%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU194+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n004.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 : Fri Sep 25 02:55:50 PM UTC 2026
% Result : Theorem 33.77s 6.30s
% Output : CNFRefutation 33.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 48 ( 13 unt; 0 def)
% Number of atoms : 177 ( 35 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 209 ( 80 ~; 93 |; 29 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 99 ( 0 sgn 94 !; 5 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f21,axiom,
! [X0,X1,X2] :
( X2 = set_intersection2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f153,axiom,
! [X0,X1] : set_difference(X0,set_difference(X0,X1)) = set_intersection2(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_xboole_1) ).
fof(f175,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_dom(relation_dom_restriction(X2,X1)))
<=> ( in(X0,relation_dom(X2))
& in(X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t86_relat_1) ).
fof(f180,conjecture,
! [X0,X1] :
( relation(X1)
=> relation_dom(relation_dom_restriction(X1,X0)) = set_intersection2(relation_dom(X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t90_relat_1) ).
fof(f181,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> relation_dom(relation_dom_restriction(X1,X0)) = set_intersection2(relation_dom(X1),X0) ),
inference(negated_conjecture,[status(cth)],[f180]) ).
fof(f260,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( in(X0,relation_dom(relation_dom_restriction(X2,X1)))
<=> ( in(X0,relation_dom(X2))
& in(X0,X1) ) ) ),
inference(ennf_transformation,[],[f175]) ).
fof(f265,plain,
? [X0,X1] :
( relation(X1)
& relation_dom(relation_dom_restriction(X1,X0)) != set_intersection2(relation_dom(X1),X0) ),
inference(ennf_transformation,[],[f181]) ).
fof(f359,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( ( ~ in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| ( in(X0,relation_dom(X2))
& in(X0,X1) ) )
& ( ~ in(X0,relation_dom(X2))
| ~ in(X0,X1)
| in(X0,relation_dom(relation_dom_restriction(X2,X1))) ) ) ),
inference(nnf_transformation,[],[f260]) ).
fof(f360,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( ( ~ in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| ( in(X0,relation_dom(X2))
& in(X0,X1) ) )
& ( ~ in(X0,relation_dom(X2))
| ~ in(X0,X1)
| in(X0,relation_dom(relation_dom_restriction(X2,X1))) ) ) ),
inference(flattening,[],[f359]) ).
fof(f361,plain,
( relation(sK7)
& relation_dom(relation_dom_restriction(sK7,sK6)) != set_intersection2(relation_dom(sK7),sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X0,sK6),skolemize(X1,sK7)],[f265]) ).
fof(f415,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X1)
| ~ in(X3,X0)
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(nnf_transformation,[],[f21]) ).
fof(f416,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X1)
| ~ in(X3,X0)
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(flattening,[],[f415]) ).
fof(f417,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( in(X4,X1)
& in(X4,X0) ) )
& ( ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(rectify,[],[f416]) ).
fof(f418,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( in(X4,X1)
& in(X4,X0) ) )
& ( ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ) ) )
& ( ( ( in(sK40(X0,X1,X2),X2)
| ( in(sK40(X0,X1,X2),X1)
& in(sK40(X0,X1,X2),X0) ) )
& ( ~ in(sK40(X0,X1,X2),X2)
| ~ in(sK40(X0,X1,X2),X1)
| ~ in(sK40(X0,X1,X2),X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40]),skolemize(X3,sK40(X0,X1,X2))],[f417]) ).
fof(f518,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1)),
inference(cnf_transformation,[],[f153]) ).
fof(f544,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| in(X0,relation_dom(X2)) ),
inference(cnf_transformation,[],[f360]) ).
fof(f545,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| in(X0,X1) ),
inference(cnf_transformation,[],[f360]) ).
fof(f546,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_dom(X2))
| ~ in(X0,X1)
| in(X0,relation_dom(relation_dom_restriction(X2,X1))) ),
inference(cnf_transformation,[],[f360]) ).
fof(f550,plain,
relation(sK7),
inference(cnf_transformation,[],[f361]) ).
fof(f551,plain,
relation_dom(relation_dom_restriction(sK7,sK6)) != set_intersection2(relation_dom(sK7),sK6),
inference(cnf_transformation,[],[f361]) ).
fof(f669,plain,
! [X2,X0,X1] :
( in(sK40(X0,X1,X2),X2)
| in(sK40(X0,X1,X2),X1)
| set_intersection2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f418]) ).
fof(f670,plain,
! [X2,X0,X1] :
( in(sK40(X0,X1,X2),X2)
| in(sK40(X0,X1,X2),X0)
| set_intersection2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f418]) ).
fof(f671,plain,
! [X2,X0,X1] :
( ~ in(sK40(X0,X1,X2),X2)
| ~ in(sK40(X0,X1,X2),X1)
| ~ in(sK40(X0,X1,X2),X0)
| set_intersection2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f418]) ).
fof(f672,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f783,plain,
relation_dom(relation_dom_restriction(sK7,sK6)) != set_difference(relation_dom(sK7),set_difference(relation_dom(sK7),sK6)),
inference(definition_unfolding,[],[f551,f518]) ).
fof(f813,plain,
! [X2,X0,X1] :
( ~ in(sK40(X0,X1,X2),X2)
| ~ in(sK40(X0,X1,X2),X1)
| ~ in(sK40(X0,X1,X2),X0)
| set_difference(X0,set_difference(X0,X1)) = X2 ),
inference(definition_unfolding,[],[f671,f518]) ).
fof(f814,plain,
! [X2,X0,X1] :
( in(sK40(X0,X1,X2),X2)
| in(sK40(X0,X1,X2),X0)
| set_difference(X0,set_difference(X0,X1)) = X2 ),
inference(definition_unfolding,[],[f670,f518]) ).
fof(f815,plain,
! [X2,X0,X1] :
( in(sK40(X0,X1,X2),X2)
| in(sK40(X0,X1,X2),X1)
| set_difference(X0,set_difference(X0,X1)) = X2 ),
inference(definition_unfolding,[],[f669,f518]) ).
fof(f819,plain,
! [X0,X1] : set_difference(X0,set_difference(X0,X1)) = set_difference(X1,set_difference(X1,X0)),
inference(definition_unfolding,[],[f672,f518,f518]) ).
tcf(c_150,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_dom(relation_dom_restriction(X1,X2)))
| ~ relation(X1)
| ~ in(X0,X2)
| ~ in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f546]) ).
tcf(c_151,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ relation(X1)
| ~ in(X0,relation_dom(relation_dom_restriction(X1,X2))) ),
inference(cnf_transformation,[],[f545]) ).
tcf(c_152,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_dom(X1))
| ~ relation(X1)
| ~ in(X0,relation_dom(relation_dom_restriction(X1,X2))) ),
inference(cnf_transformation,[],[f544]) ).
tcf(c_156,negated_conjecture,
set_difference(relation_dom(sK7),set_difference(relation_dom(sK7),sK6)) != relation_dom(relation_dom_restriction(sK7,sK6)),
inference(cnf_transformation,[],[f783]) ).
tcf(c_157,negated_conjecture,
relation(sK7),
inference(cnf_transformation,[],[f550]) ).
tcf(c_271,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(X0,set_difference(X0,X1)) = X2 )
| ~ in(sK40(X0,X1,X2),X2)
| ~ in(sK40(X0,X1,X2),X1)
| ~ in(sK40(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f813]) ).
tcf(c_272,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK40(X0,X1,X2),X2)
| in(sK40(X0,X1,X2),X0)
| ( set_difference(X0,set_difference(X0,X1)) = X2 ) ),
inference(cnf_transformation,[],[f814]) ).
tcf(c_273,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK40(X0,X1,X2),X2)
| in(sK40(X0,X1,X2),X1)
| ( set_difference(X0,set_difference(X0,X1)) = X2 ) ),
inference(cnf_transformation,[],[f815]) ).
tcf(c_277,plain,
! [X0: $i,X1: $i] : set_difference(X0,set_difference(X0,X1)) = set_difference(X1,set_difference(X1,X0)),
inference(cnf_transformation,[],[f819]) ).
tcf(c_3188,plain,
set_difference(sK6,set_difference(sK6,relation_dom(sK7))) != relation_dom(relation_dom_restriction(sK7,sK6)),
inference(demodulation,[status(thm)],[c_156,c_277]) ).
tcf(c_14098,plain,
( in(sK40(sK6,relation_dom(sK7),relation_dom(relation_dom_restriction(sK7,sK6))),sK6)
| in(sK40(sK6,relation_dom(sK7),relation_dom(relation_dom_restriction(sK7,sK6))),relation_dom(relation_dom_restriction(sK7,sK6)))
| ( set_difference(sK6,set_difference(sK6,relation_dom(sK7))) = relation_dom(relation_dom_restriction(sK7,sK6)) ) ),
inference(instantiation,[status(thm)],[c_272]) ).
tcf(c_14099,plain,
( in(sK40(sK6,relation_dom(sK7),relation_dom(relation_dom_restriction(sK7,sK6))),relation_dom(sK7))
| in(sK40(sK6,relation_dom(sK7),relation_dom(relation_dom_restriction(sK7,sK6))),relation_dom(relation_dom_restriction(sK7,sK6)))
| ( set_difference(sK6,set_difference(sK6,relation_dom(sK7))) = relation_dom(relation_dom_restriction(sK7,sK6)) ) ),
inference(instantiation,[status(thm)],[c_273]) ).
tcf(c_14353,plain,
( ( set_difference(sK6,set_difference(sK6,relation_dom(sK7))) = relation_dom(relation_dom_restriction(sK7,sK6)) )
| ~ in(sK40(sK6,relation_dom(sK7),relation_dom(relation_dom_restriction(sK7,sK6))),sK6)
| ~ in(sK40(sK6,relation_dom(sK7),relation_dom(relation_dom_restriction(sK7,sK6))),relation_dom(sK7))
| ~ in(sK40(sK6,relation_dom(sK7),relation_dom(relation_dom_restriction(sK7,sK6))),relation_dom(relation_dom_restriction(sK7,sK6))) ),
inference(instantiation,[status(thm)],[c_271]) ).
tcf(c_18925,plain,
( in(sK40(sK6,relation_dom(sK7),relation_dom(relation_dom_restriction(sK7,sK6))),relation_dom(sK7))
| ~ relation(sK7)
| ~ in(sK40(sK6,relation_dom(sK7),relation_dom(relation_dom_restriction(sK7,sK6))),relation_dom(relation_dom_restriction(sK7,sK6))) ),
inference(instantiation,[status(thm)],[c_152]) ).
tcf(c_18926,plain,
( in(sK40(sK6,relation_dom(sK7),relation_dom(relation_dom_restriction(sK7,sK6))),sK6)
| ~ relation(sK7)
| ~ in(sK40(sK6,relation_dom(sK7),relation_dom(relation_dom_restriction(sK7,sK6))),relation_dom(relation_dom_restriction(sK7,sK6))) ),
inference(instantiation,[status(thm)],[c_151]) ).
tcf(c_29439,plain,
! [X0: $i] :
( in(sK40(sK6,relation_dom(sK7),relation_dom(relation_dom_restriction(sK7,sK6))),relation_dom(relation_dom_restriction(X0,sK6)))
| ~ relation(X0)
| ~ in(sK40(sK6,relation_dom(sK7),relation_dom(relation_dom_restriction(sK7,sK6))),sK6)
| ~ in(sK40(sK6,relation_dom(sK7),relation_dom(relation_dom_restriction(sK7,sK6))),relation_dom(X0)) ),
inference(instantiation,[status(thm)],[c_150]) ).
tcf(c_60419,plain,
( in(sK40(sK6,relation_dom(sK7),relation_dom(relation_dom_restriction(sK7,sK6))),relation_dom(relation_dom_restriction(sK7,sK6)))
| ~ relation(sK7)
| ~ in(sK40(sK6,relation_dom(sK7),relation_dom(relation_dom_restriction(sK7,sK6))),sK6)
| ~ in(sK40(sK6,relation_dom(sK7),relation_dom(relation_dom_restriction(sK7,sK6))),relation_dom(sK7)) ),
inference(instantiation,[status(thm)],[c_29439]) ).
tcf(c_60420,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_60419,c_18925,c_18926,c_14353,c_14099,c_14098,c_3188,c_157]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU194+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n004.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 13:07:50 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 33.77/6.30 % SZS status Started for theBenchmark.p
% 33.77/6.30 % SZS status Theorem for theBenchmark.p
% 33.77/6.30
% 33.77/6.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 33.77/6.30
% 33.77/6.30 % ------ iProver source info
% 33.77/6.30
% 33.77/6.30 % git: date: 2026-07-19 20:42:38 +0200
% 33.77/6.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 33.77/6.30 % git: non_committed_changes: false
% 33.77/6.30
% 33.77/6.30 % ------ Parsing...
% 33.77/6.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 33.77/6.30
% 33.77/6.30 % ------ Preprocessing... sup_sim: 31 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 33.77/6.30
% 33.77/6.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 33.77/6.30
% 33.77/6.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 33.77/6.30 % ------ Proving...
% 33.77/6.30 % ------ Problem Properties
% 33.77/6.30
% 33.77/6.30 %
% 33.77/6.30 % clauses 263
% 33.77/6.30 % conjectures 1
% 33.77/6.30 % EPR 34
% 33.77/6.30 % Horn 213
% 33.77/6.30 % unary 45
% 33.77/6.30 % binary 92
% 33.77/6.30 % lits 667
% 33.77/6.30 % lits eq 137
% 33.77/6.30 % fd_pure 0
% 33.77/6.30 % fd_pseudo 0
% 33.77/6.30 % fd_cond 10
% 33.77/6.30 % fd_pseudo_cond 54
% 33.77/6.30 % AC symbols 0
% 33.77/6.30
% 33.77/6.30 % ------ Schedule dynamic 5 is on
% 33.77/6.30
% 33.77/6.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 33.77/6.30
% 33.77/6.30
% 33.77/6.30 % ------
% 33.77/6.30 % Current options:
% 33.77/6.30 % ------
% 33.77/6.30
% 33.77/6.30
% 33.77/6.30 %
% 33.77/6.30
% 33.77/6.30 % ------ Proving...
% 33.77/6.30 %
% 33.77/6.30
% 33.77/6.30 % SZS status Theorem for theBenchmark.p
% 33.77/6.30
% 33.77/6.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 33.77/6.31
% 33.77/6.31
%------------------------------------------------------------------------------