%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET928+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 : n012.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 1.17s 1.06s
% Output : CNFRefutation 1.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 49 ( 10 unt; 2 def)
% Number of atoms : 144 ( 37 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 119 ( 52 ~; 50 |; 13 &)
% ( 3 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 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; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 64 ( 0 sgn 55 !; 9 ?; 19 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f6,axiom,
! [X0,X1,X2] :
~ ( in(X0,X2)
& disjoint(unordered_pair(X0,X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_zfmisc_1) ).
fof(f7,axiom,
! [X0,X1,X2] :
~ ( ~ disjoint(unordered_pair(X0,X2),X1)
& ~ in(X2,X1)
& ~ in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_zfmisc_1) ).
fof(f8,conjecture,
! [X0,X1,X2] :
( set_difference(unordered_pair(X0,X1),X2) = unordered_pair(X0,X1)
<=> ( ~ in(X1,X2)
& ~ in(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_zfmisc_1) ).
fof(f9,negated_conjecture,
~ ! [X0,X1,X2] :
( set_difference(unordered_pair(X0,X1),X2) = unordered_pair(X0,X1)
<=> ( ~ in(X1,X2)
& ~ in(X0,X2) ) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f10,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_difference(X0,X1) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_xboole_1) ).
fof(f13,plain,
! [X0,X1,X2] :
( ~ in(X0,X2)
| ~ disjoint(unordered_pair(X0,X1),X2) ),
inference(ennf_transformation,[],[f6]) ).
fof(f14,plain,
! [X0,X1,X2] :
( disjoint(unordered_pair(X0,X2),X1)
| in(X2,X1)
| in(X0,X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f15,plain,
? [X0,X1,X2] :
( set_difference(unordered_pair(X0,X1),X2) = unordered_pair(X0,X1)
<~> ( ~ in(X1,X2)
& ~ in(X0,X2) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f18,plain,
? [X0,X1,X2] :
( ( set_difference(unordered_pair(X0,X1),X2) = unordered_pair(X0,X1)
| ( ~ in(X1,X2)
& ~ in(X0,X2) ) )
& ( unordered_pair(X0,X1) != set_difference(unordered_pair(X0,X1),X2)
| in(X1,X2)
| in(X0,X2) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f19,plain,
? [X0,X1,X2] :
( ( set_difference(unordered_pair(X0,X1),X2) = unordered_pair(X0,X1)
| ( ~ in(X1,X2)
& ~ in(X0,X2) ) )
& ( unordered_pair(X0,X1) != set_difference(unordered_pair(X0,X1),X2)
| in(X1,X2)
| in(X0,X2) ) ),
inference(flattening,[],[f18]) ).
fof(f20,plain,
( ( unordered_pair(sK2,sK3) = set_difference(unordered_pair(sK2,sK3),sK4)
| ( ~ in(sK3,sK4)
& ~ in(sK2,sK4) ) )
& ( unordered_pair(sK2,sK3) != set_difference(unordered_pair(sK2,sK3),sK4)
| 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)],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| set_difference(X0,X1) = X0 )
& ( set_difference(X0,X1) != X0
| disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f23,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f27,plain,
! [X2,X0,X1] :
( ~ in(X0,X2)
| ~ disjoint(unordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f13]) ).
fof(f28,plain,
! [X2,X0,X1] :
( disjoint(unordered_pair(X0,X2),X1)
| in(X2,X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f29,plain,
( unordered_pair(sK2,sK3) = set_difference(unordered_pair(sK2,sK3),sK4)
| ~ in(sK3,sK4) ),
inference(cnf_transformation,[],[f20]) ).
fof(f30,plain,
( unordered_pair(sK2,sK3) = set_difference(unordered_pair(sK2,sK3),sK4)
| ~ in(sK2,sK4) ),
inference(cnf_transformation,[],[f20]) ).
fof(f31,plain,
( unordered_pair(sK2,sK3) != set_difference(unordered_pair(sK2,sK3),sK4)
| in(sK3,sK4)
| in(sK2,sK4) ),
inference(cnf_transformation,[],[f20]) ).
fof(f32,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| set_difference(X0,X1) = X0 ),
inference(cnf_transformation,[],[f21]) ).
fof(f33,plain,
! [X0,X1] :
( set_difference(X0,X1) != X0
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f23]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X0,X2)
| ~ disjoint(unordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,X2)
| in(X0,X2)
| disjoint(unordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_56,negated_conjecture,
( in(sK3,sK4)
| in(sK2,sK4)
| ( set_difference(unordered_pair(sK2,sK3),sK4) != unordered_pair(sK2,sK3) ) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_57,negated_conjecture,
( ( set_difference(unordered_pair(sK2,sK3),sK4) = unordered_pair(sK2,sK3) )
| ~ in(sK2,sK4) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_58,negated_conjecture,
( ( set_difference(unordered_pair(sK2,sK3),sK4) = unordered_pair(sK2,sK3) )
| ~ in(sK3,sK4) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| ( set_difference(X0,X1) != X0 ) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,X1) = X0 )
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_345,definition,
iPr_def_10 = unordered_pair(sK2,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_346,definition,
iPr_def_11 = set_difference(iPr_def_10,sK4),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_347,negated_conjecture,
( ( iPr_def_11 = iPr_def_10 )
| ~ in(sK3,sK4) ),
inference(demodulation,[status(thm)],[c_58,c_345,c_346]) ).
tcf(c_348,negated_conjecture,
( ( iPr_def_11 = iPr_def_10 )
| ~ in(sK2,sK4) ),
inference(demodulation,[status(thm)],[c_57]) ).
tcf(c_349,negated_conjecture,
( in(sK3,sK4)
| in(sK2,sK4)
| ( iPr_def_11 != iPr_def_10 ) ),
inference(demodulation,[status(thm)],[c_56]) ).
tcf(c_667,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X1,X2)
| ~ disjoint(unordered_pair(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_50,c_54]) ).
tcf(c_669,plain,
! [X0: $i] :
( ~ disjoint(iPr_def_10,X0)
| ~ in(sK2,X0) ),
inference(superposition,[status(thm)],[c_345,c_54]) ).
tcf(c_678,plain,
( disjoint(iPr_def_10,sK4)
| ( iPr_def_10 != iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_346,c_59]) ).
tcf(c_693,plain,
! [X0: $i] :
( disjoint(iPr_def_10,X0)
| in(sK3,X0)
| in(sK2,X0) ),
inference(superposition,[status(thm)],[c_345,c_55]) ).
tcf(c_723,plain,
! [X0: $i] :
( in(sK3,X0)
| in(sK2,X0)
| ( set_difference(iPr_def_10,X0) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_693,c_60]) ).
tcf(c_760,plain,
! [X0: $i] :
( ~ disjoint(iPr_def_10,X0)
| ~ in(sK3,X0) ),
inference(superposition,[status(thm)],[c_345,c_667]) ).
tcf(c_813,plain,
( in(sK2,sK4)
| ( iPr_def_10 = iPr_def_11 )
| ( set_difference(iPr_def_10,sK4) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_723,c_347]) ).
tcf(c_814,plain,
( in(sK2,sK4)
| ( iPr_def_10 = iPr_def_11 ) ),
inference(light_normalisation,[status(thm)],[c_813,c_346]) ).
tcf(c_826,plain,
iPr_def_10 = iPr_def_11,
inference(superposition,[status(thm)],[c_814,c_348]) ).
tcf(c_827,plain,
disjoint(iPr_def_10,sK4),
inference(backward_subsumption_resolution,[status(thm)],[c_678,c_826]) ).
tcf(c_829,plain,
( in(sK3,sK4)
| in(sK2,sK4)
| ( iPr_def_10 != iPr_def_10 ) ),
inference(demodulation,[status(thm)],[c_349,c_826]) ).
tcf(c_832,plain,
( in(sK3,sK4)
| in(sK2,sK4) ),
inference(equality_resolution_simp,[status(thm)],[c_829]) ).
tcf(c_837,plain,
~ in(sK3,sK4),
inference(superposition,[status(thm)],[c_827,c_760]) ).
tcf(c_838,plain,
~ in(sK2,sK4),
inference(superposition,[status(thm)],[c_827,c_669]) ).
tcf(c_839,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_837,c_838,c_832]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET928+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Thu Sep 24 12:23:21 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/0.32 Running first-order theorem proving
% 0.03/0.32 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
% 0.03/0.33
% 0.03/0.33 % ======== iProver multi-core TPTP/SMT =========
% 0.03/0.33
% 0.06/0.33 % Detected problem language: tptp
% 0.06/0.33 % Proving...
% 1.17/1.06 % SZS status Started for theBenchmark.p
% 1.17/1.06 % SZS status Theorem for theBenchmark.p
% 1.17/1.06
% 1.17/1.06 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.17/1.06
% 1.17/1.06 % ------ iProver source info
% 1.17/1.06
% 1.17/1.06 % git: date: 2026-07-19 20:42:38 +0200
% 1.17/1.06 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.17/1.06 % git: non_committed_changes: false
% 1.17/1.06
% 1.17/1.06 % ------ Parsing...
% 1.17/1.06 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.17/1.06
% 1.17/1.06 % ------ 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 %
% 1.17/1.06
% 1.17/1.06 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.17/1.06
% 1.17/1.06 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.17/1.06 % ------ Proving...
% 1.17/1.06 % ------ Problem Properties
% 1.17/1.06
% 1.17/1.06 %
% 1.17/1.06 % clauses 13
% 1.17/1.06 % conjectures 3
% 1.17/1.06 % EPR 6
% 1.17/1.06 % Horn 11
% 1.17/1.06 % unary 4
% 1.17/1.06 % binary 7
% 1.17/1.06 % lits 24
% 1.17/1.06 % lits eq 9
% 1.17/1.06 % fd_pure 0
% 1.17/1.06 % fd_pseudo 0
% 1.17/1.06 % fd_cond 0
% 1.17/1.06 % fd_pseudo_cond 0
% 1.17/1.06 % AC symbols 0
% 1.17/1.06
% 1.17/1.06 % ------ Schedule dynamic 5 is on
% 1.17/1.06
% 1.17/1.06 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.17/1.06
% 1.17/1.06
% 1.17/1.06 % ------
% 1.17/1.06 % Current options:
% 1.17/1.06 % ------
% 1.17/1.06
% 1.17/1.06
% 1.17/1.06 %
% 1.17/1.06
% 1.17/1.06 % ------ Proving...
% 1.17/1.06 %
% 1.17/1.06
% 1.17/1.06 % SZS status Theorem for theBenchmark.p
% 1.17/1.06
% 1.17/1.06 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.17/1.06
% 1.17/1.06
%------------------------------------------------------------------------------