%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU106+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 : n019.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 3.13s 1.40s
% Output : CNFRefutation 4.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 66 ( 24 unt; 0 def)
% Number of atoms : 181 ( 17 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 198 ( 83 ~; 75 |; 27 &)
% ( 3 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 7 ( 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 : 110 ( 1 sgn 104 !; 6 ?; 35 :)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f9,axiom,
! [X0,X1] : symmetric_difference(X0,X1) = set_union2(set_difference(X0,X1),set_difference(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_xboole_0) ).
fof(f20,axiom,
! [X0,X1] : set_union2(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_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_union2(X1,X2),X0)
& in(symmetric_difference(X1,X2),X0) ) ) )
=> preboolean(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_finsub_1) ).
fof(f35,negated_conjecture,
~ ! [X0] :
( ~ empty(X0)
=> ( ! [X1] :
( element(X1,X0)
=> ! [X2] :
( element(X2,X0)
=> ( in(set_union2(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_intersection2(X0,X1) = symmetric_difference(symmetric_difference(X0,X1),set_union2(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t95_xboole_1) ).
fof(f50,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(rectify,[],[f20]) ).
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_union2(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_union2(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_union2(X1,X2),sK12)
& in(symmetric_difference(X1,X2),sK12) ) ) )
& ~ preboolean(sK12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X0,sK12)],[f83]) ).
fof(f114,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f117,plain,
! [X0,X1] : symmetric_difference(X0,X1) = set_union2(set_difference(X0,X1),set_difference(X1,X0)),
inference(cnf_transformation,[],[f9]) ).
fof(f128,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(cnf_transformation,[],[f50]) ).
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_union2(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_intersection2(X0,X1) = symmetric_difference(symmetric_difference(X0,X1),set_union2(X0,X1)),
inference(cnf_transformation,[],[f49]) ).
fof(f176,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_union2(set_difference(set_union2(set_difference(X0,X1),set_difference(X1,X0)),set_union2(X0,X1)),set_difference(set_union2(X0,X1),set_union2(set_difference(X0,X1),set_difference(X1,X0)))),
inference(definition_unfolding,[],[f175,f117,f117]) ).
fof(f177,plain,
! [X0,X1] : set_difference(X0,X1) = set_union2(set_difference(X0,set_union2(set_difference(set_union2(set_difference(X0,X1),set_difference(X1,X0)),set_union2(X0,X1)),set_difference(set_union2(X0,X1),set_union2(set_difference(X0,X1),set_difference(X1,X0))))),set_difference(set_union2(set_difference(set_union2(set_difference(X0,X1),set_difference(X1,X0)),set_union2(X0,X1)),set_difference(set_union2(X0,X1),set_union2(set_difference(X0,X1),set_difference(X1,X0)))),X0)),
inference(definition_unfolding,[],[f152,f117,f176]) ).
fof(f184,plain,
! [X2,X1] :
( ~ element(X1,sK12)
| ~ element(X2,sK12)
| in(set_union2(set_difference(X1,X2),set_difference(X2,X1)),sK12) ),
inference(definition_unfolding,[],[f160,f117]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : set_union2(set_difference(X0,set_union2(set_difference(set_union2(set_difference(X0,X1),set_difference(X1,X0)),set_union2(X0,X1)),set_difference(set_union2(X0,X1),set_union2(set_difference(X0,X1),set_difference(X1,X0))))),set_difference(set_union2(set_difference(set_union2(set_difference(X0,X1),set_difference(X1,X0)),set_union2(X0,X1)),set_difference(set_union2(X0,X1),set_union2(set_difference(X0,X1),set_difference(X1,X0)))),X0)) = set_difference(X0,X1),
inference(cnf_transformation,[],[f177]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f114]) ).
tcf(c_69,plain,
! [X0: $i] : set_union2(X0,X0) = X0,
inference(cnf_transformation,[],[f128]) ).
tcf(c_93,plain,
! [X0: $i] :
( preboolean(X0)
| ~ in(set_union2(sK10(X0),sK11(X0)),X0)
| ~ in(set_difference(sK10(X0),sK11(X0)),X0) ),
inference(cnf_transformation,[],[f157]) ).
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(set_union2(set_difference(X0,X1),set_difference(X1,X0)),sK12)
| ~ element(X1,sK12)
| ~ element(X0,sK12) ),
inference(cnf_transformation,[],[f184]) ).
tcf(c_100,negated_conjecture,
! [X0: $i,X1: $i] :
( in(set_union2(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_565,plain,
! [X0: $i,X1: $i] : set_union2(set_difference(X0,set_union2(set_difference(set_union2(X0,X1),set_union2(set_difference(X0,X1),set_difference(X1,X0))),set_difference(set_union2(set_difference(X0,X1),set_difference(X1,X0)),set_union2(X0,X1)))),set_difference(set_union2(set_difference(set_union2(X0,X1),set_union2(set_difference(X0,X1),set_difference(X1,X0))),set_difference(set_union2(set_difference(X0,X1),set_difference(X1,X0)),set_union2(X0,X1))),X0)) = set_difference(X0,X1),
inference(demodulation,[status(thm)],[c_49,c_56]) ).
tcf(c_1216,negated_conjecture,
! [X0: $i,X1: $i] :
( in(set_union2(X0,X1),sK12)
| ~ element(X1,sK12)
| ~ element(X0,sK12) ),
inference(demodulation,[status(thm)],[c_100]) ).
tcf(c_1217,negated_conjecture,
! [X0: $i,X1: $i] :
( in(set_union2(set_difference(X0,X1),set_difference(X1,X0)),sK12)
| ~ element(X1,sK12)
| ~ element(X0,sK12) ),
inference(demodulation,[status(thm)],[c_99]) ).
tcf(c_1218,negated_conjecture,
~ preboolean(sK12),
inference(demodulation,[status(thm)],[c_98]) ).
tcf(c_1659,plain,
! [X0: $i] :
( in(X0,sK12)
| ~ element(X0,sK12) ),
inference(superposition,[status(thm)],[c_69,c_1216]) ).
tcf(c_1831,plain,
! [X0: $i,X1: $i] :
( in(set_difference(X0,X1),sK12)
| ~ element(X0,sK12)
| ~ element(set_union2(set_difference(set_union2(X0,X1),set_union2(set_difference(X0,X1),set_difference(X1,X0))),set_difference(set_union2(set_difference(X0,X1),set_difference(X1,X0)),set_union2(X0,X1))),sK12) ),
inference(superposition,[status(thm)],[c_565,c_1217]) ).
tcf(c_1869,plain,
! [X0: $i] :
( preboolean(X0)
| element(sK10(X0),X0) ),
inference(superposition,[status(thm)],[c_94,c_103]) ).
tcf(c_1870,plain,
! [X0: $i] :
( preboolean(X0)
| element(sK11(X0),X0) ),
inference(superposition,[status(thm)],[c_95,c_103]) ).
tcf(c_1871,plain,
! [X0: $i,X1: $i] :
( element(set_union2(set_difference(X0,X1),set_difference(X1,X0)),sK12)
| ~ element(X1,sK12)
| ~ element(X0,sK12) ),
inference(superposition,[status(thm)],[c_1217,c_103]) ).
tcf(c_1872,plain,
! [X0: $i,X1: $i] :
( element(set_union2(X0,X1),sK12)
| ~ element(X1,sK12)
| ~ element(X0,sK12) ),
inference(superposition,[status(thm)],[c_1216,c_103]) ).
tcf(c_2048,plain,
! [X0: $i,X1: $i] :
( in(set_difference(X0,X1),sK12)
| ~ element(X0,sK12)
| ~ element(set_union2(X0,X1),sK12)
| ~ element(set_union2(set_difference(X0,X1),set_difference(X1,X0)),sK12) ),
inference(superposition,[status(thm)],[c_1871,c_1831]) ).
tcf(c_2313,plain,
! [X0: $i,X1: $i] :
( in(set_difference(X0,X1),sK12)
| ~ element(X1,sK12)
| ~ element(X0,sK12)
| ~ element(set_union2(X0,X1),sK12) ),
inference(superposition,[status(thm)],[c_1871,c_2048]) ).
tcf(c_2350,plain,
! [X0: $i,X1: $i] :
( in(set_difference(X0,X1),sK12)
| ~ element(X1,sK12)
| ~ element(X0,sK12) ),
inference(global_subsumption_just,[status(thm)],[c_2313,c_1872,c_2313]) ).
tcf(c_2603,plain,
( preboolean(sK12)
| ~ element(sK11(sK12),sK12)
| ~ element(sK10(sK12),sK12)
| ~ in(set_difference(sK10(sK12),sK11(sK12)),sK12) ),
inference(superposition,[status(thm)],[c_1216,c_93]) ).
tcf(c_2604,plain,
( ~ element(sK11(sK12),sK12)
| ~ element(sK10(sK12),sK12)
| ~ in(set_difference(sK10(sK12),sK11(sK12)),sK12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2603,c_1218]) ).
tcf(c_2616,plain,
( ~ element(sK11(sK12),sK12)
| ~ element(sK10(sK12),sK12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2604,c_2350]) ).
tcf(c_3005,plain,
( preboolean(sK12)
| ~ element(sK11(sK12),sK12) ),
inference(superposition,[status(thm)],[c_1869,c_2616]) ).
tcf(c_3007,plain,
~ element(sK11(sK12),sK12),
inference(forward_subsumption_resolution,[status(thm)],[c_3005,c_1218]) ).
tcf(c_3037,plain,
( preboolean(sK12)
| in(sK11(sK12),sK12) ),
inference(superposition,[status(thm)],[c_1870,c_1659]) ).
tcf(c_3039,plain,
in(sK11(sK12),sK12),
inference(forward_subsumption_resolution,[status(thm)],[c_3037,c_1218]) ).
tcf(c_3085,plain,
element(sK11(sK12),sK12),
inference(superposition,[status(thm)],[c_3039,c_103]) ).
tcf(c_3086,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_3085,c_3007]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU106+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.17/0.42 % Computer : n019.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Thu Sep 24 12:46:04 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.17/0.49 Running first-order theorem proving
% 0.17/0.49 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
% 0.24/0.50
% 0.24/0.51 % ======== iProver multi-core TPTP/SMT =========
% 0.24/0.51
% 0.24/0.51 % Detected problem language: tptp
% 0.24/0.52 % Proving...
% 3.13/1.40 % SZS status Started for theBenchmark.p
% 3.13/1.40 % SZS status Theorem for theBenchmark.p
% 3.13/1.40
% 3.13/1.40 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.13/1.40
% 3.13/1.40 % ------ iProver source info
% 3.13/1.40
% 3.13/1.40 % git: date: 2026-07-19 20:42:38 +0200
% 3.13/1.40 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.13/1.40 % git: non_committed_changes: false
% 3.13/1.40
% 3.13/1.40 % ------ Parsing...
% 3.13/1.40 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.13/1.40
% 3.13/1.40 % ------ Preprocessing... sup_sim: 7 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 %
% 3.13/1.40
% 3.13/1.40 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.13/1.40
% 3.13/1.40 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.13/1.40 % ------ Proving...
% 3.13/1.40 % ------ Problem Properties
% 3.13/1.40
% 3.13/1.40 %
% 3.13/1.40 % clauses 46
% 3.13/1.40 % conjectures 4
% 3.13/1.40 % EPR 14
% 3.13/1.40 % Horn 40
% 3.13/1.40 % unary 23
% 3.13/1.40 % binary 14
% 3.13/1.40 % lits 80
% 3.13/1.40 % lits eq 10
% 3.13/1.40 % fd_pure 0
% 3.13/1.40 % fd_pseudo 0
% 3.13/1.40 % fd_cond 1
% 3.13/1.40 % fd_pseudo_cond 1
% 3.13/1.40 % AC symbols 0
% 3.13/1.40
% 3.13/1.40 % ------ Schedule dynamic 5 is on
% 3.13/1.40
% 3.13/1.40 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.13/1.40
% 3.13/1.40
% 3.13/1.40 % ------
% 3.13/1.40 % Current options:
% 3.13/1.40 % ------
% 3.13/1.40
% 3.13/1.40
% 3.13/1.40 %
% 3.13/1.40
% 3.13/1.40 % ------ Proving...
% 3.13/1.40 %
% 3.13/1.40
% 3.13/1.40 % SZS status Theorem for theBenchmark.p
% 3.13/1.40
% 3.13/1.40 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.35/1.40
% 4.35/1.40
%------------------------------------------------------------------------------