%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU062+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 02:55:11 PM UTC 2026
% Result : Theorem 2.92s 1.31s
% Output : CNFRefutation 2.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 36 ( 11 unt; 1 def)
% Number of atoms : 102 ( 19 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 100 ( 43 ~; 32 |; 15 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 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 : 6 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 54 ( 0 sgn 48 !; 6 ?; 11 :)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f25,axiom,
! [X0,X1] :
( relation(X1)
=> ( in(X0,relation_rng(X1))
<=> relation_inverse_image(X1,singleton(X0)) != empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t142_funct_1) ).
fof(f26,conjecture,
! [X0,X1] :
( relation(X1)
=> ( ! [X2] :
~ ( relation_inverse_image(X1,singleton(X2)) = empty_set
& in(X2,X0) )
=> subset(X0,relation_rng(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t143_funct_1) ).
fof(f27,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> ( ! [X2] :
~ ( relation_inverse_image(X1,singleton(X2)) = empty_set
& in(X2,X0) )
=> subset(X0,relation_rng(X1)) ) ),
inference(negated_conjecture,[status(cth)],[f26]) ).
fof(f46,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f51,plain,
! [X0,X1] :
( ~ relation(X1)
| ( in(X0,relation_rng(X1))
<=> relation_inverse_image(X1,singleton(X0)) != empty_set ) ),
inference(ennf_transformation,[],[f25]) ).
fof(f52,plain,
? [X0,X1] :
( relation(X1)
& ! [X2] :
( empty_set != relation_inverse_image(X1,singleton(X2))
| ~ in(X2,X0) )
& ~ subset(X0,relation_rng(X1)) ),
inference(ennf_transformation,[],[f27]) ).
fof(f53,plain,
? [X0,X1] :
( relation(X1)
& ! [X2] :
( empty_set != relation_inverse_image(X1,singleton(X2))
| ~ in(X2,X0) )
& ~ subset(X0,relation_rng(X1)) ),
inference(flattening,[],[f52]) ).
fof(f63,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,[],[f46]) ).
fof(f64,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,[],[f63]) ).
fof(f65,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))],[f64]) ).
fof(f77,plain,
! [X0,X1] :
( ~ relation(X1)
| ( ( ~ in(X0,relation_rng(X1))
| relation_inverse_image(X1,singleton(X0)) != empty_set )
& ( empty_set = relation_inverse_image(X1,singleton(X0))
| in(X0,relation_rng(X1)) ) ) ),
inference(nnf_transformation,[],[f51]) ).
fof(f78,plain,
( relation(sK13)
& ! [X2] :
( empty_set != relation_inverse_image(sK13,singleton(X2))
| ~ in(X2,sK12) )
& ~ subset(sK12,relation_rng(sK13)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13]),skolemize(X0,sK12),skolemize(X1,sK13)],[f53]) ).
fof(f86,plain,
! [X0,X1] :
( in(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f65]) ).
fof(f87,plain,
! [X0,X1] :
( ~ in(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f65]) ).
fof(f119,plain,
! [X0,X1] :
( ~ relation(X1)
| empty_set = relation_inverse_image(X1,singleton(X0))
| in(X0,relation_rng(X1)) ),
inference(cnf_transformation,[],[f77]) ).
fof(f120,plain,
relation(sK13),
inference(cnf_transformation,[],[f78]) ).
fof(f121,plain,
! [X2] :
( empty_set != relation_inverse_image(sK13,singleton(X2))
| ~ in(X2,sK12) ),
inference(cnf_transformation,[],[f78]) ).
fof(f122,plain,
~ subset(sK12,relation_rng(sK13)),
inference(cnf_transformation,[],[f78]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f87]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f86]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i] :
( in(X1,relation_rng(X0))
| ( relation_inverse_image(X0,singleton(X1)) = empty_set )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f119]) ).
tcf(c_87,negated_conjecture,
~ subset(sK12,relation_rng(sK13)),
inference(cnf_transformation,[],[f122]) ).
tcf(c_88,negated_conjecture,
! [X0: $i] :
( ~ in(X0,sK12)
| ( relation_inverse_image(sK13,singleton(X0)) != empty_set ) ),
inference(cnf_transformation,[],[f121]) ).
tcf(c_89,negated_conjecture,
relation(sK13),
inference(cnf_transformation,[],[f120]) ).
tcf(c_2025,definition,
iPr_def_10 = relation_rng(sK13),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_2026,negated_conjecture,
relation(sK13),
inference(demodulation,[status(thm)],[c_89]) ).
tcf(c_2027,negated_conjecture,
! [X0: $i] :
( ~ in(X0,sK12)
| ( relation_inverse_image(sK13,singleton(X0)) != empty_set ) ),
inference(demodulation,[status(thm)],[c_88]) ).
tcf(c_2028,negated_conjecture,
~ subset(sK12,iPr_def_10),
inference(demodulation,[status(thm)],[c_87,c_2025]) ).
tcf(c_2933,plain,
! [X0: $i] :
( in(X0,iPr_def_10)
| ( relation_inverse_image(sK13,singleton(X0)) = empty_set )
| ~ relation(sK13) ),
inference(superposition,[status(thm)],[c_2025,c_85]) ).
tcf(c_2943,plain,
! [X0: $i] :
( in(X0,iPr_def_10)
| ( relation_inverse_image(sK13,singleton(X0)) = empty_set ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2933,c_2026]) ).
tcf(c_3018,plain,
! [X0: $i] :
( subset(X0,iPr_def_10)
| ( relation_inverse_image(sK13,singleton(sK0(X0,iPr_def_10))) = empty_set ) ),
inference(superposition,[status(thm)],[c_2943,c_52]) ).
tcf(c_3067,plain,
relation_inverse_image(sK13,singleton(sK0(sK12,iPr_def_10))) = empty_set,
inference(superposition,[status(thm)],[c_3018,c_2028]) ).
tcf(c_3073,plain,
~ in(sK0(sK12,iPr_def_10),sK12),
inference(superposition,[status(thm)],[c_3067,c_2027]) ).
tcf(c_3078,plain,
subset(sK12,iPr_def_10),
inference(superposition,[status(thm)],[c_53,c_3073]) ).
tcf(c_3079,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3078,c_2028]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU062+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n006.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 12:40:27 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.44 Running first-order theorem proving
% 0.10/0.44 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
% 0.10/0.45
% 0.10/0.45 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.45
% 0.10/0.45 % Detected problem language: tptp
% 0.10/0.46 % Proving...
% 2.92/1.31 % SZS status Started for theBenchmark.p
% 2.92/1.31 % SZS status Theorem for theBenchmark.p
% 2.92/1.31
% 2.92/1.31 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.92/1.31
% 2.92/1.31 % ------ iProver source info
% 2.92/1.31
% 2.92/1.31 % git: date: 2026-07-19 20:42:38 +0200
% 2.92/1.31 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.92/1.31 % git: non_committed_changes: false
% 2.92/1.31
% 2.92/1.31 % ------ Parsing...
% 2.92/1.31 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.92/1.31
% 2.92/1.31 % ------ Preprocessing... sup_sim: 0 sf_s rm: 6 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 2.92/1.31
% 2.92/1.31 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.92/1.31
% 2.92/1.31 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.92/1.31 % ------ Proving...
% 2.92/1.31 % ------ Problem Properties
% 2.92/1.31
% 2.92/1.31 %
% 2.92/1.31 % clauses 44
% 2.92/1.31 % conjectures 3
% 2.92/1.31 % EPR 26
% 2.92/1.31 % Horn 40
% 2.92/1.31 % unary 22
% 2.92/1.31 % binary 14
% 2.92/1.31 % lits 74
% 2.92/1.31 % lits eq 6
% 2.92/1.31 % fd_pure 0
% 2.92/1.31 % fd_pseudo 0
% 2.92/1.31 % fd_cond 1
% 2.92/1.31 % fd_pseudo_cond 1
% 2.92/1.31 % AC symbols 0
% 2.92/1.31
% 2.92/1.31 % ------ Schedule dynamic 5 is on
% 2.92/1.31
% 2.92/1.31 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.92/1.31
% 2.92/1.31
% 2.92/1.31 % ------
% 2.92/1.31 % Current options:
% 2.92/1.31 % ------
% 2.92/1.31
% 2.92/1.31
% 2.92/1.31 %
% 2.92/1.31
% 2.92/1.31 % ------ Proving...
% 2.92/1.31 %
% 2.92/1.31
% 2.92/1.31 % SZS status Theorem for theBenchmark.p
% 2.92/1.31
% 2.92/1.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.92/1.31
% 2.92/1.31
%------------------------------------------------------------------------------