%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU103+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n018.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 48.33s 21.09s
% Output : CNFRefutation 48.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 72 ( 21 unt; 0 def)
% Number of atoms : 231 ( 34 equ)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 276 ( 117 ~; 123 |; 28 &)
% ( 0 <=>; 8 =>; 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 : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 117 ( 0 sgn 111 !; 6 ?; 53 :)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X0,X1] : symmetric_difference(X0,X1) = set_union2(set_difference(X0,X1),set_difference(X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_xboole_0) ).
fof(f10,axiom,
! [X0,X1,X2] :
( ( element(X2,X0)
& element(X1,X0)
& preboolean(X0)
& ~ empty(X0) )
=> element(prebool_union2(X0,X1,X2),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_finsub_1) ).
fof(f11,axiom,
! [X0,X1,X2] :
( ( element(X2,X0)
& element(X1,X0)
& preboolean(X0)
& ~ empty(X0) )
=> element(prebool_difference(X0,X1,X2),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_finsub_1) ).
fof(f31,axiom,
! [X0,X1,X2] :
( ( element(X2,X0)
& element(X1,X0)
& preboolean(X0)
& ~ empty(X0) )
=> prebool_union2(X0,X1,X2) = set_union2(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_finsub_1) ).
fof(f32,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/sandbox/benchmark/theBenchmark.p',redefinition_k2_finsub_1) ).
fof(f34,conjecture,
! [X0,X1,X2] :
( ( preboolean(X2)
& ~ empty(X2) )
=> ( ( element(X1,X2)
& element(X0,X2) )
=> element(symmetric_difference(X0,X1),X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_finsub_1) ).
fof(f35,negated_conjecture,
~ ! [X0,X1,X2] :
( ( preboolean(X2)
& ~ empty(X2) )
=> ( ( element(X1,X2)
& element(X0,X2) )
=> element(symmetric_difference(X0,X1),X2) ) ),
inference(negated_conjecture,[status(cth)],[f34]) ).
fof(f67,plain,
! [X0,X1,X2] :
( ~ element(X2,X0)
| ~ element(X1,X0)
| ~ preboolean(X0)
| empty(X0)
| element(prebool_union2(X0,X1,X2),X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f68,plain,
! [X0,X1,X2] :
( ~ element(X2,X0)
| ~ element(X1,X0)
| ~ preboolean(X0)
| empty(X0)
| element(prebool_union2(X0,X1,X2),X0) ),
inference(flattening,[],[f67]) ).
fof(f69,plain,
! [X0,X1,X2] :
( ~ element(X2,X0)
| ~ element(X1,X0)
| ~ preboolean(X0)
| empty(X0)
| element(prebool_difference(X0,X1,X2),X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f70,plain,
! [X0,X1,X2] :
( ~ element(X2,X0)
| ~ element(X1,X0)
| ~ preboolean(X0)
| empty(X0)
| element(prebool_difference(X0,X1,X2),X0) ),
inference(flattening,[],[f69]) ).
fof(f83,plain,
! [X0,X1,X2] :
( ~ element(X2,X0)
| ~ element(X1,X0)
| ~ preboolean(X0)
| empty(X0)
| prebool_union2(X0,X1,X2) = set_union2(X1,X2) ),
inference(ennf_transformation,[],[f31]) ).
fof(f84,plain,
! [X0,X1,X2] :
( ~ element(X2,X0)
| ~ element(X1,X0)
| ~ preboolean(X0)
| empty(X0)
| prebool_union2(X0,X1,X2) = set_union2(X1,X2) ),
inference(flattening,[],[f83]) ).
fof(f85,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,[],[f32]) ).
fof(f86,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,[],[f85]) ).
fof(f87,plain,
? [X0,X1,X2] :
( preboolean(X2)
& ~ empty(X2)
& element(X1,X2)
& element(X0,X2)
& ~ element(symmetric_difference(X0,X1),X2) ),
inference(ennf_transformation,[],[f35]) ).
fof(f88,plain,
? [X0,X1,X2] :
( preboolean(X2)
& ~ empty(X2)
& element(X1,X2)
& element(X0,X2)
& ~ element(symmetric_difference(X0,X1),X2) ),
inference(flattening,[],[f87]) ).
fof(f109,plain,
( preboolean(sK12)
& ~ empty(sK12)
& element(sK11,sK12)
& element(sK10,sK12)
& ~ element(symmetric_difference(sK10,sK11),sK12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12]),skolemize(X0,sK10),skolemize(X1,sK11),skolemize(X2,sK12)],[f88]) ).
fof(f119,plain,
! [X0,X1] : symmetric_difference(X0,X1) = set_union2(set_difference(X0,X1),set_difference(X1,X0)),
inference(cnf_transformation,[],[f9]) ).
fof(f120,plain,
! [X2,X0,X1] :
( ~ element(X2,X0)
| ~ element(X1,X0)
| ~ preboolean(X0)
| empty(X0)
| element(prebool_union2(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f121,plain,
! [X2,X0,X1] :
( ~ element(X2,X0)
| ~ element(X1,X0)
| ~ preboolean(X0)
| empty(X0)
| element(prebool_difference(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f70]) ).
fof(f153,plain,
! [X2,X0,X1] :
( ~ element(X2,X0)
| ~ element(X1,X0)
| ~ preboolean(X0)
| empty(X0)
| prebool_union2(X0,X1,X2) = set_union2(X1,X2) ),
inference(cnf_transformation,[],[f84]) ).
fof(f154,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,[],[f86]) ).
fof(f156,plain,
preboolean(sK12),
inference(cnf_transformation,[],[f109]) ).
fof(f157,plain,
~ empty(sK12),
inference(cnf_transformation,[],[f109]) ).
fof(f158,plain,
element(sK11,sK12),
inference(cnf_transformation,[],[f109]) ).
fof(f159,plain,
element(sK10,sK12),
inference(cnf_transformation,[],[f109]) ).
fof(f160,plain,
~ element(symmetric_difference(sK10,sK11),sK12),
inference(cnf_transformation,[],[f109]) ).
fof(f175,plain,
~ element(set_union2(set_difference(sK10,sK11),set_difference(sK11,sK10)),sK12),
inference(definition_unfolding,[],[f160,f119]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X1)
| element(prebool_union2(X1,X0,X2),X1)
| ~ preboolean(X1)
| ~ element(X2,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f120]) ).
tcf(c_59,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,[],[f121]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X1)
| ( prebool_union2(X1,X0,X2) = set_union2(X0,X2) )
| ~ preboolean(X1)
| ~ element(X2,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f153]) ).
tcf(c_92,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,[],[f154]) ).
tcf(c_94,negated_conjecture,
~ element(set_union2(set_difference(sK10,sK11),set_difference(sK11,sK10)),sK12),
inference(cnf_transformation,[],[f175]) ).
tcf(c_95,negated_conjecture,
element(sK10,sK12),
inference(cnf_transformation,[],[f159]) ).
tcf(c_96,negated_conjecture,
element(sK11,sK12),
inference(cnf_transformation,[],[f158]) ).
tcf(c_97,negated_conjecture,
~ empty(sK12),
inference(cnf_transformation,[],[f157]) ).
tcf(c_98,negated_conjecture,
preboolean(sK12),
inference(cnf_transformation,[],[f156]) ).
tcf(c_565,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_92,c_98]) ).
tcf(c_566,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_565]) ).
tcf(c_568,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_566,c_97,c_566]) ).
tcf(c_569,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_568]) ).
tcf(c_580,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X0)
| ( prebool_union2(X0,X1,X2) = set_union2(X1,X2) )
| ~ element(X2,X0)
| ~ element(X1,X0)
| ( X0 != sK12 ) ),
inference(resolution_lifted,[status(thm)],[c_91,c_98]) ).
tcf(c_581,plain,
! [X0: $i,X1: $i] :
( empty(sK12)
| ( prebool_union2(sK12,X0,X1) = set_union2(X0,X1) )
| ~ element(X1,sK12)
| ~ element(X0,sK12) ),
inference(unflattening,[status(thm)],[c_580]) ).
tcf(c_583,plain,
! [X0: $i,X1: $i] :
( ~ element(X0,sK12)
| ~ element(X1,sK12)
| ( prebool_union2(sK12,X0,X1) = set_union2(X0,X1) ) ),
inference(global_subsumption_just,[status(thm)],[c_581,c_97,c_581]) ).
tcf(c_584,plain,
! [X0: $i,X1: $i] :
( ( prebool_union2(sK12,X0,X1) = set_union2(X0,X1) )
| ~ element(X1,sK12)
| ~ element(X0,sK12) ),
inference(renaming,[status(thm)],[c_583]) ).
tcf(c_610,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_59,c_98]) ).
tcf(c_611,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_610]) ).
tcf(c_613,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_611,c_97,c_611]) ).
tcf(c_614,plain,
! [X0: $i,X1: $i] :
( element(prebool_difference(sK12,X0,X1),sK12)
| ~ element(X1,sK12)
| ~ element(X0,sK12) ),
inference(renaming,[status(thm)],[c_613]) ).
tcf(c_625,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X0)
| element(prebool_union2(X0,X1,X2),X0)
| ~ element(X2,X0)
| ~ element(X1,X0)
| ( X0 != sK12 ) ),
inference(resolution_lifted,[status(thm)],[c_58,c_98]) ).
tcf(c_626,plain,
! [X0: $i,X1: $i] :
( empty(sK12)
| element(prebool_union2(sK12,X0,X1),sK12)
| ~ element(X1,sK12)
| ~ element(X0,sK12) ),
inference(unflattening,[status(thm)],[c_625]) ).
tcf(c_628,plain,
! [X0: $i,X1: $i] :
( ~ element(X0,sK12)
| ~ element(X1,sK12)
| element(prebool_union2(sK12,X0,X1),sK12) ),
inference(global_subsumption_just,[status(thm)],[c_626,c_97,c_626]) ).
tcf(c_629,plain,
! [X0: $i,X1: $i] :
( element(prebool_union2(sK12,X0,X1),sK12)
| ~ element(X1,sK12)
| ~ element(X0,sK12) ),
inference(renaming,[status(thm)],[c_628]) ).
tcf(c_1916,plain,
! [X0: $i] :
( ( prebool_difference(sK12,X0,sK10) = set_difference(X0,sK10) )
| ~ element(X0,sK12) ),
inference(superposition,[status(thm)],[c_95,c_569]) ).
tcf(c_1917,plain,
! [X0: $i] :
( ( prebool_difference(sK12,X0,sK11) = set_difference(X0,sK11) )
| ~ element(X0,sK12) ),
inference(superposition,[status(thm)],[c_96,c_569]) ).
tcf(c_1941,plain,
prebool_difference(sK12,sK11,sK10) = set_difference(sK11,sK10),
inference(superposition,[status(thm)],[c_96,c_1916]) ).
tcf(c_2010,plain,
( element(set_difference(sK11,sK10),sK12)
| ~ element(sK11,sK12)
| ~ element(sK10,sK12) ),
inference(superposition,[status(thm)],[c_1941,c_614]) ).
tcf(c_2030,plain,
prebool_difference(sK12,sK10,sK11) = set_difference(sK10,sK11),
inference(superposition,[status(thm)],[c_95,c_1917]) ).
tcf(c_2050,plain,
( element(set_difference(sK10,sK11),sK12)
| ~ element(sK11,sK12)
| ~ element(sK10,sK12) ),
inference(superposition,[status(thm)],[c_2030,c_614]) ).
tcf(c_2383,plain,
! [X0: $i] :
( ( prebool_difference(sK12,X0,sK10) = set_difference(X0,sK10) )
| ~ element(X0,sK12) ),
inference(superposition,[status(thm)],[c_95,c_569]) ).
tcf(c_2384,plain,
! [X0: $i] :
( ( prebool_difference(sK12,X0,sK11) = set_difference(X0,sK11) )
| ~ element(X0,sK12) ),
inference(superposition,[status(thm)],[c_96,c_569]) ).
tcf(c_2396,plain,
prebool_difference(sK12,sK11,sK10) = set_difference(sK11,sK10),
inference(superposition,[status(thm)],[c_96,c_2383]) ).
tcf(c_2408,plain,
( element(set_difference(sK11,sK10),sK12)
| ~ element(sK11,sK12)
| ~ element(sK10,sK12) ),
inference(superposition,[status(thm)],[c_2396,c_614]) ).
tcf(c_2417,plain,
prebool_difference(sK12,sK10,sK11) = set_difference(sK10,sK11),
inference(superposition,[status(thm)],[c_95,c_2384]) ).
tcf(c_2444,plain,
( element(set_difference(sK10,sK11),sK12)
| ~ element(sK11,sK12)
| ~ element(sK10,sK12) ),
inference(superposition,[status(thm)],[c_2417,c_614]) ).
tcf(c_2802,plain,
element(set_difference(sK11,sK10),sK12),
inference(global_subsumption_just,[status(thm)],[c_2408,c_96,c_95,c_2010]) ).
tcf(c_2805,plain,
! [X0: $i] :
( ( prebool_union2(sK12,X0,set_difference(sK11,sK10)) = set_union2(X0,set_difference(sK11,sK10)) )
| ~ element(X0,sK12) ),
inference(superposition,[status(thm)],[c_2802,c_584]) ).
tcf(c_23429,plain,
element(set_difference(sK10,sK11),sK12),
inference(global_subsumption_just,[status(thm)],[c_2444,c_96,c_95,c_2050]) ).
tcf(c_24169,plain,
prebool_union2(sK12,set_difference(sK10,sK11),set_difference(sK11,sK10)) = set_union2(set_difference(sK10,sK11),set_difference(sK11,sK10)),
inference(superposition,[status(thm)],[c_23429,c_2805]) ).
tcf(c_34718,plain,
( element(set_union2(set_difference(sK10,sK11),set_difference(sK11,sK10)),sK12)
| ~ element(set_difference(sK11,sK10),sK12)
| ~ element(set_difference(sK10,sK11),sK12) ),
inference(superposition,[status(thm)],[c_24169,c_629]) ).
tcf(c_34719,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_34718,c_2050,c_2010,c_94,c_95,c_96]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU103+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/10.40 % Computer : n018.cluster.edu
% 0.13/10.40 % Model : x86_64 x86_64
% 0.13/10.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/10.40 % Memory : 8046.5625MB
% 0.13/10.40 % OS : Linux 6.8.0-71-generic
% 0.13/10.40 % CPULimit : 300
% 0.13/10.40 % WCLimit : 300
% 0.13/10.40 % DateTime : Thu Sep 24 12:48:00 UTC 2026
% 0.13/10.40 % CPUTime :
% 0.13/10.40 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/10.45 Running first-order theorem proving
% 0.13/10.45 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/10.47
% 0.13/10.47 % ======== iProver multi-core TPTP/SMT =========
% 0.13/10.47
% 0.13/10.47 % Detected problem language: tptp
% 0.13/10.48 % Proving...
% 48.33/21.09 % SZS status Started for theBenchmark.p
% 48.33/21.09 % SZS status Theorem for theBenchmark.p
% 48.33/21.09
% 48.33/21.09 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 48.33/21.09
% 48.33/21.09 % ------ iProver source info
% 48.33/21.09
% 48.33/21.09 % git: date: 2026-07-19 20:42:38 +0200
% 48.33/21.09 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 48.33/21.09 % git: non_committed_changes: false
% 48.33/21.09
% 48.33/21.09 % ------ Parsing...
% 48.33/21.09 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 48.33/21.09
% 48.33/21.09 % ------ Preprocessing... sup_sim: 1 sf_s rm: 11 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 %
% 48.33/21.09
% 48.33/21.09 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 48.33/21.09
% 48.33/21.09 % ------ Preprocessing... sf_s rm: 3 0s sf_e sf_s rm: 2 0s sf_e sf_s rm: 0 0s sf_e
% 48.33/21.09 % ------ Proving...
% 48.33/21.09 % ------ Problem Properties
% 48.33/21.09
% 48.33/21.09 %
% 48.33/21.09 % clauses 53
% 48.33/21.09 % conjectures 4
% 48.33/21.09 % EPR 18
% 48.33/21.09 % Horn 47
% 48.33/21.09 % unary 21
% 48.33/21.09 % binary 16
% 48.33/21.09 % lits 101
% 48.33/21.09 % lits eq 15
% 48.33/21.09 % fd_pure 0
% 48.33/21.09 % fd_pseudo 0
% 48.33/21.09 % fd_cond 1
% 48.33/21.09 % fd_pseudo_cond 1
% 48.33/21.09 % AC symbols 0
% 48.33/21.09
% 48.33/21.09 % ------ Input Options Time Limit: Unbounded
% 48.33/21.09
% 48.33/21.09
% 48.33/21.09 % ------
% 48.33/21.09 % Current options:
% 48.33/21.09 % ------
% 48.33/21.09
% 48.33/21.09
% 48.33/21.09 %
% 48.33/21.09
% 48.33/21.09 % ------ Proving...
% 48.33/21.09 %
% 48.33/21.09
% 48.33/21.09 % SZS status Theorem for theBenchmark.p
% 48.33/21.09
% 48.33/21.09 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 48.33/21.09
% 48.33/21.09
%------------------------------------------------------------------------------