%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET882+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 : n016.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 02:48:53 PM UTC 2026
% Result : Theorem 1.88s 1.29s
% Output : CNFRefutation 1.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 37 ( 14 unt; 4 def)
% Number of atoms : 120 ( 65 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 113 ( 47 ~; 43 |; 18 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 52 ( 0 sgn 48 !; 4 ?; 9 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f4,axiom,
! [X0,X1,X2] :
( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
<=> ( ( X0 = X1
| in(X1,X2) )
& ~ in(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l39_zfmisc_1) ).
fof(f7,conjecture,
! [X0,X1] :
( X0 != X1
=> set_difference(unordered_pair(X0,X1),singleton(X1)) = singleton(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_zfmisc_1) ).
fof(f8,negated_conjecture,
~ ! [X0,X1] :
( X0 != X1
=> set_difference(unordered_pair(X0,X1),singleton(X1)) = singleton(X0) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f10,plain,
? [X0,X1] :
( X0 != X1
& singleton(X0) != set_difference(unordered_pair(X0,X1),singleton(X1)) ),
inference(ennf_transformation,[],[f8]) ).
fof(f11,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,[],[f3]) ).
fof(f12,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,[],[f11]) ).
fof(f13,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))],[f12]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ( singleton(X0) != set_difference(unordered_pair(X0,X1),X2)
| ( ( X0 = X1
| in(X1,X2) )
& ~ in(X0,X2) ) )
& ( ( X0 != X1
& ~ in(X1,X2) )
| in(X0,X2)
| set_difference(unordered_pair(X0,X1),X2) = singleton(X0) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f15,plain,
! [X0,X1,X2] :
( ( singleton(X0) != set_difference(unordered_pair(X0,X1),X2)
| ( ( X0 = X1
| in(X1,X2) )
& ~ in(X0,X2) ) )
& ( ( X0 != X1
& ~ in(X1,X2) )
| in(X0,X2)
| set_difference(unordered_pair(X0,X1),X2) = singleton(X0) ) ),
inference(flattening,[],[f14]) ).
fof(f18,plain,
( sK3 != sK4
& singleton(sK3) != set_difference(unordered_pair(sK3,sK4),singleton(sK4)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f10]) ).
fof(f21,plain,
! [X3,X0,X1] :
( singleton(X0) != X1
| ~ in(X3,X1)
| X0 = X3 ),
inference(cnf_transformation,[],[f13]) ).
fof(f22,plain,
! [X3,X0,X1] :
( singleton(X0) != X1
| X0 != X3
| in(X3,X1) ),
inference(cnf_transformation,[],[f13]) ).
fof(f28,plain,
! [X2,X0,X1] :
( ~ in(X1,X2)
| in(X0,X2)
| singleton(X0) = set_difference(unordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f15]) ).
fof(f31,plain,
sK3 != sK4,
inference(cnf_transformation,[],[f18]) ).
fof(f32,plain,
singleton(sK3) != set_difference(unordered_pair(sK3,sK4),singleton(sK4)),
inference(cnf_transformation,[],[f18]) ).
fof(f33,plain,
! [X3,X1] :
( singleton(X3) != X1
| in(X3,X1) ),
inference(equality_resolution,[],[f22]) ).
fof(f34,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f33]) ).
fof(f35,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f21]) ).
tcf(c_53,plain,
! [X0: $i] : in(X0,singleton(X0)),
inference(cnf_transformation,[],[f34]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ in(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X1)
| ( set_difference(unordered_pair(X2,X0),X1) = singleton(X2) )
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_61,negated_conjecture,
set_difference(unordered_pair(sK3,sK4),singleton(sK4)) != singleton(sK3),
inference(cnf_transformation,[],[f32]) ).
tcf(c_62,negated_conjecture,
sK3 != sK4,
inference(cnf_transformation,[],[f31]) ).
tcf(c_269,definition,
iPr_def_10 = unordered_pair(sK3,sK4),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_270,definition,
iPr_def_11 = singleton(sK4),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_271,definition,
iPr_def_12 = set_difference(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_272,definition,
iPr_def_13 = singleton(sK3),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_273,negated_conjecture,
sK3 != sK4,
inference(demodulation,[status(thm)],[c_62]) ).
tcf(c_274,negated_conjecture,
iPr_def_12 != iPr_def_13,
inference(demodulation,[status(thm)],[c_61,c_272,c_270,c_269,c_271]) ).
tcf(c_468,plain,
in(sK4,iPr_def_11),
inference(superposition,[status(thm)],[c_270,c_53]) ).
tcf(c_482,plain,
! [X0: $i] :
( ( X0 = sK4 )
| ~ in(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_270,c_54]) ).
tcf(c_608,plain,
! [X0: $i] :
( in(X0,iPr_def_11)
| ( set_difference(unordered_pair(X0,sK4),iPr_def_11) = singleton(X0) ) ),
inference(superposition,[status(thm)],[c_468,c_55]) ).
tcf(c_677,plain,
! [X0: $i] :
( ( X0 = sK4 )
| ( set_difference(unordered_pair(X0,sK4),iPr_def_11) = singleton(X0) ) ),
inference(superposition,[status(thm)],[c_608,c_482]) ).
tcf(c_834,plain,
( ( sK3 = sK4 )
| ( set_difference(iPr_def_10,iPr_def_11) = singleton(sK3) ) ),
inference(superposition,[status(thm)],[c_269,c_677]) ).
tcf(c_838,plain,
( ( iPr_def_12 = iPr_def_13 )
| ( sK3 = sK4 ) ),
inference(light_normalisation,[status(thm)],[c_834,c_271,c_272]) ).
tcf(c_839,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_838,c_274,c_273]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET882+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n016.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 12:23:57 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 1.88/1.29 % SZS status Started for theBenchmark.p
% 1.88/1.29 % SZS status Theorem for theBenchmark.p
% 1.88/1.29
% 1.88/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.88/1.29
% 1.88/1.29 % ------ iProver source info
% 1.88/1.29
% 1.88/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 1.88/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.88/1.29 % git: non_committed_changes: false
% 1.88/1.29
% 1.88/1.29 % ------ Parsing...
% 1.88/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.88/1.29
% 1.88/1.29 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 1.88/1.29
% 1.88/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.88/1.29
% 1.88/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.88/1.29 % ------ Proving...
% 1.88/1.29 % ------ Problem Properties
% 1.88/1.29
% 1.88/1.29 %
% 1.88/1.29 % clauses 17
% 1.88/1.29 % conjectures 2
% 1.88/1.29 % EPR 4
% 1.88/1.29 % Horn 13
% 1.88/1.29 % unary 9
% 1.88/1.29 % binary 4
% 1.88/1.29 % lits 29
% 1.88/1.29 % lits eq 18
% 1.88/1.29 % fd_pure 0
% 1.88/1.29 % fd_pseudo 0
% 1.88/1.29 % fd_cond 0
% 1.88/1.29 % fd_pseudo_cond 3
% 1.88/1.29 % AC symbols 0
% 1.88/1.29
% 1.88/1.29 % ------ Schedule dynamic 5 is on
% 1.88/1.29
% 1.88/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.88/1.29
% 1.88/1.29
% 1.88/1.29 % ------
% 1.88/1.29 % Current options:
% 1.88/1.29 % ------
% 1.88/1.29
% 1.88/1.29
% 1.88/1.29 %
% 1.88/1.29
% 1.88/1.29 % ------ Proving...
% 1.88/1.29 %
% 1.88/1.29
% 1.88/1.29 % SZS status Theorem for theBenchmark.p
% 1.88/1.29
% 1.88/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.88/1.29
% 1.88/1.29
%------------------------------------------------------------------------------