%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET991+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 : n006.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 02:49:16 PM UTC 2026
% Result : Theorem 2.52s 1.28s
% Output : CNFRefutation 2.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 33 ( 16 unt; 3 def)
% Number of atoms : 139 ( 30 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 155 ( 59 ~; 55 |; 30 &)
% ( 6 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 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 : 8 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 52 ( 0 sgn 39 !; 13 ?; 2 :)
% Comments :
%------------------------------------------------------------------------------
fof(f30,conjecture,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( in(X0,relation_dom(X1))
=> in(apply(X1,X0),relation_rng(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_funct_1) ).
fof(f31,negated_conjecture,
~ ! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( in(X0,relation_dom(X1))
=> in(apply(X1,X0),relation_rng(X1)) ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
fof(f32,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_funct_1) ).
fof(f57,plain,
? [X0,X1] :
( function(X1)
& relation(X1)
& in(X0,relation_dom(X1))
& ~ in(apply(X1,X0),relation_rng(X1)) ),
inference(ennf_transformation,[],[f31]) ).
fof(f58,plain,
? [X0,X1] :
( function(X1)
& relation(X1)
& in(X0,relation_dom(X1))
& ~ in(apply(X1,X0),relation_rng(X1)) ),
inference(flattening,[],[f57]) ).
fof(f59,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) ) ) ),
inference(ennf_transformation,[],[f32]) ).
fof(f60,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) ) ) ),
inference(flattening,[],[f59]) ).
fof(f70,plain,
( function(sK10)
& relation(sK10)
& in(sK9,relation_dom(sK10))
& ~ in(apply(sK10,sK9),relation_rng(sK10)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10]),skolemize(X0,sK9),skolemize(X1,sK10)],[f58]) ).
fof(f71,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| ? [X3] :
( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) )
& ( ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) )
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X3] :
( X2 = apply(X0,X3)
& in(X3,relation_dom(X0)) ) )
& ( ~ in(X2,X1)
| ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) ) ) )
| X1 = relation_rng(X0) ) ) ),
inference(nnf_transformation,[],[f60]) ).
fof(f72,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ? [X7] :
( apply(X0,X7) = X5
& in(X7,relation_dom(X0)) ) )
& ( ! [X6] :
( apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0)) )
| in(X5,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X4] :
( apply(X0,X4) = X2
& in(X4,relation_dom(X0)) ) )
& ( ~ in(X2,X1)
| ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) ) ) )
| X1 = relation_rng(X0) ) ) ),
inference(rectify,[],[f71]) ).
fof(f73,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ( apply(X0,sK13(X0,X5)) = X5
& in(sK13(X0,X5),relation_dom(X0)) ) )
& ( ! [X6] :
( apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0)) )
| in(X5,X1) ) ) )
& ( ( ( in(sK11(X0,X1),X1)
| ( sK11(X0,X1) = apply(X0,sK12(X0,X1))
& in(sK12(X0,X1),relation_dom(X0)) ) )
& ( ~ in(sK11(X0,X1),X1)
| ! [X3] :
( apply(X0,X3) != sK11(X0,X1)
| ~ in(X3,relation_dom(X0)) ) ) )
| X1 = relation_rng(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12,sK13]),skolemize(X2,sK11(X0,X1)),skolemize(X4,sK12(X0,X1)),skolemize(X7,sK13(X0,X5))],[f72]) ).
fof(f112,plain,
function(sK10),
inference(cnf_transformation,[],[f70]) ).
fof(f113,plain,
relation(sK10),
inference(cnf_transformation,[],[f70]) ).
fof(f114,plain,
in(sK9,relation_dom(sK10)),
inference(cnf_transformation,[],[f70]) ).
fof(f115,plain,
~ in(apply(sK10,sK9),relation_rng(sK10)),
inference(cnf_transformation,[],[f70]) ).
fof(f118,plain,
! [X0,X1,X6,X5] :
( ~ function(X0)
| ~ relation(X0)
| relation_rng(X0) != X1
| apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0))
| in(X5,X1) ),
inference(cnf_transformation,[],[f73]) ).
fof(f122,plain,
! [X0,X1,X6] :
( ~ function(X0)
| ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(X6,relation_dom(X0))
| in(apply(X0,X6),X1) ),
inference(equality_resolution,[],[f118]) ).
fof(f123,plain,
! [X0,X6] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X6,relation_dom(X0))
| in(apply(X0,X6),relation_rng(X0)) ),
inference(equality_resolution,[],[f122]) ).
tcf(c_87,negated_conjecture,
~ in(apply(sK10,sK9),relation_rng(sK10)),
inference(cnf_transformation,[],[f115]) ).
tcf(c_88,negated_conjecture,
in(sK9,relation_dom(sK10)),
inference(cnf_transformation,[],[f114]) ).
tcf(c_89,negated_conjecture,
relation(sK10),
inference(cnf_transformation,[],[f113]) ).
tcf(c_90,negated_conjecture,
function(sK10),
inference(cnf_transformation,[],[f112]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i] :
( in(apply(X1,X0),relation_rng(X1))
| ~ function(X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f123]) ).
tcf(c_3491,definition,
iPr_def_10 = relation_dom(sK10),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_3492,definition,
iPr_def_11 = apply(sK10,sK9),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_3493,definition,
iPr_def_12 = relation_rng(sK10),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_3494,negated_conjecture,
function(sK10),
inference(demodulation,[status(thm)],[c_90]) ).
tcf(c_3495,negated_conjecture,
relation(sK10),
inference(demodulation,[status(thm)],[c_89]) ).
tcf(c_3496,negated_conjecture,
in(sK9,iPr_def_10),
inference(demodulation,[status(thm)],[c_88,c_3491]) ).
tcf(c_3497,negated_conjecture,
~ in(iPr_def_11,iPr_def_12),
inference(demodulation,[status(thm)],[c_87,c_3493,c_3492]) ).
tcf(c_4304,plain,
( in(iPr_def_11,relation_rng(sK10))
| ~ function(sK10)
| ~ relation(sK10)
| ~ in(sK9,relation_dom(sK10)) ),
inference(superposition,[status(thm)],[c_3492,c_94]) ).
tcf(c_4314,plain,
( in(iPr_def_11,iPr_def_12)
| ~ function(sK10)
| ~ relation(sK10)
| ~ in(sK9,iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_4304,c_3491,c_3493]) ).
tcf(c_4315,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4314,c_3497,c_3494,c_3495,c_3496]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET991+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.38 % Computer : n006.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Thu Sep 24 12:31:56 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.42 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
% 0.11/0.43
% 0.11/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.43
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 2.52/1.28 % SZS status Started for theBenchmark.p
% 2.52/1.28 % SZS status Theorem for theBenchmark.p
% 2.52/1.28
% 2.52/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.52/1.28
% 2.52/1.28 % ------ iProver source info
% 2.52/1.28
% 2.52/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 2.52/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.52/1.28 % git: non_committed_changes: false
% 2.52/1.28
% 2.52/1.28 % ------ Parsing...
% 2.52/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.52/1.28
% 2.52/1.28 % ------ 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 %
% 2.52/1.28
% 2.52/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.52/1.28
% 2.52/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.52/1.28 % ------ Proving...
% 2.52/1.28 % ------ Problem Properties
% 2.52/1.28
% 2.52/1.28 %
% 2.52/1.28 % clauses 47
% 2.52/1.28 % conjectures 4
% 2.52/1.28 % EPR 23
% 2.52/1.28 % Horn 43
% 2.52/1.28 % unary 23
% 2.52/1.28 % binary 12
% 2.52/1.28 % lits 93
% 2.52/1.28 % lits eq 11
% 2.52/1.28 % fd_pure 0
% 2.52/1.28 % fd_pseudo 0
% 2.52/1.28 % fd_cond 1
% 2.52/1.28 % fd_pseudo_cond 4
% 2.52/1.28 % AC symbols 0
% 2.52/1.28
% 2.52/1.28 % ------ Schedule dynamic 5 is on
% 2.52/1.28
% 2.52/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.52/1.28
% 2.52/1.28
% 2.52/1.28 % ------
% 2.52/1.28 % Current options:
% 2.52/1.28 % ------
% 2.52/1.28
% 2.52/1.28
% 2.52/1.28 %
% 2.52/1.28
% 2.52/1.28 % ------ Proving...
% 2.52/1.28 %
% 2.52/1.28
% 2.52/1.28 % SZS status Theorem for theBenchmark.p
% 2.52/1.28
% 2.52/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.52/1.28
% 2.52/1.28
%------------------------------------------------------------------------------