%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU105+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 : n002.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 1.61s 1.07s
% Output : CNFRefutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 58 ( 17 unt; 0 def)
% Number of atoms : 168 ( 8 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 190 ( 80 ~; 70 |; 27 &)
% ( 3 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 83 ( 1 sgn 77 !; 6 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
fof(f21,axiom,
! [X0,X1] : set_intersection2(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
fof(f32,axiom,
! [X0,X1] : set_difference(X0,X1) = symmetric_difference(X0,set_intersection2(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t100_xboole_1) ).
fof(f33,axiom,
! [X0] :
( preboolean(X0)
<=> ! [X1,X2] :
( ( in(X2,X0)
& in(X1,X0) )
=> ( in(set_difference(X1,X2),X0)
& in(set_union2(X1,X2),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_finsub_1) ).
fof(f34,conjecture,
! [X0] :
( ~ empty(X0)
=> ( ! [X1] :
( element(X1,X0)
=> ! [X2] :
( element(X2,X0)
=> ( in(set_intersection2(X1,X2),X0)
& in(symmetric_difference(X1,X2),X0) ) ) )
=> preboolean(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_finsub_1) ).
fof(f35,negated_conjecture,
~ ! [X0] :
( ~ empty(X0)
=> ( ! [X1] :
( element(X1,X0)
=> ! [X2] :
( element(X2,X0)
=> ( in(set_intersection2(X1,X2),X0)
& in(symmetric_difference(X1,X2),X0) ) ) )
=> preboolean(X0) ) ),
inference(negated_conjecture,[status(cth)],[f34]) ).
fof(f37,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f49,axiom,
! [X0,X1] : set_union2(X0,X1) = symmetric_difference(symmetric_difference(X0,X1),set_intersection2(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t94_xboole_1) ).
fof(f51,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(rectify,[],[f21]) ).
fof(f80,plain,
! [X0] :
( preboolean(X0)
<=> ! [X1,X2] :
( ~ in(X2,X0)
| ~ in(X1,X0)
| ( in(set_difference(X1,X2),X0)
& in(set_union2(X1,X2),X0) ) ) ),
inference(ennf_transformation,[],[f33]) ).
fof(f81,plain,
! [X0] :
( preboolean(X0)
<=> ! [X1,X2] :
( ~ in(X2,X0)
| ~ in(X1,X0)
| ( in(set_difference(X1,X2),X0)
& in(set_union2(X1,X2),X0) ) ) ),
inference(flattening,[],[f80]) ).
fof(f82,plain,
? [X0] :
( ~ empty(X0)
& ! [X1] :
( ~ element(X1,X0)
| ! [X2] :
( ~ element(X2,X0)
| ( in(set_intersection2(X1,X2),X0)
& in(symmetric_difference(X1,X2),X0) ) ) )
& ~ preboolean(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f83,plain,
? [X0] :
( ~ empty(X0)
& ! [X1] :
( ~ element(X1,X0)
| ! [X2] :
( ~ element(X2,X0)
| ( in(set_intersection2(X1,X2),X0)
& in(symmetric_difference(X1,X2),X0) ) ) )
& ~ preboolean(X0) ),
inference(flattening,[],[f82]) ).
fof(f84,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f104,plain,
! [X0] :
( ( ~ preboolean(X0)
| ! [X1,X2] :
( ~ in(X2,X0)
| ~ in(X1,X0)
| ( in(set_difference(X1,X2),X0)
& in(set_union2(X1,X2),X0) ) ) )
& ( ? [X1,X2] :
( in(X2,X0)
& in(X1,X0)
& ( ~ in(set_difference(X1,X2),X0)
| ~ in(set_union2(X1,X2),X0) ) )
| preboolean(X0) ) ),
inference(nnf_transformation,[],[f81]) ).
fof(f105,plain,
! [X0] :
( ( ~ preboolean(X0)
| ! [X3,X4] :
( ~ in(X4,X0)
| ~ in(X3,X0)
| ( in(set_difference(X3,X4),X0)
& in(set_union2(X3,X4),X0) ) ) )
& ( ? [X1,X2] :
( in(X2,X0)
& in(X1,X0)
& ( ~ in(set_difference(X1,X2),X0)
| ~ in(set_union2(X1,X2),X0) ) )
| preboolean(X0) ) ),
inference(rectify,[],[f104]) ).
fof(f106,plain,
! [X0] :
( ( ~ preboolean(X0)
| ! [X3,X4] :
( ~ in(X4,X0)
| ~ in(X3,X0)
| ( in(set_difference(X3,X4),X0)
& in(set_union2(X3,X4),X0) ) ) )
& ( ( in(sK11(X0),X0)
& in(sK10(X0),X0)
& ( ~ in(set_difference(sK10(X0),sK11(X0)),X0)
| ~ in(set_union2(sK10(X0),sK11(X0)),X0) ) )
| preboolean(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11]),skolemize(X1,sK10(X0)),skolemize(X2,sK11(X0))],[f105]) ).
fof(f107,plain,
( ~ empty(sK12)
& ! [X1] :
( ~ element(X1,sK12)
| ! [X2] :
( ~ element(X2,sK12)
| ( in(set_intersection2(X1,X2),sK12)
& in(symmetric_difference(X1,X2),sK12) ) ) )
& ~ preboolean(sK12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X0,sK12)],[f83]) ).
fof(f129,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(cnf_transformation,[],[f51]) ).
fof(f152,plain,
! [X0,X1] : set_difference(X0,X1) = symmetric_difference(X0,set_intersection2(X0,X1)),
inference(cnf_transformation,[],[f32]) ).
fof(f155,plain,
! [X0] :
( in(sK11(X0),X0)
| preboolean(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f156,plain,
! [X0] :
( in(sK10(X0),X0)
| preboolean(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f157,plain,
! [X0] :
( ~ in(set_difference(sK10(X0),sK11(X0)),X0)
| ~ in(set_union2(sK10(X0),sK11(X0)),X0)
| preboolean(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f159,plain,
! [X2,X1] :
( ~ element(X1,sK12)
| ~ element(X2,sK12)
| in(set_intersection2(X1,X2),sK12) ),
inference(cnf_transformation,[],[f107]) ).
fof(f160,plain,
! [X2,X1] :
( ~ element(X1,sK12)
| ~ element(X2,sK12)
| in(symmetric_difference(X1,X2),sK12) ),
inference(cnf_transformation,[],[f107]) ).
fof(f161,plain,
~ preboolean(sK12),
inference(cnf_transformation,[],[f107]) ).
fof(f163,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(cnf_transformation,[],[f84]) ).
fof(f175,plain,
! [X0,X1] : set_union2(X0,X1) = symmetric_difference(symmetric_difference(X0,X1),set_intersection2(X0,X1)),
inference(cnf_transformation,[],[f49]) ).
fof(f183,plain,
! [X0] :
( ~ in(symmetric_difference(sK10(X0),set_intersection2(sK10(X0),sK11(X0))),X0)
| ~ in(symmetric_difference(symmetric_difference(sK10(X0),sK11(X0)),set_intersection2(sK10(X0),sK11(X0))),X0)
| preboolean(X0) ),
inference(definition_unfolding,[],[f157,f175,f152]) ).
tcf(c_70,plain,
! [X0: $i] : set_intersection2(X0,X0) = X0,
inference(cnf_transformation,[],[f129]) ).
tcf(c_93,plain,
! [X0: $i] :
( preboolean(X0)
| ~ in(symmetric_difference(sK10(X0),set_intersection2(sK10(X0),sK11(X0))),X0)
| ~ in(symmetric_difference(symmetric_difference(sK10(X0),sK11(X0)),set_intersection2(sK10(X0),sK11(X0))),X0) ),
inference(cnf_transformation,[],[f183]) ).
tcf(c_94,plain,
! [X0: $i] :
( preboolean(X0)
| in(sK10(X0),X0) ),
inference(cnf_transformation,[],[f156]) ).
tcf(c_95,plain,
! [X0: $i] :
( preboolean(X0)
| in(sK11(X0),X0) ),
inference(cnf_transformation,[],[f155]) ).
tcf(c_98,negated_conjecture,
~ preboolean(sK12),
inference(cnf_transformation,[],[f161]) ).
tcf(c_99,negated_conjecture,
! [X0: $i,X1: $i] :
( in(symmetric_difference(X0,X1),sK12)
| ~ element(X1,sK12)
| ~ element(X0,sK12) ),
inference(cnf_transformation,[],[f160]) ).
tcf(c_100,negated_conjecture,
! [X0: $i,X1: $i] :
( in(set_intersection2(X0,X1),sK12)
| ~ element(X1,sK12)
| ~ element(X0,sK12) ),
inference(cnf_transformation,[],[f159]) ).
tcf(c_103,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f163]) ).
tcf(c_1209,negated_conjecture,
! [X0: $i,X1: $i] :
( in(set_intersection2(X0,X1),sK12)
| ~ element(X1,sK12)
| ~ element(X0,sK12) ),
inference(demodulation,[status(thm)],[c_100]) ).
tcf(c_1210,negated_conjecture,
! [X0: $i,X1: $i] :
( in(symmetric_difference(X0,X1),sK12)
| ~ element(X1,sK12)
| ~ element(X0,sK12) ),
inference(demodulation,[status(thm)],[c_99]) ).
tcf(c_1211,negated_conjecture,
~ preboolean(sK12),
inference(demodulation,[status(thm)],[c_98]) ).
tcf(c_1650,plain,
! [X0: $i] :
( in(X0,sK12)
| ~ element(X0,sK12) ),
inference(superposition,[status(thm)],[c_70,c_1209]) ).
tcf(c_1721,plain,
! [X0: $i] :
( preboolean(X0)
| element(sK10(X0),X0) ),
inference(superposition,[status(thm)],[c_94,c_103]) ).
tcf(c_1722,plain,
! [X0: $i] :
( preboolean(X0)
| element(sK11(X0),X0) ),
inference(superposition,[status(thm)],[c_95,c_103]) ).
tcf(c_1723,plain,
! [X0: $i,X1: $i] :
( element(symmetric_difference(X0,X1),sK12)
| ~ element(X1,sK12)
| ~ element(X0,sK12) ),
inference(superposition,[status(thm)],[c_1210,c_103]) ).
tcf(c_1724,plain,
! [X0: $i,X1: $i] :
( element(set_intersection2(X0,X1),sK12)
| ~ element(X1,sK12)
| ~ element(X0,sK12) ),
inference(superposition,[status(thm)],[c_1209,c_103]) ).
tcf(c_1744,plain,
( preboolean(sK12)
| in(sK10(sK12),sK12) ),
inference(superposition,[status(thm)],[c_1721,c_1650]) ).
tcf(c_1745,plain,
in(sK10(sK12),sK12),
inference(forward_subsumption_resolution,[status(thm)],[c_1744,c_1211]) ).
tcf(c_1746,plain,
element(sK10(sK12),sK12),
inference(superposition,[status(thm)],[c_1745,c_103]) ).
tcf(c_2377,plain,
( preboolean(sK12)
| in(sK11(sK12),sK12) ),
inference(superposition,[status(thm)],[c_1722,c_1650]) ).
tcf(c_2379,plain,
in(sK11(sK12),sK12),
inference(forward_subsumption_resolution,[status(thm)],[c_2377,c_1211]) ).
tcf(c_2396,plain,
element(sK11(sK12),sK12),
inference(superposition,[status(thm)],[c_2379,c_103]) ).
tcf(c_2683,plain,
( preboolean(sK12)
| ~ element(set_intersection2(sK10(sK12),sK11(sK12)),sK12)
| ~ element(symmetric_difference(sK10(sK12),sK11(sK12)),sK12)
| ~ in(symmetric_difference(sK10(sK12),set_intersection2(sK10(sK12),sK11(sK12))),sK12) ),
inference(superposition,[status(thm)],[c_1210,c_93]) ).
tcf(c_2684,plain,
( ~ element(set_intersection2(sK10(sK12),sK11(sK12)),sK12)
| ~ element(symmetric_difference(sK10(sK12),sK11(sK12)),sK12)
| ~ in(symmetric_difference(sK10(sK12),set_intersection2(sK10(sK12),sK11(sK12))),sK12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2683,c_1211]) ).
tcf(c_2865,plain,
( ~ element(sK10(sK12),sK12)
| ~ element(set_intersection2(sK10(sK12),sK11(sK12)),sK12)
| ~ element(symmetric_difference(sK10(sK12),sK11(sK12)),sK12) ),
inference(superposition,[status(thm)],[c_1210,c_2684]) ).
tcf(c_2866,plain,
( ~ element(set_intersection2(sK10(sK12),sK11(sK12)),sK12)
| ~ element(symmetric_difference(sK10(sK12),sK11(sK12)),sK12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2865,c_1746]) ).
tcf(c_2875,plain,
( ~ element(sK11(sK12),sK12)
| ~ element(sK10(sK12),sK12)
| ~ element(set_intersection2(sK10(sK12),sK11(sK12)),sK12) ),
inference(superposition,[status(thm)],[c_1723,c_2866]) ).
tcf(c_2876,plain,
~ element(set_intersection2(sK10(sK12),sK11(sK12)),sK12),
inference(forward_subsumption_resolution,[status(thm)],[c_2875,c_2396,c_1746]) ).
tcf(c_2879,plain,
( ~ element(sK11(sK12),sK12)
| ~ element(sK10(sK12),sK12) ),
inference(superposition,[status(thm)],[c_1724,c_2876]) ).
tcf(c_2880,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2879,c_2396,c_1746]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU105+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n002.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
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 12:48:34 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.42
% 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...
% 1.61/1.07 % SZS status Started for theBenchmark.p
% 1.61/1.07 % SZS status Theorem for theBenchmark.p
% 1.61/1.07
% 1.61/1.07 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.61/1.07
% 1.61/1.07 % ------ iProver source info
% 1.61/1.07
% 1.61/1.07 % git: date: 2026-07-19 20:42:38 +0200
% 1.61/1.07 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.61/1.07 % git: non_committed_changes: false
% 1.61/1.07
% 1.61/1.07 % ------ Parsing...
% 1.61/1.07 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.61/1.07
% 1.61/1.07 % ------ Preprocessing... sup_sim: 4 sf_s rm: 13 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e %
% 1.61/1.07
% 1.61/1.07 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.61/1.07
% 1.61/1.07 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.61/1.07 % ------ Proving...
% 1.61/1.07 % ------ Problem Properties
% 1.61/1.07
% 1.61/1.07 %
% 1.61/1.07 % clauses 46
% 1.61/1.07 % conjectures 4
% 1.61/1.07 % EPR 14
% 1.61/1.07 % Horn 40
% 1.61/1.07 % unary 23
% 1.61/1.07 % binary 14
% 1.61/1.07 % lits 80
% 1.61/1.07 % lits eq 10
% 1.61/1.07 % fd_pure 0
% 1.61/1.07 % fd_pseudo 0
% 1.61/1.07 % fd_cond 1
% 1.61/1.07 % fd_pseudo_cond 1
% 1.61/1.07 % AC symbols 0
% 1.61/1.07
% 1.61/1.07 % ------ Schedule dynamic 5 is on
% 1.61/1.07
% 1.61/1.07 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.61/1.07
% 1.61/1.07
% 1.61/1.07 % ------
% 1.61/1.07 % Current options:
% 1.61/1.07 % ------
% 1.61/1.07
% 1.61/1.07
% 1.61/1.07 %
% 1.61/1.07
% 1.61/1.07 % ------ Proving...
% 1.61/1.07 %
% 1.61/1.07
% 1.61/1.07 % SZS status Theorem for theBenchmark.p
% 1.61/1.07
% 1.61/1.07 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.61/1.07
% 1.61/1.07
%------------------------------------------------------------------------------