%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET992+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 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 02:49:17 PM UTC 2026
% Result : Theorem 19.50s 3.97s
% Output : CNFRefutation 19.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 3
% Syntax : Number of formulae : 61 ( 15 unt; 0 def)
% Number of atoms : 239 ( 106 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 291 ( 113 ~; 126 |; 39 &)
% ( 8 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-2 aty)
% Number of variables : 112 ( 0 sgn 97 !; 15 ?; 23 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_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(f25,conjecture,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( relation_dom(X1) = singleton(X0)
=> relation_rng(X1) = singleton(apply(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_funct_1) ).
fof(f26,negated_conjecture,
~ ! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( relation_dom(X1) = singleton(X0)
=> relation_rng(X1) = singleton(apply(X1,X0)) ) ),
inference(negated_conjecture,[status(cth)],[f25]) ).
fof(f43,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(f44,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,[],[f43]) ).
fof(f52,plain,
? [X0,X1] :
( function(X1)
& relation(X1)
& relation_dom(X1) = singleton(X0)
& relation_rng(X1) != singleton(apply(X1,X0)) ),
inference(ennf_transformation,[],[f26]) ).
fof(f53,plain,
? [X0,X1] :
( function(X1)
& relation(X1)
& relation_dom(X1) = singleton(X0)
& relation_rng(X1) != singleton(apply(X1,X0)) ),
inference(flattening,[],[f52]) ).
fof(f65,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| X2 = X0 )
& ( X0 != X2
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| X2 = X0 )
& ( ~ in(X2,X1)
| X0 != X2 ) )
| X1 = singleton(X0) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f66,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| X0 = X3 )
& ( X0 != X3
| in(X3,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| X2 = X0 )
& ( ~ in(X2,X1)
| X0 != X2 ) )
| X1 = singleton(X0) ) ),
inference(rectify,[],[f65]) ).
fof(f67,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| X0 = X3 )
& ( X0 != X3
| in(X3,X1) ) ) )
& ( ( ( in(sK0(X0,X1),X1)
| sK0(X0,X1) = X0 )
& ( ~ in(sK0(X0,X1),X1)
| sK0(X0,X1) != X0 ) )
| X1 = singleton(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f66]) ).
fof(f68,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,[],[f44]) ).
fof(f69,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,[],[f68]) ).
fof(f70,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))],[f69]) ).
fof(f80,plain,
( function(sK14)
& relation(sK14)
& singleton(sK13) = relation_dom(sK14)
& relation_rng(sK14) != singleton(apply(sK14,sK13)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14]),skolemize(X0,sK13),skolemize(X1,sK14)],[f53]) ).
fof(f86,plain,
! [X3,X0,X1] :
( singleton(X0) != X1
| ~ in(X3,X1)
| X0 = X3 ),
inference(cnf_transformation,[],[f67]) ).
fof(f87,plain,
! [X3,X0,X1] :
( singleton(X0) != X1
| X0 != X3
| in(X3,X1) ),
inference(cnf_transformation,[],[f67]) ).
fof(f88,plain,
! [X0,X1] :
( in(sK0(X0,X1),X1)
| sK0(X0,X1) = X0
| singleton(X0) = X1 ),
inference(cnf_transformation,[],[f67]) ).
fof(f89,plain,
! [X0,X1] :
( ~ in(sK0(X0,X1),X1)
| sK0(X0,X1) != X0
| singleton(X0) = X1 ),
inference(cnf_transformation,[],[f67]) ).
fof(f90,plain,
! [X0,X1,X5] :
( ~ function(X0)
| ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(X5,X1)
| apply(X0,sK3(X0,X5)) = X5 ),
inference(cnf_transformation,[],[f70]) ).
fof(f91,plain,
! [X0,X1,X5] :
( ~ function(X0)
| ~ relation(X0)
| relation_rng(X0) != X1
| ~ in(X5,X1)
| in(sK3(X0,X5),relation_dom(X0)) ),
inference(cnf_transformation,[],[f70]) ).
fof(f92,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,[],[f70]) ).
fof(f124,plain,
function(sK14),
inference(cnf_transformation,[],[f80]) ).
fof(f125,plain,
relation(sK14),
inference(cnf_transformation,[],[f80]) ).
fof(f126,plain,
singleton(sK13) = relation_dom(sK14),
inference(cnf_transformation,[],[f80]) ).
fof(f127,plain,
relation_rng(sK14) != singleton(apply(sK14,sK13)),
inference(cnf_transformation,[],[f80]) ).
fof(f138,plain,
! [X3,X1] :
( singleton(X3) != X1
| in(X3,X1) ),
inference(equality_resolution,[],[f87]) ).
fof(f139,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f138]) ).
fof(f140,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f86]) ).
fof(f141,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,[],[f92]) ).
fof(f142,plain,
! [X0,X6] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X6,relation_dom(X0))
| in(apply(X0,X6),relation_rng(X0)) ),
inference(equality_resolution,[],[f141]) ).
fof(f143,plain,
! [X0,X5] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X5,relation_rng(X0))
| in(sK3(X0,X5),relation_dom(X0)) ),
inference(equality_resolution,[],[f91]) ).
fof(f144,plain,
! [X0,X5] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X5,relation_rng(X0))
| apply(X0,sK3(X0,X5)) = X5 ),
inference(equality_resolution,[],[f90]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( ( singleton(X0) = X1 )
| ~ in(sK0(X0,X1),X1)
| ( sK0(X0,X1) != X0 ) ),
inference(cnf_transformation,[],[f89]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( in(sK0(X0,X1),X1)
| ( singleton(X0) = X1 )
| ( sK0(X0,X1) = X0 ) ),
inference(cnf_transformation,[],[f88]) ).
tcf(c_54,plain,
! [X0: $i] : in(X0,singleton(X0)),
inference(cnf_transformation,[],[f139]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ in(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f140]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( in(apply(X1,X0),relation_rng(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(cnf_transformation,[],[f142]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( in(sK3(X1,X0),relation_dom(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(cnf_transformation,[],[f143]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( ( apply(X1,sK3(X1,X0)) = X0 )
| ~ relation(X1)
| ~ function(X1)
| ~ in(X0,relation_rng(X1)) ),
inference(cnf_transformation,[],[f144]) ).
tcf(c_90,negated_conjecture,
singleton(apply(sK14,sK13)) != relation_rng(sK14),
inference(cnf_transformation,[],[f127]) ).
tcf(c_91,negated_conjecture,
singleton(sK13) = relation_dom(sK14),
inference(cnf_transformation,[],[f126]) ).
tcf(c_92,negated_conjecture,
relation(sK14),
inference(cnf_transformation,[],[f125]) ).
tcf(c_93,negated_conjecture,
function(sK14),
inference(cnf_transformation,[],[f124]) ).
tcf(c_7819,plain,
! [X0: $i,X1: $i] :
( ( singleton(X1) = relation_rng(X0) )
| ( sK0(X1,relation_rng(X0)) = X1 )
| ( apply(X0,sK3(X0,sK0(X1,relation_rng(X0)))) = sK0(X1,relation_rng(X0)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(superposition,[status(thm)],[c_53,c_61]) ).
tcf(c_7831,plain,
! [X0: $i] :
( ( singleton(X0) = relation_rng(sK14) )
| ( sK0(X0,relation_rng(sK14)) = X0 )
| ( apply(sK14,sK3(sK14,sK0(X0,relation_rng(sK14)))) = sK0(X0,relation_rng(sK14)) )
| ~ relation(sK14) ),
inference(superposition,[status(thm)],[c_93,c_7819]) ).
tcf(c_7839,plain,
! [X0: $i] :
( ( singleton(X0) = relation_rng(sK14) )
| ( sK0(X0,relation_rng(sK14)) = X0 )
| ( apply(sK14,sK3(sK14,sK0(X0,relation_rng(sK14)))) = sK0(X0,relation_rng(sK14)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7831,c_92]) ).
tcf(c_8048,plain,
! [X0: $i] :
( ( X0 = sK13 )
| ~ in(X0,relation_dom(sK14)) ),
inference(superposition,[status(thm)],[c_91,c_55]) ).
tcf(c_8056,plain,
in(sK13,relation_dom(sK14)),
inference(superposition,[status(thm)],[c_91,c_54]) ).
tcf(c_9709,plain,
! [X0: $i] :
( ( sK3(sK14,X0) = sK13 )
| ~ relation(sK14)
| ~ function(sK14)
| ~ in(X0,relation_rng(sK14)) ),
inference(superposition,[status(thm)],[c_60,c_8048]) ).
tcf(c_9716,plain,
! [X0: $i] :
( ( sK3(sK14,X0) = sK13 )
| ~ in(X0,relation_rng(sK14)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9709,c_92,c_93]) ).
tcf(c_12152,plain,
! [X0: $i] :
( ( singleton(X0) = relation_rng(sK14) )
| ( sK0(X0,relation_rng(sK14)) = X0 )
| ( sK3(sK14,sK0(X0,relation_rng(sK14))) = sK13 ) ),
inference(superposition,[status(thm)],[c_53,c_9716]) ).
tcf(c_12174,plain,
! [X0: $i] :
( ( singleton(X0) = relation_rng(sK14) )
| ( sK0(X0,relation_rng(sK14)) = X0 )
| ( sK0(X0,relation_rng(sK14)) = apply(sK14,sK13) ) ),
inference(superposition,[status(thm)],[c_12152,c_7839]) ).
tcf(c_12299,plain,
! [X0: $i] :
( ( singleton(X0) = relation_rng(sK14) )
| ( sK0(X0,relation_rng(sK14)) = X0 )
| ( apply(sK14,sK13) != X0 ) ),
inference(equality_factoring,[status(thm)],[c_12174]) ).
tcf(c_12385,plain,
( ( singleton(apply(sK14,sK13)) = relation_rng(sK14) )
| ( sK0(apply(sK14,sK13),relation_rng(sK14)) = apply(sK14,sK13) ) ),
inference(equality_resolution,[status(thm)],[c_12299]) ).
tcf(c_12386,plain,
sK0(apply(sK14,sK13),relation_rng(sK14)) = apply(sK14,sK13),
inference(forward_subsumption_resolution,[status(thm)],[c_12385,c_90]) ).
tcf(c_12422,plain,
( ( singleton(apply(sK14,sK13)) = relation_rng(sK14) )
| ~ in(sK0(apply(sK14,sK13),relation_rng(sK14)),relation_rng(sK14)) ),
inference(superposition,[status(thm)],[c_12386,c_52]) ).
tcf(c_12427,plain,
~ in(sK0(apply(sK14,sK13),relation_rng(sK14)),relation_rng(sK14)),
inference(forward_subsumption_resolution,[status(thm)],[c_12422,c_90]) ).
tcf(c_12428,plain,
~ in(apply(sK14,sK13),relation_rng(sK14)),
inference(demodulation,[status(thm)],[c_12427,c_12386]) ).
tcf(c_12429,plain,
( ~ relation(sK14)
| ~ function(sK14)
| ~ in(sK13,relation_dom(sK14)) ),
inference(superposition,[status(thm)],[c_59,c_12428]) ).
tcf(c_12430,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_12429,c_92,c_93,c_8056]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET992+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.58 % Computer : n006.cluster.edu
% 0.10/0.58 % Model : x86_64 x86_64
% 0.10/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.58 % Memory : 8046.5625MB
% 0.10/0.58 % OS : Linux 6.8.0-71-generic
% 0.10/0.58 % CPULimit : 300
% 0.10/0.58 % WCLimit : 300
% 0.10/0.58 % DateTime : Thu Sep 24 12:31:42 UTC 2026
% 0.10/0.58 % CPUTime :
% 0.10/0.58 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.62 Running first-order theorem proving
% 0.10/0.62 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
% 0.10/0.63
% 0.10/0.63 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.63
% 0.14/0.63 % Detected problem language: tptp
% 0.14/0.64 % Proving...
% 19.50/3.97 % SZS status Started for theBenchmark.p
% 19.50/3.97 % SZS status Theorem for theBenchmark.p
% 19.50/3.97
% 19.50/3.97 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 19.50/3.97
% 19.50/3.97 % ------ iProver source info
% 19.50/3.97
% 19.50/3.97 % git: date: 2026-07-19 20:42:38 +0200
% 19.50/3.97 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 19.50/3.97 % git: non_committed_changes: false
% 19.50/3.97
% 19.50/3.97 % ------ Parsing...
% 19.50/3.97 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 19.50/3.97
% 19.50/3.97 % ------ 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 %
% 19.50/3.97
% 19.50/3.97 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 19.50/3.97
% 19.50/3.97 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 19.50/3.97 % ------ Proving...
% 19.50/3.97 % ------ Problem Properties
% 19.50/3.97
% 19.50/3.97 %
% 19.50/3.97 % clauses 51
% 19.50/3.97 % conjectures 4
% 19.50/3.97 % EPR 21
% 19.50/3.97 % Horn 45
% 19.50/3.97 % unary 22
% 19.50/3.97 % binary 13
% 19.50/3.97 % lits 106
% 19.50/3.97 % lits eq 17
% 19.50/3.97 % fd_pure 0
% 19.50/3.97 % fd_pseudo 0
% 19.50/3.97 % fd_cond 1
% 19.50/3.97 % fd_pseudo_cond 8
% 19.50/3.97 % AC symbols 0
% 19.50/3.97
% 19.50/3.97 % ------ Input Options Time Limit: Unbounded
% 19.50/3.97
% 19.50/3.97
% 19.50/3.97 % ------
% 19.50/3.97 % Current options:
% 19.50/3.97 % ------
% 19.50/3.97
% 19.50/3.97
% 19.50/3.97 %
% 19.50/3.97
% 19.50/3.97 % ------ Proving...
% 19.50/3.97 %
% 19.50/3.97
% 19.50/3.97 % SZS status Theorem for theBenchmark.p
% 19.50/3.97
% 19.50/3.97 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 19.50/3.97
% 19.50/3.97
%------------------------------------------------------------------------------