%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU037+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 08:44:56 AM UTC 2026
% Result : Theorem 0.13s 10.58s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 15 unt; 0 def)
% Number of atoms : 99 ( 33 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 111 ( 48 ~; 40 |; 13 &)
% ( 1 <=>; 9 =>; 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 : 62 ( 10 sgn 16 !; 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(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(t71_funct_1,conjecture,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,set_intersection2(relation_dom(C),A))
=> apply(relation_dom_restriction(C,A),B) = apply(C,B) ) ),
file('theBenchmark.p',t71_funct_1) ).
fof(t71_funct_1_neg,negated_conjecture,
~ ! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,set_intersection2(relation_dom(C),A))
=> apply(relation_dom_restriction(C,A),B) = apply(C,B) ) ),
inference(assume_negation,[status(cth)],[t71_funct_1]) ).
cnf(c_46,plain,
set_intersection2(A,B) = set_intersection2(B,A),
inference(clausify,[status(thm)],[commutativity_k3_xboole_0]) ).
cnf(c_47,plain,
( relation(relation_dom_restriction(A,B))
| ~ relation(A) ),
inference(clausify,[status(thm)],[dt_k7_relat_1]) ).
cnf(c_55,plain,
( function(relation_dom_restriction(A,B))
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[fc4_funct_1]) ).
cnf(c_84,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]) ).
cnf(c_85,plain,
( apply(B,D) = apply(A,D)
| ~ in(D,relation_dom(A))
| relation_dom_restriction(B,C) != A
| ~ function(B)
| ~ relation(B)
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[t68_funct_1]) ).
fof(nnf_38,plain,
? [A,B,C] :
( apply(relation_dom_restriction(C,A),B) != apply(C,B)
& in(B,set_intersection2(relation_dom(C),A))
& function(C)
& relation(C) ),
inference(fof_nnf,[status(thm)],[t71_funct_1_neg]) ).
fof(sk_t71_funct_1_neg,plain,
( apply(relation_dom_restriction(sK0,sK2),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_38]) ).
cnf(c_91,negated_conjecture,
relation(sK0),
inference(split_conjunct,[status(thm)],[sk_t71_funct_1_neg]) ).
cnf(c_92,negated_conjecture,
function(sK0),
inference(split_conjunct,[status(thm)],[sk_t71_funct_1_neg]) ).
cnf(c_93,negated_conjecture,
in(sK1,set_intersection2(relation_dom(sK0),sK2)),
inference(split_conjunct,[status(thm)],[sk_t71_funct_1_neg]) ).
cnf(c_94,negated_conjecture,
in(sK1,set_intersection2(sK2,relation_dom(sK0))),
inference(paramod,[status(thm)],[c_46,c_93]) ).
cnf(c_95,negated_conjecture,
apply(relation_dom_restriction(sK0,sK2),sK1) != apply(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_t71_funct_1_neg]) ).
cnf(c_226,plain,
relation(relation_dom_restriction(sK0,A)),
inference(resolve,[status(thm)],[c_91,c_47]) ).
cnf(c_647,negated_conjecture,
( function(relation_dom_restriction(sK0,A))
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_92,c_55]) ).
cnf(c_237,negated_conjecture,
function(relation_dom_restriction(sK0,A)),
inference(resolve,[status(thm)],[c_91,c_647]) ).
cnf(c_648,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_84,c_226]) ).
cnf(c_649,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_648,c_237]) ).
cnf(c_650,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_649,c_91]) ).
cnf(c_651,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_650,c_92]) ).
cnf(c_645,plain,
relation_dom(relation_dom_restriction(sK0,A)) = set_intersection2(relation_dom(sK0),A),
inference(xxres,[status(thm)],[c_651]) ).
cnf(c_652,plain,
( apply(B,D) = apply(relation_dom_restriction(sK0,A),D)
| ~ in(D,relation_dom(relation_dom_restriction(sK0,A)))
| 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_85,c_226]) ).
cnf(c_653,plain,
( apply(A,D) = apply(relation_dom_restriction(sK0,C),D)
| ~ in(D,relation_dom(relation_dom_restriction(sK0,C)))
| relation_dom_restriction(A,B) != relation_dom_restriction(sK0,C)
| ~ function(A)
| ~ relation(A) ),
inference(resolve,[status(thm)],[c_652,c_237]) ).
cnf(c_654,negated_conjecture,
( apply(sK0,C) = apply(relation_dom_restriction(sK0,B),C)
| ~ in(C,relation_dom(relation_dom_restriction(sK0,B)))
| relation_dom_restriction(sK0,A) != relation_dom_restriction(sK0,B)
| ~ function(sK0) ),
inference(resolve,[status(thm)],[c_653,c_91]) ).
cnf(c_655,negated_conjecture,
( apply(sK0,C) = apply(relation_dom_restriction(sK0,B),C)
| ~ in(C,relation_dom(relation_dom_restriction(sK0,B)))
| relation_dom_restriction(sK0,A) != relation_dom_restriction(sK0,B) ),
inference(resolve,[status(thm)],[c_654,c_92]) ).
cnf(c_656,plain,
( apply(sK0,A) = apply(relation_dom_restriction(sK0,B),A)
| ~ in(A,relation_dom(relation_dom_restriction(sK0,B))) ),
inference(xxres,[status(thm)],[c_655]) ).
cnf(c_657,negated_conjecture,
apply(sK0,sK1) != apply(relation_dom_restriction(sK0,sK2),sK1),
inference(copy,[status(thm)],[c_95]) ).
cnf(c_658,negated_conjecture,
~ in(sK1,relation_dom(relation_dom_restriction(sK0,sK2))),
inference(resolve,[status(thm)],[c_656,c_657]) ).
cnf(c_659,negated_conjecture,
~ in(sK1,set_intersection2(relation_dom(sK0),sK2)),
inference(paramod,[status(thm)],[c_645,c_658]) ).
cnf(c_660,negated_conjecture,
~ in(sK1,set_intersection2(sK2,relation_dom(sK0))),
inference(paramod,[status(thm)],[c_46,c_659]) ).
cnf(c_646,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_94,c_660]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU037+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/10.38 % Computer : n019.cluster.edu
% 0.08/10.38 % Model : x86_64 x86_64
% 0.08/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/10.38 % Memory : 8046.5625MB
% 0.08/10.38 % OS : Linux 6.8.0-71-generic
% 0.08/10.38 % CPULimit : 300
% 0.08/10.38 % WCLimit : 300
% 0.08/10.38 % DateTime : Sat Sep 26 08:32:30 UTC 2026
% 0.08/10.38 % CPUTime :
% 0.08/10.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/10.38 % Process 859400 was started by sandbox2 on n019,
% 0.08/10.38 % Sat Sep 26 08:32:30 2026
% 0.08/10.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/10.39
% 0.08/10.39 % From the command line: assign(max_seconds, 300).
% 0.13/10.58
% 0.13/10.58 % SZS status Theorem for theBenchmark
% 0.13/10.58
% 0.13/10.58 % Proof 1 at 0.08 (+ 0.03) seconds.
% 0.13/10.58 % Length of proof is 19.
% 0.13/10.58 % Level of proof is 4.
% 0.13/10.58 % Maximum clause weight is 35.000.
% 0.13/10.58 % Given clauses 110.
% 0.13/10.58
% 0.13/10.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------