%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU224+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 08:45:29 AM UTC 2026
% Result : Theorem 0.21s 0.96s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 51 ( 13 unt; 0 def)
% Number of atoms : 147 ( 30 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 157 ( 61 ~; 62 |; 22 &)
% ( 5 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 76 ( 17 sgn 20 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('theBenchmark.p',commutativity_k3_xboole_0) ).
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_k7_relat_1,axiom,
! [A,B] :
( relation(A)
=> relation(relation_dom_restriction(A,B)) ),
file('theBenchmark.p',dt_k7_relat_1) ).
fof(fc4_funct_1,axiom,
! [A,B] :
( ( function(A)
& relation(A) )
=> ( function(relation_dom_restriction(A,B))
& relation(relation_dom_restriction(A,B)) ) ),
file('theBenchmark.p',fc4_funct_1) ).
fof(t68_funct_1,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( B = relation_dom_restriction(C,A)
<=> ( ! [D] :
( in(D,relation_dom(B))
=> apply(B,D) = apply(C,D) )
& relation_dom(B) = set_intersection2(relation_dom(C),A) ) ) ) ),
file('theBenchmark.p',t68_funct_1) ).
fof(l82_funct_1,conjecture,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,relation_dom(relation_dom_restriction(C,A)))
<=> ( in(B,A)
& in(B,relation_dom(C)) ) ) ),
file('theBenchmark.p',l82_funct_1) ).
fof(l82_funct_1_neg,negated_conjecture,
~ ! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,relation_dom(relation_dom_restriction(C,A)))
<=> ( in(B,A)
& in(B,relation_dom(C)) ) ) ),
inference(assume_negation,[status(cth)],[l82_funct_1]) ).
cnf(c_45,plain,
set_intersection2(A,B) = set_intersection2(B,A),
inference(clausify,[status(thm)],[commutativity_k3_xboole_0]) ).
cnf(c_46,plain,
( in(D,A)
| ~ in(D,C)
| set_intersection2(A,B) != C ),
inference(clausify,[status(thm)],[d3_xboole_0]) ).
cnf(c_47,plain,
( in(D,B)
| ~ in(D,C)
| set_intersection2(A,B) != C ),
inference(clausify,[status(thm)],[d3_xboole_0]) ).
cnf(c_48,plain,
( ~ in(D,B)
| ~ in(D,A)
| in(D,C)
| set_intersection2(A,B) != C ),
inference(clausify,[status(thm)],[d3_xboole_0]) ).
cnf(c_52,plain,
( relation(relation_dom_restriction(A,B))
| ~ relation(A) ),
inference(clausify,[status(thm)],[dt_k7_relat_1]) ).
cnf(c_58,plain,
( function(relation_dom_restriction(A,B))
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[fc4_funct_1]) ).
cnf(c_79,plain,
( relation_dom(A) = set_intersection2(relation_dom(B),C)
| relation_dom_restriction(B,C) != A
| ~ function(B)
| ~ relation(B)
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t68_funct_1]) ).
fof(nnf_37,plain,
? [A,B,C] :
( ( ~ in(B,A)
| ~ in(B,relation_dom(C))
| ~ in(B,relation_dom(relation_dom_restriction(C,A))) )
& ( ( in(B,A)
& in(B,relation_dom(C)) )
| in(B,relation_dom(relation_dom_restriction(C,A))) )
& function(C)
& relation(C) ),
inference(fof_nnf,[status(thm)],[l82_funct_1_neg]) ).
fof(sk_l82_funct_1_neg_sk,plain,
( ( ~ in(sK1,sK2)
| ~ in(sK1,relation_dom(sK0))
| ~ in(sK1,relation_dom(relation_dom_restriction(sK0,sK2))) )
& ( ( in(sK1,sK2)
& in(sK1,relation_dom(sK0)) )
| in(sK1,relation_dom(relation_dom_restriction(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_37]) ).
fof(sk_l82_funct_1_neg,plain,
( ( ~ in(sK1,sK2)
| ~ in(sK1,relation_dom(sK0))
| ~ in(sK1,relation_dom(relation_dom_restriction(sK0,sK2))) )
& ( in(sK1,sK2)
| in(sK1,relation_dom(relation_dom_restriction(sK0,sK2))) )
& ( in(sK1,relation_dom(sK0))
| in(sK1,relation_dom(relation_dom_restriction(sK0,sK2))) )
& function(sK0)
& relation(sK0) ),
inference(cnf_transformation,[status(thm)],[sk_l82_funct_1_neg_sk]) ).
cnf(c_86,negated_conjecture,
relation(sK0),
inference(split_conjunct,[status(thm)],[sk_l82_funct_1_neg]) ).
cnf(c_87,negated_conjecture,
function(sK0),
inference(split_conjunct,[status(thm)],[sk_l82_funct_1_neg]) ).
cnf(c_88,negated_conjecture,
( in(sK1,relation_dom(sK0))
| in(sK1,relation_dom(relation_dom_restriction(sK0,sK2))) ),
inference(split_conjunct,[status(thm)],[sk_l82_funct_1_neg]) ).
cnf(c_89,negated_conjecture,
( in(sK1,sK2)
| in(sK1,relation_dom(relation_dom_restriction(sK0,sK2))) ),
inference(split_conjunct,[status(thm)],[sk_l82_funct_1_neg]) ).
cnf(c_90,negated_conjecture,
( ~ in(sK1,sK2)
| ~ in(sK1,relation_dom(sK0))
| ~ in(sK1,relation_dom(relation_dom_restriction(sK0,sK2))) ),
inference(split_conjunct,[status(thm)],[sk_l82_funct_1_neg]) ).
cnf(c_279,plain,
relation(relation_dom_restriction(sK0,A)),
inference(resolve,[status(thm)],[c_86,c_52]) ).
cnf(c_903,negated_conjecture,
( function(relation_dom_restriction(sK0,A))
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_87,c_58]) ).
cnf(c_290,negated_conjecture,
function(relation_dom_restriction(sK0,A)),
inference(resolve,[status(thm)],[c_86,c_903]) ).
cnf(c_904,negated_conjecture,
( in(sK1,B)
| set_intersection2(A,B) != relation_dom(relation_dom_restriction(sK0,sK2))
| in(sK1,relation_dom(sK0)) ),
inference(resolve,[status(thm)],[c_88,c_47]) ).
cnf(c_296,negated_conjecture,
( in(sK1,B)
| relation_dom(relation_dom_restriction(sK0,sK2)) != set_intersection2(A,B)
| in(sK1,relation_dom(sK0)) ),
inference(copy,[status(thm)],[c_904]) ).
cnf(c_301,plain,
( relation_dom(relation_dom_restriction(sK0,sK2)) != set_intersection2(A,relation_dom(sK0))
| in(sK1,relation_dom(sK0)) ),
inference(factor,[status(thm)],[c_296]) ).
cnf(c_905,negated_conjecture,
( in(sK1,A)
| set_intersection2(A,B) != relation_dom(relation_dom_restriction(sK0,sK2))
| in(sK1,sK2) ),
inference(resolve,[status(thm)],[c_89,c_46]) ).
cnf(c_308,negated_conjecture,
( in(sK1,A)
| relation_dom(relation_dom_restriction(sK0,sK2)) != set_intersection2(A,B)
| in(sK1,sK2) ),
inference(copy,[status(thm)],[c_905]) ).
cnf(c_313,plain,
( relation_dom(relation_dom_restriction(sK0,sK2)) != set_intersection2(sK2,A)
| in(sK1,sK2) ),
inference(factor,[status(thm)],[c_308]) ).
cnf(c_906,plain,
( relation_dom(relation_dom_restriction(sK0,A)) = set_intersection2(relation_dom(B),C)
| relation_dom_restriction(B,C) != relation_dom_restriction(sK0,A)
| ~ function(B)
| ~ relation(B)
| ~ function(relation_dom_restriction(sK0,A)) ),
inference(resolve,[status(thm)],[c_79,c_279]) ).
cnf(c_907,plain,
( relation_dom(relation_dom_restriction(sK0,C)) = set_intersection2(relation_dom(A),B)
| relation_dom_restriction(A,B) != relation_dom_restriction(sK0,C)
| ~ function(A)
| ~ relation(A) ),
inference(resolve,[status(thm)],[c_906,c_290]) ).
cnf(c_908,negated_conjecture,
( relation_dom(relation_dom_restriction(sK0,B)) = set_intersection2(relation_dom(sK0),A)
| relation_dom_restriction(sK0,A) != relation_dom_restriction(sK0,B)
| ~ function(sK0) ),
inference(resolve,[status(thm)],[c_907,c_86]) ).
cnf(c_909,negated_conjecture,
( relation_dom(relation_dom_restriction(sK0,B)) = set_intersection2(relation_dom(sK0),A)
| relation_dom_restriction(sK0,A) != relation_dom_restriction(sK0,B) ),
inference(resolve,[status(thm)],[c_908,c_87]) ).
cnf(c_829,plain,
relation_dom(relation_dom_restriction(sK0,A)) = set_intersection2(relation_dom(sK0),A),
inference(xxres,[status(thm)],[c_909]) ).
cnf(c_910,plain,
( set_intersection2(relation_dom(sK0),sK2) != set_intersection2(sK2,A)
| in(sK1,sK2) ),
inference(paramod,[status(thm)],[c_829,c_313]) ).
cnf(c_911,plain,
( set_intersection2(sK2,relation_dom(sK0)) != set_intersection2(sK2,A)
| in(sK1,sK2) ),
inference(paramod,[status(thm)],[c_45,c_910]) ).
cnf(c_852,plain,
in(sK1,sK2),
inference(copy,[status(thm)],[c_911]) ).
cnf(c_912,plain,
( set_intersection2(relation_dom(sK0),sK2) != set_intersection2(A,relation_dom(sK0))
| in(sK1,relation_dom(sK0)) ),
inference(paramod,[status(thm)],[c_829,c_301]) ).
cnf(c_913,plain,
( set_intersection2(sK2,relation_dom(sK0)) != set_intersection2(A,relation_dom(sK0))
| in(sK1,relation_dom(sK0)) ),
inference(paramod,[status(thm)],[c_45,c_912]) ).
cnf(c_854,plain,
in(sK1,relation_dom(sK0)),
inference(copy,[status(thm)],[c_913]) ).
cnf(c_914,negated_conjecture,
( ~ in(sK1,sK2)
| ~ in(sK1,relation_dom(sK0))
| ~ in(sK1,set_intersection2(relation_dom(sK0),sK2)) ),
inference(paramod,[status(thm)],[c_829,c_90]) ).
cnf(c_915,negated_conjecture,
( ~ in(sK1,sK2)
| ~ in(sK1,relation_dom(sK0))
| ~ in(sK1,set_intersection2(sK2,relation_dom(sK0))) ),
inference(paramod,[status(thm)],[c_45,c_914]) ).
cnf(c_916,negated_conjecture,
( ~ in(sK1,sK2)
| ~ in(sK1,set_intersection2(sK2,relation_dom(sK0))) ),
inference(resolve,[status(thm)],[c_854,c_915]) ).
cnf(c_855,negated_conjecture,
~ in(sK1,set_intersection2(sK2,relation_dom(sK0))),
inference(resolve,[status(thm)],[c_852,c_916]) ).
cnf(c_917,plain,
( ~ in(A,B)
| ~ in(A,C)
| in(A,set_intersection2(B,C)) ),
inference(resolve,[status(thm)],[c_48,c_45]) ).
cnf(c_918,plain,
( ~ in(sK1,A)
| in(sK1,set_intersection2(A,sK2)) ),
inference(resolve,[status(thm)],[c_917,c_852]) ).
cnf(c_919,plain,
in(sK1,set_intersection2(relation_dom(sK0),sK2)),
inference(resolve,[status(thm)],[c_918,c_854]) ).
cnf(c_920,plain,
in(sK1,set_intersection2(sK2,relation_dom(sK0))),
inference(paramod,[status(thm)],[c_45,c_919]) ).
cnf(c_902,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_855,c_920]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU224+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.63 % Computer : n014.cluster.edu
% 0.16/0.63 % Model : x86_64 x86_64
% 0.16/0.63 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.63 % Memory : 8046.5625MB
% 0.16/0.63 % OS : Linux 6.8.0-71-generic
% 0.16/0.63 % CPULimit : 300
% 0.16/0.63 % WCLimit : 300
% 0.16/0.63 % DateTime : Sat Sep 26 08:53:33 UTC 2026
% 0.16/0.63 % CPUTime :
% 0.16/0.64 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.64 % Process 2693131 was started by sandbox2 on n014,
% 0.16/0.64 % Sat Sep 26 08:53:33 2026
% 0.16/0.64 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.21/0.65
% 0.21/0.65 % From the command line: assign(max_seconds, 300).
% 0.21/0.96
% 0.21/0.96 % SZS status Theorem for theBenchmark
% 0.21/0.96
% 0.21/0.96 % Proof 1 at 0.22 (+ 0.07) seconds.
% 0.21/0.96 % Length of proof is 29.
% 0.21/0.96 % Level of proof is 6.
% 0.21/0.96 % Maximum clause weight is 35.000.
% 0.21/0.96 % Given clauses 120.
% 0.21/0.96
% 0.21/0.96 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------