%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET997+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 : n014.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 02:49:17 PM UTC 2026
% Result : Theorem 3.90s 1.27s
% Output : CNFRefutation 3.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 50 ( 13 unt; 2 def)
% Number of atoms : 214 ( 39 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 227 ( 87 ~; 83 |; 43 &)
% ( 8 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 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 : 8 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-2 aty)
% Number of variables : 93 ( 0 sgn 76 !; 17 ?; 11 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f5,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(f24,conjecture,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( ! [X2] :
~ ( ! [X3] :
~ ( X2 = apply(X1,X3)
& in(X3,relation_dom(X1)) )
& in(X2,X0) )
=> subset(X0,relation_rng(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_funct_1) ).
fof(f25,negated_conjecture,
~ ! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( ! [X2] :
~ ( ! [X3] :
~ ( X2 = apply(X1,X3)
& in(X3,relation_dom(X1)) )
& in(X2,X0) )
=> subset(X0,relation_rng(X1)) ) ),
inference(negated_conjecture,[status(cth)],[f24]) ).
fof(f40,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f41,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,[],[f5]) ).
fof(f42,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,[],[f41]) ).
fof(f50,plain,
? [X0,X1] :
( function(X1)
& relation(X1)
& ! [X2] :
( ? [X3] :
( X2 = apply(X1,X3)
& in(X3,relation_dom(X1)) )
| ~ in(X2,X0) )
& ~ subset(X0,relation_rng(X1)) ),
inference(ennf_transformation,[],[f25]) ).
fof(f51,plain,
? [X0,X1] :
( function(X1)
& relation(X1)
& ! [X2] :
( ? [X3] :
( X2 = apply(X1,X3)
& in(X3,relation_dom(X1)) )
| ~ in(X2,X0) )
& ~ subset(X0,relation_rng(X1)) ),
inference(flattening,[],[f50]) ).
fof(f61,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(nnf_transformation,[],[f40]) ).
fof(f62,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(rectify,[],[f61]) ).
fof(f63,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK0(X0,X1),X0)
& ~ in(sK0(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f62]) ).
fof(f64,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,[],[f42]) ).
fof(f65,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,[],[f64]) ).
fof(f66,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ! [X1] :
( ( relation_rng(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ( apply(X0,sK3(X0,X5)) = X5
& in(sK3(X0,X5),relation_dom(X0)) ) )
& ( ! [X6] :
( apply(X0,X6) != X5
| ~ in(X6,relation_dom(X0)) )
| in(X5,X1) ) ) )
& ( ( ( in(sK1(X0,X1),X1)
| ( sK1(X0,X1) = apply(X0,sK2(X0,X1))
& in(sK2(X0,X1),relation_dom(X0)) ) )
& ( ~ in(sK1(X0,X1),X1)
| ! [X3] :
( apply(X0,X3) != sK1(X0,X1)
| ~ in(X3,relation_dom(X0)) ) ) )
| X1 = relation_rng(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X2,sK1(X0,X1)),skolemize(X4,sK2(X0,X1)),skolemize(X7,sK3(X0,X5))],[f65]) ).
fof(f76,plain,
( function(sK14)
& relation(sK14)
& ! [X2] :
( ( apply(sK14,sK15(X2)) = X2
& in(sK15(X2),relation_dom(sK14)) )
| ~ in(X2,sK13) )
& ~ subset(sK13,relation_rng(sK14)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14,sK15]),skolemize(X0,sK13),skolemize(X1,sK14),skolemize(X3,sK15(X2))],[f51]) ).
fof(f82,plain,
! [X0,X1] :
( in(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f83,plain,
! [X0,X1] :
( ~ in(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f86,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,[],[f66]) ).
fof(f117,plain,
function(sK14),
inference(cnf_transformation,[],[f76]) ).
fof(f118,plain,
relation(sK14),
inference(cnf_transformation,[],[f76]) ).
fof(f119,plain,
! [X2] :
( apply(sK14,sK15(X2)) = X2
| ~ in(X2,sK13) ),
inference(cnf_transformation,[],[f76]) ).
fof(f120,plain,
! [X2] :
( in(sK15(X2),relation_dom(sK14))
| ~ in(X2,sK13) ),
inference(cnf_transformation,[],[f76]) ).
fof(f121,plain,
~ subset(sK13,relation_rng(sK14)),
inference(cnf_transformation,[],[f76]) ).
fof(f131,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,[],[f86]) ).
fof(f132,plain,
! [X0,X6] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X6,relation_dom(X0))
| in(apply(X0,X6),relation_rng(X0)) ),
inference(equality_resolution,[],[f131]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f83]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f82]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( in(apply(X1,X0),relation_rng(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f132]) ).
tcf(c_88,negated_conjecture,
~ subset(sK13,relation_rng(sK14)),
inference(cnf_transformation,[],[f121]) ).
tcf(c_89,negated_conjecture,
! [X0: $i] :
( in(sK15(X0),relation_dom(sK14))
| ~ in(X0,sK13) ),
inference(cnf_transformation,[],[f120]) ).
tcf(c_90,negated_conjecture,
! [X0: $i] :
( ( apply(sK14,sK15(X0)) = X0 )
| ~ in(X0,sK13) ),
inference(cnf_transformation,[],[f119]) ).
tcf(c_91,negated_conjecture,
relation(sK14),
inference(cnf_transformation,[],[f118]) ).
tcf(c_92,negated_conjecture,
function(sK14),
inference(cnf_transformation,[],[f117]) ).
tcf(c_4468,definition,
iPr_def_10 = relation_dom(sK14),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_4469,definition,
iPr_def_11 = relation_rng(sK14),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_4470,negated_conjecture,
function(sK14),
inference(demodulation,[status(thm)],[c_92]) ).
tcf(c_4471,negated_conjecture,
relation(sK14),
inference(demodulation,[status(thm)],[c_91]) ).
tcf(c_4472,negated_conjecture,
! [X0: $i] :
( ( apply(sK14,sK15(X0)) = X0 )
| ~ in(X0,sK13) ),
inference(demodulation,[status(thm)],[c_90]) ).
tcf(c_4473,negated_conjecture,
! [X0: $i] :
( in(sK15(X0),iPr_def_10)
| ~ in(X0,sK13) ),
inference(demodulation,[status(thm)],[c_89,c_4468]) ).
tcf(c_4474,negated_conjecture,
~ subset(sK13,iPr_def_11),
inference(demodulation,[status(thm)],[c_88,c_4469]) ).
tcf(c_5551,plain,
! [X0: $i] :
( subset(sK13,X0)
| ( apply(sK14,sK15(sK0(sK13,X0))) = sK0(sK13,X0) ) ),
inference(superposition,[status(thm)],[c_53,c_4472]) ).
tcf(c_5568,plain,
apply(sK14,sK15(sK0(sK13,iPr_def_11))) = sK0(sK13,iPr_def_11),
inference(superposition,[status(thm)],[c_5551,c_4474]) ).
tcf(c_5878,plain,
( in(sK0(sK13,iPr_def_11),relation_rng(sK14))
| ~ relation(sK14)
| ~ function(sK14)
| ~ in(sK15(sK0(sK13,iPr_def_11)),relation_dom(sK14)) ),
inference(superposition,[status(thm)],[c_5568,c_58]) ).
tcf(c_5910,plain,
( in(sK0(sK13,iPr_def_11),iPr_def_11)
| ~ relation(sK14)
| ~ function(sK14)
| ~ in(sK15(sK0(sK13,iPr_def_11)),iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_5878,c_4468,c_4469]) ).
tcf(c_5911,plain,
( in(sK0(sK13,iPr_def_11),iPr_def_11)
| ~ in(sK15(sK0(sK13,iPr_def_11)),iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5910,c_4471,c_4470]) ).
tcf(c_5925,plain,
( subset(sK13,iPr_def_11)
| ~ in(sK0(sK13,iPr_def_11),iPr_def_11) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_5926,plain,
( subset(sK13,iPr_def_11)
| in(sK0(sK13,iPr_def_11),sK13) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_6216,plain,
( in(sK15(sK0(sK13,iPr_def_11)),iPr_def_10)
| ~ in(sK0(sK13,iPr_def_11),sK13) ),
inference(instantiation,[status(thm)],[c_4473]) ).
tcf(c_6217,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_6216,c_5926,c_5925,c_5911,c_4474]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET997+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n014.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Thu Sep 24 12:32:33 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.39 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
% 0.12/0.40
% 0.12/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.40
% 0.12/0.40 % Detected problem language: tptp
% 0.12/0.41 % Proving...
% 3.90/1.27 % SZS status Started for theBenchmark.p
% 3.90/1.27 % SZS status Theorem for theBenchmark.p
% 3.90/1.27
% 3.90/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.90/1.27
% 3.90/1.27 % ------ iProver source info
% 3.90/1.27
% 3.90/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 3.90/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.90/1.27 % git: non_committed_changes: false
% 3.90/1.27
% 3.90/1.27 % ------ Parsing...
% 3.90/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.90/1.27
% 3.90/1.27 % ------ Preprocessing... sup_sim: 0 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 %
% 3.90/1.27
% 3.90/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.90/1.27
% 3.90/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.90/1.27 % ------ Proving...
% 3.90/1.27 % ------ Problem Properties
% 3.90/1.27
% 3.90/1.27 %
% 3.90/1.27 % clauses 52
% 3.90/1.27 % conjectures 5
% 3.90/1.27 % EPR 26
% 3.90/1.27 % Horn 47
% 3.90/1.27 % unary 21
% 3.90/1.27 % binary 18
% 3.90/1.27 % lits 106
% 3.90/1.27 % lits eq 11
% 3.90/1.27 % fd_pure 0
% 3.90/1.27 % fd_pseudo 0
% 3.90/1.27 % fd_cond 1
% 3.90/1.27 % fd_pseudo_cond 4
% 3.90/1.27 % AC symbols 0
% 3.90/1.27
% 3.90/1.27 % ------ Schedule dynamic 5 is on
% 3.90/1.27
% 3.90/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.90/1.27
% 3.90/1.27
% 3.90/1.27 % ------
% 3.90/1.27 % Current options:
% 3.90/1.27 % ------
% 3.90/1.27
% 3.90/1.27
% 3.90/1.27 %
% 3.90/1.27
% 3.90/1.27 % ------ Proving...
% 3.90/1.27 %
% 3.90/1.27
% 3.90/1.27 % SZS status Theorem for theBenchmark.p
% 3.90/1.27
% 3.90/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.90/1.27
% 3.90/1.27
%------------------------------------------------------------------------------