%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU102+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 : 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 02:55:25 PM UTC 2026
% Result : Theorem 1.70s 1.18s
% Output : CNFRefutation 1.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 6
% Syntax : Number of formulae : 53 ( 24 unt; 2 def)
% Number of atoms : 160 ( 22 equ)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 161 ( 69 ~; 64 |; 22 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 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; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 70 ( 0 sgn 64 !; 6 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1,X2] :
( ( element(X2,X0)
& element(X1,X0)
& preboolean(X0)
& ~ empty(X0) )
=> element(prebool_difference(X0,X1,X2),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_finsub_1) ).
fof(f24,axiom,
! [X0,X1,X2] :
( ( element(X2,X0)
& element(X1,X0)
& preboolean(X0)
& ~ empty(X0) )
=> prebool_difference(X0,X1,X2) = set_difference(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_finsub_1) ).
fof(f26,conjecture,
! [X0,X1,X2] :
( ( preboolean(X2)
& ~ empty(X2) )
=> ( ( element(X1,X2)
& element(X0,X2) )
=> element(set_intersection2(X0,X1),X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_finsub_1) ).
fof(f27,negated_conjecture,
~ ! [X0,X1,X2] :
( ( preboolean(X2)
& ~ empty(X2) )
=> ( ( element(X1,X2)
& element(X0,X2) )
=> element(set_intersection2(X0,X1),X2) ) ),
inference(negated_conjecture,[status(cth)],[f26]) ).
fof(f33,axiom,
! [X0,X1] : set_difference(X0,set_difference(X0,X1)) = set_intersection2(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_xboole_1) ).
fof(f57,plain,
! [X0,X1,X2] :
( ~ element(X2,X0)
| ~ element(X1,X0)
| ~ preboolean(X0)
| empty(X0)
| element(prebool_difference(X0,X1,X2),X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f58,plain,
! [X0,X1,X2] :
( ~ element(X2,X0)
| ~ element(X1,X0)
| ~ preboolean(X0)
| empty(X0)
| element(prebool_difference(X0,X1,X2),X0) ),
inference(flattening,[],[f57]) ).
fof(f65,plain,
! [X0,X1,X2] :
( ~ element(X2,X0)
| ~ element(X1,X0)
| ~ preboolean(X0)
| empty(X0)
| prebool_difference(X0,X1,X2) = set_difference(X1,X2) ),
inference(ennf_transformation,[],[f24]) ).
fof(f66,plain,
! [X0,X1,X2] :
( ~ element(X2,X0)
| ~ element(X1,X0)
| ~ preboolean(X0)
| empty(X0)
| prebool_difference(X0,X1,X2) = set_difference(X1,X2) ),
inference(flattening,[],[f65]) ).
fof(f67,plain,
? [X0,X1,X2] :
( preboolean(X2)
& ~ empty(X2)
& element(X1,X2)
& element(X0,X2)
& ~ element(set_intersection2(X0,X1),X2) ),
inference(ennf_transformation,[],[f27]) ).
fof(f68,plain,
? [X0,X1,X2] :
( preboolean(X2)
& ~ empty(X2)
& element(X1,X2)
& element(X0,X2)
& ~ element(set_intersection2(X0,X1),X2) ),
inference(flattening,[],[f67]) ).
fof(f89,plain,
( preboolean(sK12)
& ~ empty(sK12)
& element(sK11,sK12)
& element(sK10,sK12)
& ~ element(set_intersection2(sK10,sK11),sK12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12]),skolemize(X0,sK10),skolemize(X1,sK11),skolemize(X2,sK12)],[f68]) ).
fof(f97,plain,
! [X2,X0,X1] :
( ~ element(X2,X0)
| ~ element(X1,X0)
| ~ preboolean(X0)
| empty(X0)
| element(prebool_difference(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f58]) ).
fof(f126,plain,
! [X2,X0,X1] :
( ~ element(X2,X0)
| ~ element(X1,X0)
| ~ preboolean(X0)
| empty(X0)
| prebool_difference(X0,X1,X2) = set_difference(X1,X2) ),
inference(cnf_transformation,[],[f66]) ).
fof(f128,plain,
preboolean(sK12),
inference(cnf_transformation,[],[f89]) ).
fof(f129,plain,
~ empty(sK12),
inference(cnf_transformation,[],[f89]) ).
fof(f130,plain,
element(sK11,sK12),
inference(cnf_transformation,[],[f89]) ).
fof(f131,plain,
element(sK10,sK12),
inference(cnf_transformation,[],[f89]) ).
fof(f132,plain,
~ element(set_intersection2(sK10,sK11),sK12),
inference(cnf_transformation,[],[f89]) ).
fof(f138,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1)),
inference(cnf_transformation,[],[f33]) ).
fof(f149,plain,
~ element(set_difference(sK10,set_difference(sK10,sK11)),sK12),
inference(definition_unfolding,[],[f132,f138]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X1)
| element(prebool_difference(X1,X0,X2),X1)
| ~ preboolean(X1)
| ~ element(X2,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f97]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X1)
| ( prebool_difference(X1,X0,X2) = set_difference(X0,X2) )
| ~ preboolean(X1)
| ~ element(X2,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f126]) ).
tcf(c_87,negated_conjecture,
~ element(set_difference(sK10,set_difference(sK10,sK11)),sK12),
inference(cnf_transformation,[],[f149]) ).
tcf(c_88,negated_conjecture,
element(sK10,sK12),
inference(cnf_transformation,[],[f131]) ).
tcf(c_89,negated_conjecture,
element(sK11,sK12),
inference(cnf_transformation,[],[f130]) ).
tcf(c_90,negated_conjecture,
~ empty(sK12),
inference(cnf_transformation,[],[f129]) ).
tcf(c_91,negated_conjecture,
preboolean(sK12),
inference(cnf_transformation,[],[f128]) ).
tcf(c_486,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X0)
| ( prebool_difference(X0,X1,X2) = set_difference(X1,X2) )
| ~ element(X2,X0)
| ~ element(X1,X0)
| ( X0 != sK12 ) ),
inference(resolution_lifted,[status(thm)],[c_85,c_91]) ).
tcf(c_487,plain,
! [X0: $i,X1: $i] :
( empty(sK12)
| ( prebool_difference(sK12,X0,X1) = set_difference(X0,X1) )
| ~ element(X1,sK12)
| ~ element(X0,sK12) ),
inference(unflattening,[status(thm)],[c_486]) ).
tcf(c_489,plain,
! [X0: $i,X1: $i] :
( ~ element(X0,sK12)
| ~ element(X1,sK12)
| ( prebool_difference(sK12,X0,X1) = set_difference(X0,X1) ) ),
inference(global_subsumption_just,[status(thm)],[c_487,c_90,c_487]) ).
tcf(c_490,plain,
! [X0: $i,X1: $i] :
( ( prebool_difference(sK12,X0,X1) = set_difference(X0,X1) )
| ~ element(X1,sK12)
| ~ element(X0,sK12) ),
inference(renaming,[status(thm)],[c_489]) ).
tcf(c_501,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X0)
| element(prebool_difference(X0,X1,X2),X0)
| ~ element(X2,X0)
| ~ element(X1,X0)
| ( X0 != sK12 ) ),
inference(resolution_lifted,[status(thm)],[c_56,c_91]) ).
tcf(c_502,plain,
! [X0: $i,X1: $i] :
( empty(sK12)
| element(prebool_difference(sK12,X0,X1),sK12)
| ~ element(X1,sK12)
| ~ element(X0,sK12) ),
inference(unflattening,[status(thm)],[c_501]) ).
tcf(c_504,plain,
! [X0: $i,X1: $i] :
( ~ element(X0,sK12)
| ~ element(X1,sK12)
| element(prebool_difference(sK12,X0,X1),sK12) ),
inference(global_subsumption_just,[status(thm)],[c_502,c_90,c_502]) ).
tcf(c_505,plain,
! [X0: $i,X1: $i] :
( element(prebool_difference(sK12,X0,X1),sK12)
| ~ element(X1,sK12)
| ~ element(X0,sK12) ),
inference(renaming,[status(thm)],[c_504]) ).
tcf(c_749,definition,
iPr_def_10 = set_difference(sK10,sK11),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_750,definition,
iPr_def_11 = set_difference(sK10,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_751,plain,
! [X0: $i,X1: $i] :
( element(prebool_difference(sK12,X0,X1),sK12)
| ~ element(X1,sK12)
| ~ element(X0,sK12) ),
inference(demodulation,[status(thm)],[c_505]) ).
tcf(c_752,plain,
! [X0: $i,X1: $i] :
( ( prebool_difference(sK12,X0,X1) = set_difference(X0,X1) )
| ~ element(X1,sK12)
| ~ element(X0,sK12) ),
inference(demodulation,[status(thm)],[c_490]) ).
tcf(c_754,negated_conjecture,
element(sK11,sK12),
inference(demodulation,[status(thm)],[c_89]) ).
tcf(c_755,negated_conjecture,
element(sK10,sK12),
inference(demodulation,[status(thm)],[c_88]) ).
tcf(c_756,negated_conjecture,
~ element(iPr_def_11,sK12),
inference(demodulation,[status(thm)],[c_87,c_749,c_750]) ).
tcf(c_1108,plain,
! [X0: $i] :
( ( prebool_difference(sK12,X0,sK11) = set_difference(X0,sK11) )
| ~ element(X0,sK12) ),
inference(superposition,[status(thm)],[c_754,c_752]) ).
tcf(c_1152,plain,
prebool_difference(sK12,sK10,sK11) = set_difference(sK10,sK11),
inference(superposition,[status(thm)],[c_755,c_1108]) ).
tcf(c_1157,plain,
prebool_difference(sK12,sK10,sK11) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_1152,c_749]) ).
tcf(c_1164,plain,
( element(iPr_def_10,sK12)
| ~ element(sK11,sK12)
| ~ element(sK10,sK12) ),
inference(superposition,[status(thm)],[c_1157,c_751]) ).
tcf(c_1165,plain,
element(iPr_def_10,sK12),
inference(forward_subsumption_resolution,[status(thm)],[c_1164,c_754,c_755]) ).
tcf(c_1166,plain,
! [X0: $i] :
( ( prebool_difference(sK12,X0,iPr_def_10) = set_difference(X0,iPr_def_10) )
| ~ element(X0,sK12) ),
inference(superposition,[status(thm)],[c_1165,c_752]) ).
tcf(c_1294,plain,
prebool_difference(sK12,sK10,iPr_def_10) = set_difference(sK10,iPr_def_10),
inference(superposition,[status(thm)],[c_755,c_1166]) ).
tcf(c_1306,plain,
prebool_difference(sK12,sK10,iPr_def_10) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_1294,c_750]) ).
tcf(c_1332,plain,
( element(iPr_def_11,sK12)
| ~ element(iPr_def_10,sK12)
| ~ element(sK10,sK12) ),
inference(superposition,[status(thm)],[c_1306,c_751]) ).
tcf(c_1333,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1332,c_756,c_1165,c_755]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU102+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n006.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 12:44:56 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 1.70/1.18 % SZS status Started for theBenchmark.p
% 1.70/1.18 % SZS status Theorem for theBenchmark.p
% 1.70/1.18
% 1.70/1.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.70/1.18
% 1.70/1.18 % ------ iProver source info
% 1.70/1.18
% 1.70/1.18 % git: date: 2026-07-19 20:42:38 +0200
% 1.70/1.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.70/1.18 % git: non_committed_changes: false
% 1.70/1.18
% 1.70/1.18 % ------ Parsing...
% 1.70/1.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.70/1.18
% 1.70/1.18 % ------ Preprocessing... sup_sim: 2 sf_s rm: 10 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 5 0s sf_e pe_s pe_e %
% 1.70/1.18
% 1.70/1.18 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.70/1.18
% 1.70/1.18 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.70/1.18 % ------ Proving...
% 1.70/1.18 % ------ Problem Properties
% 1.70/1.18
% 1.70/1.18 %
% 1.70/1.18 % clauses 40
% 1.70/1.18 % conjectures 4
% 1.70/1.18 % EPR 15
% 1.70/1.18 % Horn 36
% 1.70/1.18 % unary 22
% 1.70/1.18 % binary 10
% 1.70/1.18 % lits 66
% 1.70/1.18 % lits eq 10
% 1.70/1.18 % fd_pure 0
% 1.70/1.18 % fd_pseudo 0
% 1.70/1.18 % fd_cond 1
% 1.70/1.18 % fd_pseudo_cond 1
% 1.70/1.18 % AC symbols 0
% 1.70/1.18
% 1.70/1.18 % ------ Schedule dynamic 5 is on
% 1.70/1.18
% 1.70/1.18 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.70/1.18
% 1.70/1.18
% 1.70/1.18 % ------
% 1.70/1.18 % Current options:
% 1.70/1.18 % ------
% 1.70/1.18
% 1.70/1.18
% 1.70/1.18 %
% 1.70/1.18
% 1.70/1.18 % ------ Proving...
% 1.70/1.18 %
% 1.70/1.18
% 1.70/1.18 % SZS status Theorem for theBenchmark.p
% 1.70/1.18
% 1.70/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.70/1.19
% 1.70/1.19
%------------------------------------------------------------------------------