%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU096+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n005.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 02:55:24 PM UTC 2026
% Result : Theorem 2.60s 1.43s
% Output : CNFRefutation 2.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 38 ( 20 unt; 2 def)
% Number of atoms : 103 ( 11 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 95 ( 38 ~; 31 |; 18 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 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 : 8 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 30 ( 0 sgn 26 !; 4 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
fof(f50,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( subset(X0,relation_rng(X1))
=> relation_image(X1,relation_inverse_image(X1,X0)) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t147_funct_1) ).
fof(f51,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( finite(X0)
=> finite(relation_image(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_finset_1) ).
fof(f53,conjecture,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( ( finite(relation_inverse_image(X1,X0))
& subset(X0,relation_rng(X1)) )
=> finite(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_finset_1) ).
fof(f54,negated_conjecture,
~ ! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( ( finite(relation_inverse_image(X1,X0))
& subset(X0,relation_rng(X1)) )
=> finite(X0) ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f107,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_rng(X1))
| relation_image(X1,relation_inverse_image(X1,X0)) = X0 ),
inference(ennf_transformation,[],[f50]) ).
fof(f108,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_rng(X1))
| relation_image(X1,relation_inverse_image(X1,X0)) = X0 ),
inference(flattening,[],[f107]) ).
fof(f109,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ finite(X0)
| finite(relation_image(X1,X0)) ),
inference(ennf_transformation,[],[f51]) ).
fof(f110,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ finite(X0)
| finite(relation_image(X1,X0)) ),
inference(flattening,[],[f109]) ).
fof(f112,plain,
? [X0,X1] :
( function(X1)
& relation(X1)
& finite(relation_inverse_image(X1,X0))
& subset(X0,relation_rng(X1))
& ~ finite(X0) ),
inference(ennf_transformation,[],[f54]) ).
fof(f113,plain,
? [X0,X1] :
( function(X1)
& relation(X1)
& finite(relation_inverse_image(X1,X0))
& subset(X0,relation_rng(X1))
& ~ finite(X0) ),
inference(flattening,[],[f112]) ).
fof(f148,plain,
( function(sK27)
& relation(sK27)
& finite(relation_inverse_image(sK27,sK26))
& subset(sK26,relation_rng(sK27))
& ~ finite(sK26) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26,sK27]),skolemize(X0,sK26),skolemize(X1,sK27)],[f113]) ).
fof(f262,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ subset(X0,relation_rng(X1))
| relation_image(X1,relation_inverse_image(X1,X0)) = X0 ),
inference(cnf_transformation,[],[f108]) ).
fof(f263,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ finite(X0)
| finite(relation_image(X1,X0)) ),
inference(cnf_transformation,[],[f110]) ).
fof(f265,plain,
function(sK27),
inference(cnf_transformation,[],[f148]) ).
fof(f266,plain,
relation(sK27),
inference(cnf_transformation,[],[f148]) ).
fof(f267,plain,
finite(relation_inverse_image(sK27,sK26)),
inference(cnf_transformation,[],[f148]) ).
fof(f268,plain,
subset(sK26,relation_rng(sK27)),
inference(cnf_transformation,[],[f148]) ).
fof(f269,plain,
~ finite(sK26),
inference(cnf_transformation,[],[f148]) ).
tcf(c_157,plain,
! [X0: $i,X1: $i] :
( ( relation_image(X1,relation_inverse_image(X1,X0)) = X0 )
| ~ relation(X1)
| ~ function(X1)
| ~ subset(X0,relation_rng(X1)) ),
inference(cnf_transformation,[],[f262]) ).
tcf(c_158,plain,
! [X0: $i,X1: $i] :
( finite(relation_image(X1,X0))
| ~ relation(X1)
| ~ function(X1)
| ~ finite(X0) ),
inference(cnf_transformation,[],[f263]) ).
tcf(c_160,negated_conjecture,
~ finite(sK26),
inference(cnf_transformation,[],[f269]) ).
tcf(c_161,negated_conjecture,
subset(sK26,relation_rng(sK27)),
inference(cnf_transformation,[],[f268]) ).
tcf(c_162,negated_conjecture,
finite(relation_inverse_image(sK27,sK26)),
inference(cnf_transformation,[],[f267]) ).
tcf(c_163,negated_conjecture,
relation(sK27),
inference(cnf_transformation,[],[f266]) ).
tcf(c_164,negated_conjecture,
function(sK27),
inference(cnf_transformation,[],[f265]) ).
tcf(c_3932,definition,
iPr_def_10 = relation_inverse_image(sK27,sK26),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_3933,definition,
iPr_def_11 = relation_rng(sK27),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_3934,negated_conjecture,
function(sK27),
inference(demodulation,[status(thm)],[c_164]) ).
tcf(c_3935,negated_conjecture,
relation(sK27),
inference(demodulation,[status(thm)],[c_163]) ).
tcf(c_3936,negated_conjecture,
finite(iPr_def_10),
inference(demodulation,[status(thm)],[c_162,c_3932]) ).
tcf(c_3937,negated_conjecture,
subset(sK26,iPr_def_11),
inference(demodulation,[status(thm)],[c_161,c_3933]) ).
tcf(c_3938,negated_conjecture,
~ finite(sK26),
inference(demodulation,[status(thm)],[c_160]) ).
tcf(c_5175,plain,
! [X0: $i] :
( ( relation_image(sK27,relation_inverse_image(sK27,X0)) = X0 )
| ~ relation(sK27)
| ~ function(sK27)
| ~ subset(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_3933,c_157]) ).
tcf(c_5182,plain,
! [X0: $i] :
( ( relation_image(sK27,relation_inverse_image(sK27,X0)) = X0 )
| ~ subset(X0,iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5175,c_3935,c_3934]) ).
tcf(c_5231,plain,
relation_image(sK27,relation_inverse_image(sK27,sK26)) = sK26,
inference(superposition,[status(thm)],[c_3937,c_5182]) ).
tcf(c_5233,plain,
relation_image(sK27,iPr_def_10) = sK26,
inference(light_normalisation,[status(thm)],[c_5231,c_3932]) ).
tcf(c_5236,plain,
( finite(sK26)
| ~ relation(sK27)
| ~ function(sK27)
| ~ finite(iPr_def_10) ),
inference(superposition,[status(thm)],[c_5233,c_158]) ).
tcf(c_5237,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_5236,c_3938,c_3935,c_3934,c_3936]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU096+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.18/0.44 % Computer : n005.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Thu Sep 24 12:44:17 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.45 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.18/0.49 Running first-order theorem proving
% 0.18/0.49 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
% 0.25/0.51
% 0.25/0.51 % ======== iProver multi-core TPTP/SMT =========
% 0.25/0.51
% 0.25/0.51 % Detected problem language: tptp
% 0.25/0.53 % Proving...
% 2.60/1.43 % SZS status Started for theBenchmark.p
% 2.60/1.43 % SZS status Theorem for theBenchmark.p
% 2.60/1.43
% 2.60/1.43 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.60/1.43
% 2.60/1.43 % ------ iProver source info
% 2.60/1.43
% 2.60/1.43 % git: date: 2026-07-19 20:42:38 +0200
% 2.60/1.43 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.60/1.43 % git: non_committed_changes: false
% 2.60/1.43
% 2.60/1.43 % ------ Parsing...
% 2.60/1.43 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.60/1.43
% 2.60/1.43 % ------ Preprocessing... sup_sim: 0 sf_s rm: 40 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e %
% 2.60/1.43
% 2.60/1.43 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.60/1.43
% 2.60/1.43 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.60/1.43 % ------ Proving...
% 2.60/1.43 % ------ Problem Properties
% 2.60/1.43
% 2.60/1.43 %
% 2.60/1.43 % clauses 80
% 2.60/1.43 % conjectures 5
% 2.60/1.43 % EPR 57
% 2.60/1.43 % Horn 76
% 2.60/1.43 % unary 56
% 2.60/1.43 % binary 16
% 2.60/1.43 % lits 114
% 2.60/1.43 % lits eq 5
% 2.60/1.43 % fd_pure 0
% 2.60/1.43 % fd_pseudo 0
% 2.60/1.43 % fd_cond 1
% 2.60/1.43 % fd_pseudo_cond 1
% 2.60/1.43 % AC symbols 0
% 2.60/1.43
% 2.60/1.43 % ------ Schedule dynamic 5 is on
% 2.60/1.43
% 2.60/1.43 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.60/1.43
% 2.60/1.43
% 2.60/1.43 % ------
% 2.60/1.43 % Current options:
% 2.60/1.43 % ------
% 2.60/1.43
% 2.60/1.43
% 2.60/1.43 %
% 2.60/1.43
% 2.60/1.43 % ------ Proving...
% 2.60/1.43 %
% 2.60/1.43
% 2.60/1.43 % SZS status Theorem for theBenchmark.p
% 2.60/1.43
% 2.60/1.43 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.60/1.43
% 2.60/1.43
%------------------------------------------------------------------------------