%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU019+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/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 02:55:05 PM UTC 2026
% Result : Theorem 4.25s 6.33s
% Output : CNFRefutation 4.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 61 ( 27 unt; 1 def)
% Number of atoms : 258 ( 75 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 271 ( 113 ~; 116 |; 32 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 2 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 81 ( 0 sgn 73 !; 8 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
<=> ! [X1,X2] :
( ( apply(X0,X1) = apply(X0,X2)
& in(X2,relation_dom(X0))
& in(X1,relation_dom(X0)) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_funct_1) ).
fof(f5,axiom,
! [X0] : relation(identity_relation(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_relat_1) ).
fof(f10,axiom,
! [X0] :
( function(identity_relation(X0))
& relation(identity_relation(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(f25,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( X1 = identity_relation(X0)
<=> ( ! [X2] :
( in(X2,X0)
=> apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_funct_1) ).
fof(f28,conjecture,
! [X0] : one_to_one(identity_relation(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_funct_1) ).
fof(f29,negated_conjecture,
~ ! [X0] : one_to_one(identity_relation(X0)),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f41,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( one_to_one(X0)
<=> ! [X1,X2] :
( apply(X0,X1) != apply(X0,X2)
| ~ in(X2,relation_dom(X0))
| ~ in(X1,relation_dom(X0))
| X1 = X2 ) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f42,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( one_to_one(X0)
<=> ! [X1,X2] :
( apply(X0,X1) != apply(X0,X2)
| ~ in(X2,relation_dom(X0))
| ~ in(X1,relation_dom(X0))
| X1 = X2 ) ) ),
inference(flattening,[],[f41]) ).
fof(f50,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( X1 = identity_relation(X0)
<=> ( ! [X2] :
( ~ in(X2,X0)
| apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) ) ),
inference(ennf_transformation,[],[f25]) ).
fof(f51,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( X1 = identity_relation(X0)
<=> ( ! [X2] :
( ~ in(X2,X0)
| apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) ) ),
inference(flattening,[],[f50]) ).
fof(f55,plain,
? [X0] : ~ one_to_one(identity_relation(X0)),
inference(ennf_transformation,[],[f29]) ).
fof(f60,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( ( ~ one_to_one(X0)
| ! [X1,X2] :
( apply(X0,X1) != apply(X0,X2)
| ~ in(X2,relation_dom(X0))
| ~ in(X1,relation_dom(X0))
| X1 = X2 ) )
& ( ? [X1,X2] :
( apply(X0,X1) = apply(X0,X2)
& in(X2,relation_dom(X0))
& in(X1,relation_dom(X0))
& X1 != X2 )
| one_to_one(X0) ) ) ),
inference(nnf_transformation,[],[f42]) ).
fof(f61,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( ( ~ one_to_one(X0)
| ! [X3,X4] :
( apply(X0,X3) != apply(X0,X4)
| ~ in(X4,relation_dom(X0))
| ~ in(X3,relation_dom(X0))
| X3 = X4 ) )
& ( ? [X1,X2] :
( apply(X0,X1) = apply(X0,X2)
& in(X2,relation_dom(X0))
& in(X1,relation_dom(X0))
& X1 != X2 )
| one_to_one(X0) ) ) ),
inference(rectify,[],[f60]) ).
fof(f62,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( ( ~ one_to_one(X0)
| ! [X3,X4] :
( apply(X0,X3) != apply(X0,X4)
| ~ in(X4,relation_dom(X0))
| ~ in(X3,relation_dom(X0))
| X3 = X4 ) )
& ( ( apply(X0,sK0(X0)) = apply(X0,sK1(X0))
& in(sK1(X0),relation_dom(X0))
& in(sK0(X0),relation_dom(X0))
& sK0(X0) != sK1(X0) )
| one_to_one(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X1,sK0(X0)),skolemize(X2,sK1(X0))],[f61]) ).
fof(f72,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( ( identity_relation(X0) != X1
| ( ! [X2] :
( ~ in(X2,X0)
| apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) )
& ( ? [X2] :
( in(X2,X0)
& apply(X1,X2) != X2 )
| relation_dom(X1) != X0
| X1 = identity_relation(X0) ) ) ),
inference(nnf_transformation,[],[f51]) ).
fof(f73,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( ( identity_relation(X0) != X1
| ( ! [X2] :
( ~ in(X2,X0)
| apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) )
& ( ? [X2] :
( in(X2,X0)
& apply(X1,X2) != X2 )
| relation_dom(X1) != X0
| X1 = identity_relation(X0) ) ) ),
inference(flattening,[],[f72]) ).
fof(f74,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( ( identity_relation(X0) != X1
| ( ! [X3] :
( ~ in(X3,X0)
| apply(X1,X3) = X3 )
& relation_dom(X1) = X0 ) )
& ( ? [X2] :
( in(X2,X0)
& apply(X1,X2) != X2 )
| relation_dom(X1) != X0
| X1 = identity_relation(X0) ) ) ),
inference(rectify,[],[f73]) ).
fof(f75,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ( ( identity_relation(X0) != X1
| ( ! [X3] :
( ~ in(X3,X0)
| apply(X1,X3) = X3 )
& relation_dom(X1) = X0 ) )
& ( ( in(sK11(X0,X1),X0)
& sK11(X0,X1) != apply(X1,sK11(X0,X1)) )
| relation_dom(X1) != X0
| X1 = identity_relation(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X2,sK11(X0,X1))],[f74]) ).
fof(f76,plain,
~ one_to_one(identity_relation(sK12)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X0,sK12)],[f55]) ).
fof(f81,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| apply(X0,sK0(X0)) = apply(X0,sK1(X0))
| one_to_one(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f82,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| in(sK1(X0),relation_dom(X0))
| one_to_one(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f83,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| in(sK0(X0),relation_dom(X0))
| one_to_one(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f84,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| sK0(X0) != sK1(X0)
| one_to_one(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f85,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f5]) ).
fof(f91,plain,
! [X0] : function(identity_relation(X0)),
inference(cnf_transformation,[],[f10]) ).
fof(f92,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f10]) ).
fof(f114,plain,
! [X3,X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| identity_relation(X0) != X1
| ~ in(X3,X0)
| apply(X1,X3) = X3 ),
inference(cnf_transformation,[],[f75]) ).
fof(f115,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| identity_relation(X0) != X1
| relation_dom(X1) = X0 ),
inference(cnf_transformation,[],[f75]) ).
fof(f120,plain,
~ one_to_one(identity_relation(sK12)),
inference(cnf_transformation,[],[f76]) ).
fof(f127,plain,
! [X0] :
( ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| relation_dom(identity_relation(X0)) = X0 ),
inference(equality_resolution,[],[f115]) ).
fof(f128,plain,
! [X3,X0] :
( ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0))
| ~ in(X3,X0)
| apply(identity_relation(X0),X3) = X3 ),
inference(equality_resolution,[],[f114]) ).
tcf(c_52,plain,
! [X0: $i] :
( one_to_one(X0)
| ~ relation(X0)
| ~ function(X0)
| ( sK0(X0) != sK1(X0) ) ),
inference(cnf_transformation,[],[f84]) ).
tcf(c_53,plain,
! [X0: $i] :
( one_to_one(X0)
| in(sK0(X0),relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f83]) ).
tcf(c_54,plain,
! [X0: $i] :
( one_to_one(X0)
| in(sK1(X0),relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f82]) ).
tcf(c_55,plain,
! [X0: $i] :
( one_to_one(X0)
| ( apply(X0,sK0(X0)) = apply(X0,sK1(X0)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f81]) ).
tcf(c_57,plain,
! [X0: $i] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f85]) ).
tcf(c_63,plain,
! [X0: $i] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f92]) ).
tcf(c_64,plain,
! [X0: $i] : function(identity_relation(X0)),
inference(cnf_transformation,[],[f91]) ).
tcf(c_88,plain,
! [X0: $i] :
( ( relation_dom(identity_relation(X0)) = X0 )
| ~ relation(identity_relation(X0))
| ~ function(identity_relation(X0)) ),
inference(cnf_transformation,[],[f127]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),X0) = X0 )
| ~ relation(identity_relation(X1))
| ~ function(identity_relation(X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f128]) ).
tcf(c_92,negated_conjecture,
~ one_to_one(identity_relation(sK12)),
inference(cnf_transformation,[],[f120]) ).
tcf(c_120,plain,
! [X0: $i] : relation_dom(identity_relation(X0)) = X0,
inference(global_subsumption_just,[status(thm)],[c_88,c_64,c_63,c_88]) ).
tcf(c_143,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),X0) = X0 )
| ~ function(identity_relation(X1))
| ~ in(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_89,c_57]) ).
tcf(c_146,plain,
! [X0: $i,X1: $i] :
( ( apply(identity_relation(X1),X0) = X0 )
| ~ in(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_143,c_64]) ).
tcf(c_3638,definition,
iPr_def_10 = identity_relation(sK12),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_3639,negated_conjecture,
~ one_to_one(iPr_def_10),
inference(demodulation,[status(thm)],[c_92,c_3638]) ).
tcf(c_4165,plain,
function(iPr_def_10),
inference(superposition,[status(thm)],[c_3638,c_64]) ).
tcf(c_4166,plain,
relation(iPr_def_10),
inference(superposition,[status(thm)],[c_3638,c_63]) ).
tcf(c_4167,plain,
relation_dom(iPr_def_10) = sK12,
inference(superposition,[status(thm)],[c_3638,c_120]) ).
tcf(c_4521,plain,
( one_to_one(iPr_def_10)
| in(sK0(iPr_def_10),sK12)
| ~ relation(iPr_def_10)
| ~ function(iPr_def_10) ),
inference(superposition,[status(thm)],[c_4167,c_53]) ).
tcf(c_4530,plain,
in(sK0(iPr_def_10),sK12),
inference(forward_subsumption_resolution,[status(thm)],[c_4521,c_3639,c_4166,c_4165]) ).
tcf(c_4564,plain,
( one_to_one(iPr_def_10)
| in(sK1(iPr_def_10),sK12)
| ~ relation(iPr_def_10)
| ~ function(iPr_def_10) ),
inference(superposition,[status(thm)],[c_4167,c_54]) ).
tcf(c_4569,plain,
in(sK1(iPr_def_10),sK12),
inference(forward_subsumption_resolution,[status(thm)],[c_4564,c_3639,c_4166,c_4165]) ).
tcf(c_4594,plain,
( one_to_one(iPr_def_10)
| ~ relation(iPr_def_10)
| ~ function(iPr_def_10)
| ( sK0(iPr_def_10) != sK1(iPr_def_10) ) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_4615,plain,
( one_to_one(iPr_def_10)
| ( apply(iPr_def_10,sK0(iPr_def_10)) = apply(iPr_def_10,sK1(iPr_def_10)) )
| ~ relation(iPr_def_10) ),
inference(superposition,[status(thm)],[c_4165,c_55]) ).
tcf(c_4616,plain,
apply(iPr_def_10,sK0(iPr_def_10)) = apply(iPr_def_10,sK1(iPr_def_10)),
inference(forward_subsumption_resolution,[status(thm)],[c_4615,c_3639,c_4166]) ).
tcf(c_4634,plain,
apply(identity_relation(sK12),sK0(iPr_def_10)) = sK0(iPr_def_10),
inference(superposition,[status(thm)],[c_4530,c_146]) ).
tcf(c_4638,plain,
apply(iPr_def_10,sK0(iPr_def_10)) = sK0(iPr_def_10),
inference(light_normalisation,[status(thm)],[c_4634,c_3638]) ).
tcf(c_4644,plain,
apply(identity_relation(sK12),sK1(iPr_def_10)) = sK1(iPr_def_10),
inference(superposition,[status(thm)],[c_4569,c_146]) ).
tcf(c_4648,plain,
sK0(iPr_def_10) = sK1(iPr_def_10),
inference(light_normalisation,[status(thm)],[c_4644,c_3638,c_4616,c_4638]) ).
tcf(c_4650,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_4648,c_4594,c_4165,c_4166,c_3639]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU019+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/5.39 % Computer : n004.cluster.edu
% 0.12/5.39 % Model : x86_64 x86_64
% 0.12/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.39 % Memory : 8046.5625MB
% 0.12/5.39 % OS : Linux 6.8.0-71-generic
% 0.12/5.39 % CPULimit : 300
% 0.12/5.39 % WCLimit : 300
% 0.12/5.39 % DateTime : Thu Sep 24 12:34:42 UTC 2026
% 0.12/5.40 % CPUTime :
% 0.12/5.40 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/5.44 Running first-order theorem proving
% 0.16/5.44 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/5.45
% 0.16/5.45 % ======== iProver multi-core TPTP/SMT =========
% 0.16/5.45
% 0.16/5.45 % Detected problem language: tptp
% 0.16/5.46 % Proving...
% 4.25/6.33 % SZS status Started for theBenchmark.p
% 4.25/6.33 % SZS status Theorem for theBenchmark.p
% 4.25/6.33
% 4.25/6.33 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.25/6.33
% 4.25/6.33 % ------ iProver source info
% 4.25/6.33
% 4.25/6.33 % git: date: 2026-07-19 20:42:38 +0200
% 4.25/6.33 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.25/6.33 % git: non_committed_changes: false
% 4.25/6.33
% 4.25/6.33 % ------ Parsing...
% 4.25/6.33 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.25/6.33
% 4.25/6.33 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 4.25/6.33
% 4.25/6.33 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.25/6.33
% 4.25/6.33 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.25/6.33 % ------ Proving...
% 4.25/6.33 % ------ Problem Properties
% 4.25/6.33
% 4.25/6.33 %
% 4.25/6.33 % clauses 44
% 4.25/6.33 % conjectures 1
% 4.25/6.33 % EPR 20
% 4.25/6.33 % Horn 38
% 4.25/6.33 % unary 21
% 4.25/6.33 % binary 11
% 4.25/6.33 % lits 89
% 4.25/6.33 % lits eq 12
% 4.25/6.33 % fd_pure 0
% 4.25/6.33 % fd_pseudo 0
% 4.25/6.33 % fd_cond 1
% 4.25/6.33 % fd_pseudo_cond 2
% 4.25/6.33 % AC symbols 0
% 4.25/6.33
% 4.25/6.33 % ------ Schedule dynamic 5 is on
% 4.25/6.33
% 4.25/6.33 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.25/6.33
% 4.25/6.33
% 4.25/6.33 % ------
% 4.25/6.33 % Current options:
% 4.25/6.33 % ------
% 4.25/6.33
% 4.25/6.33
% 4.25/6.33 %
% 4.25/6.33
% 4.25/6.33 % ------ Proving...
% 4.25/6.33 %
% 4.25/6.33
% 4.25/6.33 % SZS status Theorem for theBenchmark.p
% 4.25/6.33
% 4.25/6.33 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.25/6.34
% 4.25/6.34
%------------------------------------------------------------------------------