg,plain,
( apply(relation_composition(identity_relation(sK2),sK0),sK1) != apply(sK0,sK1)
& in(sK1,set_intersection2(relation_dom(sK0),sK2))
& function(sK0)
& relation(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(A,sK2),skolemize(B,sK1),skolemize(C,sK0)],[nnf_40]) ).
cnf(c_98,negated_conjecture,
relation(sK0),
inference(split_conjunct,[status(thm)],[sk_t38_funct_1_neg]) ).
cnf(c_99,negated_conjecture,
function(sK0),
inference(split_conjunct,[status(thm)],[sk_t38_funct_1_neg]) ).
cnf(c_100,negated_conjecture,
in(sK1,set_intersection2(relation_dom(sK0),sK2)),
inference(split_conjunct,[status(thm)],[sk_t38_funct_1_neg]) ).
cnf(c_101,negated_conjecture,
apply(relation_composition(identity_relation(sK2),sK0),sK1) != apply(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_t38_funct_1_neg]) ).
cnf(c_12588,plain,
( apply(relation_composition(identity_relation(A),B),C) = apply(B,apply(identity_relation(A),C))
| ~ in(C,relation_dom(identity_relation(A)))
| ~ function(B)
| ~ relation(B)
| ~ function(identity_relation(A)) ),
inference(resolve,[status(thm)],[c_86,c_56]) ).
cnf(c_408,plain,
( apply(relation_composition(identity_relation(C),A),B) = apply(A,apply(identity_relation(C),B))
| ~ in(B,relation_dom(identity_relation(C)))
| ~ function(A)
| ~ relation(A) ),
inference(resolve,[status(thm)],[c_65,c_12588]) ).
cnf(c_12589,plain,
A = set_intersection2(A,A),
inference(copy,[status(thm)],[c_71]) ).
cnf(c_12590,plain,
( relation_dom(set_intersection2(identity_relation(A),identity_relation(A))) = A
| ~ function(set_intersection2(identity_relation(A),identity_relation(A)))
| ~ relation(set_intersection2(identity_relation(A),identity_relation(A))) ),
inference(resolve,[status(thm)],[c_89,c_12589]) ).
cnf(c_12591,plain,
( relation_dom(set_intersection2(identity_relation(A),identity_relation(A))) = A
| ~ function(set_intersection2(identity_relation(A),identity_relation(A)))
| ~ relation(identity_relation(A)) ),
inference(paramod,[status(thm)],[c_71,c_12590]) ).
cnf(c_12592,plain,
( relation_dom(set_intersection2(identity_relation(A),identity_relation(A))) = A
| ~ function(identity_relation(A))
| ~ relation(identity_relation(A)) ),
inference(paramod,[status(thm)],[c_71,c_12591]) ).
cnf(c_12593,plain,
( relation_dom(identity_relation(A)) = A
| ~ function(identity_relation(A))
| ~ relation(identity_relation(A)) ),
inference(paramod,[status(thm)],[c_71,c_12592]) ).
cnf(c_12594,plain,
( relation_dom(identity_relation(A)) = A
| ~ function(identity_relation(A)) ),
inference(resolve,[status(thm)],[c_56,c_12593]) ).
cnf(c_439,plain,
relation_dom(identity_relation(A)) = A,
inference(resolve,[status(thm)],[c_65,c_12594]) ).
cnf(c_441,plain,
( apply(relation_composition(identity_relation(C),A),B) = apply(A,apply(identity_relation(C),B))
| ~ in(B,C)
| ~ function(A)
| ~ relation(A) ),
inference(paramod,[status(thm)],[c_439,c_408]) ).
cnf(c_12595,plain,
( in(A,C)
| ~ in(A,set_intersection2(B,C)) ),
inference(xxres,[status(thm)],[c_50]) ).
cnf(c_623,negated_conjecture,
in(sK1,sK2),
inference(resolve,[status(thm)],[c_12595,c_100]) ).
cnf(c_12596,plain,
( apply(identity_relation(A),C) = C
| ~ in(C,B)
| identity_relation(B) != identity_relation(A)
| ~ function(identity_relation(A)) ),
inference(resolve,[status(thm)],[c_90,c_56]) ).
cnf(c_12597,plain,
( apply(identity_relation(B),C) = C
| ~ in(C,A)
| identity_relation(A) != identity_relation(B) ),
inference(resolve,[status(thm)],[c_12596,c_65]) ).
cnf(c_12598,plain,
( apply(identity_relation(B),A) = A
| ~ in(A,B) ),
inference(xxres,[status(thm)],[c_12597]) ).
cnf(c_782,plain,
apply(identity_relation(sK2),sK1) = sK1,
inference(resolve,[status(thm)],[c_12598,c_623]) ).
cnf(c_12599,negated_conjecture,
( apply(relation_composition(identity_relation(B),sK0),A) = apply(sK0,apply(identity_relation(B),A))
| ~ in(A,B)
| ~ function(sK0) ),
inference(resolve,[status(thm)],[c_441,c_98]) ).
cnf(c_12600,negated_conjecture,
( apply(relation_composition(identity_relation(B),sK0),A) = apply(sK0,apply(identity_relation(B),A))
| ~ in(A,B) ),
inference(resolve,[status(thm)],[c_12599,c_99]) ).
cnf(c_12601,negated_conjecture,
apply(relation_composition(identity_relation(sK2),sK0),sK1) = apply(sK0,apply(identity_relation(sK2),sK1)),
inference(resolve,[status(thm)],[c_12600,c_623]) ).
cnf(c_12602,negated_conjecture,
apply(relation_composition(identity_relation(sK2),sK0),sK1) = apply(sK0,sK1),
inference(paramod,[status(thm)],[c_782,c_12601]) ).
cnf(c_12587,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_101,c_12602]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU008+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n010.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sat Sep 26 08:31:00 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.36 % Process 2911251 was started by sandbox on n010,
% 0.13/0.36 % Sat Sep 26 08:31:00 2026
% 0.13/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 243.31/32.26
% 243.31/32.26 % SZS status Theorem for theBenchmark
% 243.31/32.26
% 243.31/32.26 % Proof 1 at 5.94 (+ 1.77) seconds.
% 243.31/32.26 % Length of proof is 24.
% 243.31/32.26 % Level of proof is 4.
% 243.31/32.26 % Maximum clause weight is 25.000.
% 243.31/32.26 % Given clauses 491.
% 243.31/32.26
% 243.31/32.26 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------