%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET927+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n013.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 02:49:08 PM UTC 2026
% Result : Theorem 2.05s 1.30s
% Output : CNFRefutation 2.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 51 ( 14 unt; 3 def)
% Number of atoms : 149 ( 73 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 149 ( 61 ~; 64 |; 19 &)
% ( 3 <=>; 1 =>; 0 <=; 1 <~>)
% 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 : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 58 ( 0 sgn 49 !; 9 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f5,conjecture,
! [X0,X1,X2] :
( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
<=> ( ( X0 = X1
| in(X1,X2) )
& ~ in(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_zfmisc_1) ).
fof(f6,negated_conjecture,
~ ! [X0,X1,X2] :
( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
<=> ( ( X0 = X1
| in(X1,X2) )
& ~ in(X0,X2) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f7,axiom,
! [X0,X1,X2] :
( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
<=> ( ( X0 = X1
| in(X1,X2) )
& ~ in(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l39_zfmisc_1) ).
fof(f8,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f9,plain,
? [X0,X1,X2] :
( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
<~> ( ( X0 = X1
| in(X1,X2) )
& ~ in(X0,X2) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f12,plain,
? [X0,X1,X2] :
( ( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
| ( ( X0 = X1
| in(X1,X2) )
& ~ in(X0,X2) ) )
& ( set_difference(unordered_pair(X0,X1),X2) != singleton(X0)
| ( X0 != X1
& ~ in(X1,X2) )
| in(X0,X2) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f13,plain,
? [X0,X1,X2] :
( ( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
| ( ( X0 = X1
| in(X1,X2) )
& ~ in(X0,X2) ) )
& ( set_difference(unordered_pair(X0,X1),X2) != singleton(X0)
| ( X0 != X1
& ~ in(X1,X2) )
| in(X0,X2) ) ),
inference(flattening,[],[f12]) ).
fof(f14,plain,
( ( set_difference(unordered_pair(sK2,sK3),sK4) = singleton(sK2)
| ( ( sK2 = sK3
| in(sK3,sK4) )
& ~ in(sK2,sK4) ) )
& ( set_difference(unordered_pair(sK2,sK3),sK4) != singleton(sK2)
| ( sK2 != sK3
& ~ in(sK3,sK4) )
| in(sK2,sK4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f13]) ).
fof(f15,plain,
! [X0,X1,X2] :
( ( set_difference(unordered_pair(X0,X1),X2) != singleton(X0)
| ( ( 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,[],[f7]) ).
fof(f16,plain,
! [X0,X1,X2] :
( ( set_difference(unordered_pair(X0,X1),X2) != singleton(X0)
| ( ( 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,[],[f15]) ).
fof(f18,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f8]) ).
fof(f21,plain,
( set_difference(unordered_pair(sK2,sK3),sK4) = singleton(sK2)
| sK2 = sK3
| in(sK3,sK4) ),
inference(cnf_transformation,[],[f14]) ).
fof(f22,plain,
( set_difference(unordered_pair(sK2,sK3),sK4) = singleton(sK2)
| ~ in(sK2,sK4) ),
inference(cnf_transformation,[],[f14]) ).
fof(f23,plain,
( set_difference(unordered_pair(sK2,sK3),sK4) != singleton(sK2)
| sK2 != sK3
| in(sK2,sK4) ),
inference(cnf_transformation,[],[f14]) ).
fof(f24,plain,
( set_difference(unordered_pair(sK2,sK3),sK4) != singleton(sK2)
| ~ in(sK3,sK4)
| in(sK2,sK4) ),
inference(cnf_transformation,[],[f14]) ).
fof(f25,plain,
! [X2,X0,X1] :
( set_difference(unordered_pair(X0,X1),X2) != singleton(X0)
| X0 = X1
| in(X1,X2) ),
inference(cnf_transformation,[],[f16]) ).
fof(f26,plain,
! [X2,X0,X1] :
( set_difference(unordered_pair(X0,X1),X2) != singleton(X0)
| ~ in(X0,X2) ),
inference(cnf_transformation,[],[f16]) ).
fof(f27,plain,
! [X2,X0,X1] :
( X0 != X1
| in(X0,X2)
| set_difference(unordered_pair(X0,X1),X2) = singleton(X0) ),
inference(cnf_transformation,[],[f16]) ).
fof(f28,plain,
! [X2,X0,X1] :
( ~ in(X1,X2)
| in(X0,X2)
| set_difference(unordered_pair(X0,X1),X2) = singleton(X0) ),
inference(cnf_transformation,[],[f16]) ).
fof(f29,plain,
! [X2,X1] :
( in(X1,X2)
| set_difference(unordered_pair(X1,X1),X2) = singleton(X1) ),
inference(equality_resolution,[],[f27]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_53,negated_conjecture,
( in(sK2,sK4)
| ~ in(sK3,sK4)
| ( set_difference(unordered_pair(sK2,sK3),sK4) != singleton(sK2) ) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_54,negated_conjecture,
( in(sK2,sK4)
| ( sK2 != sK3 )
| ( set_difference(unordered_pair(sK2,sK3),sK4) != singleton(sK2) ) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_55,negated_conjecture,
( ( set_difference(unordered_pair(sK2,sK3),sK4) = singleton(sK2) )
| ~ in(sK2,sK4) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_56,negated_conjecture,
( in(sK3,sK4)
| ( sK2 = sK3 )
| ( set_difference(unordered_pair(sK2,sK3),sK4) = singleton(sK2) ) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_57,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_58,plain,
! [X0: $i,X1: $i] :
( in(X0,X1)
| ( set_difference(unordered_pair(X0,X0),X1) = singleton(X0) ) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X0,X2)
| ( set_difference(unordered_pair(X0,X1),X2) != singleton(X0) ) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,X2)
| ( X0 = X1 )
| ( set_difference(unordered_pair(X0,X1),X2) != singleton(X0) ) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_81,plain,
~ in(sK2,sK4),
inference(forward_subsumption_resolution,[status(thm)],[c_55,c_59]) ).
tcf(c_85,plain,
( ~ in(sK3,sK4)
| ( set_difference(unordered_pair(sK2,sK3),sK4) != singleton(sK2) ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_53,c_81]) ).
tcf(c_86,plain,
( ( sK2 != sK3 )
| ( set_difference(unordered_pair(sK2,sK3),sK4) != singleton(sK2) ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_54,c_81]) ).
tcf(c_102,plain,
( in(sK3,sK4)
| ( sK2 = sK3 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_56,c_60]) ).
tcf(c_168,plain,
set_difference(unordered_pair(sK2,sK3),sK4) != singleton(sK2),
inference(global_subsumption_just,[status(thm)],[c_86,c_53,c_54,c_81,c_102]) ).
tcf(c_170,plain,
set_difference(unordered_pair(sK2,sK3),sK4) != singleton(sK2),
inference(global_subsumption_just,[status(thm)],[c_85,c_53,c_54,c_81,c_102]) ).
tcf(c_310,definition,
iPr_def_10 = unordered_pair(sK2,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_311,definition,
iPr_def_11 = set_difference(iPr_def_10,sK4),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_312,definition,
iPr_def_12 = singleton(sK2),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_313,plain,
iPr_def_11 != iPr_def_12,
inference(demodulation,[status(thm)],[c_170,c_312,c_310,c_311]) ).
tcf(c_314,plain,
( in(sK3,sK4)
| ( sK2 = sK3 ) ),
inference(demodulation,[status(thm)],[c_102]) ).
tcf(c_315,plain,
~ in(sK2,sK4),
inference(demodulation,[status(thm)],[c_81]) ).
tcf(c_483,plain,
( ( sK2 = sK3 )
| ~ in(sK4,sK3) ),
inference(superposition,[status(thm)],[c_314,c_50]) ).
tcf(c_491,plain,
set_difference(unordered_pair(sK2,sK2),sK4) = singleton(sK2),
inference(superposition,[status(thm)],[c_58,c_315]) ).
tcf(c_492,plain,
set_difference(unordered_pair(sK2,sK2),sK4) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_491,c_312]) ).
tcf(c_514,plain,
! [X0: $i] :
( in(X0,sK4)
| ( sK2 = sK3 )
| ( set_difference(unordered_pair(X0,sK3),sK4) = singleton(X0) ) ),
inference(superposition,[status(thm)],[c_314,c_57]) ).
tcf(c_521,plain,
( in(sK2,sK4)
| ( sK2 = sK3 )
| ( set_difference(unordered_pair(sK2,sK3),sK4) = singleton(sK2) ) ),
inference(instantiation,[status(thm)],[c_514]) ).
tcf(c_539,plain,
sK2 = sK3,
inference(global_subsumption_just,[status(thm)],[c_483,c_81,c_168,c_521]) ).
tcf(c_541,plain,
unordered_pair(sK2,sK2) = iPr_def_10,
inference(demodulation,[status(thm)],[c_310,c_539]) ).
tcf(c_544,plain,
iPr_def_11 = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_492,c_311,c_541]) ).
tcf(c_545,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_544,c_313]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET927+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.37 % Computer : n013.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Thu Sep 24 12:23:06 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.43
% 0.12/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.43
% 0.12/0.43 % Detected problem language: tptp
% 0.12/0.45 % Proving...
% 2.05/1.30 % SZS status Started for theBenchmark.p
% 2.05/1.30 % SZS status Theorem for theBenchmark.p
% 2.05/1.30
% 2.05/1.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.05/1.30
% 2.05/1.30 % ------ iProver source info
% 2.05/1.30
% 2.05/1.30 % git: date: 2026-07-19 20:42:38 +0200
% 2.05/1.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.05/1.30 % git: non_committed_changes: false
% 2.05/1.30
% 2.05/1.30 % ------ Parsing...
% 2.05/1.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.05/1.30
% 2.05/1.30 % ------ 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 sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 2.05/1.30
% 2.05/1.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.05/1.30
% 2.05/1.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.05/1.30 % ------ Proving...
% 2.05/1.30 % ------ Problem Properties
% 2.05/1.30
% 2.05/1.30 %
% 2.05/1.30 % clauses 13
% 2.05/1.30 % conjectures 0
% 2.05/1.30 % EPR 5
% 2.05/1.30 % Horn 9
% 2.05/1.30 % unary 7
% 2.05/1.30 % binary 4
% 2.05/1.30 % lits 21
% 2.05/1.30 % lits eq 12
% 2.05/1.30 % fd_pure 0
% 2.05/1.30 % fd_pseudo 0
% 2.05/1.30 % fd_cond 0
% 2.05/1.30 % fd_pseudo_cond 1
% 2.05/1.30 % AC symbols 0
% 2.05/1.30
% 2.05/1.30 % ------ Schedule dynamic 5 is on
% 2.05/1.30
% 2.05/1.30 % ------ no conjectures: strip conj schedule
% 2.05/1.30
% 2.05/1.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 2.05/1.30
% 2.05/1.30
% 2.05/1.30 % ------
% 2.05/1.30 % Current options:
% 2.05/1.30 % ------
% 2.05/1.30
% 2.05/1.30
% 2.05/1.30 %
% 2.05/1.30
% 2.05/1.30 % ------ Proving...
% 2.05/1.30 %
% 2.05/1.30
% 2.05/1.30 % SZS status Theorem for theBenchmark.p
% 2.05/1.30
% 2.05/1.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.05/1.30
% 2.05/1.30
%------------------------------------------------------------------------------