%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU107+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 : n026.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 0.90s 1.30s
% Output : CNFRefutation 0.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 59 ( 21 unt; 0 def)
% Number of atoms : 158 ( 20 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 176 ( 77 ~; 78 |; 15 &)
% ( 1 <=>; 5 =>; 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; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-3 aty)
% Number of variables : 90 ( 1 sgn 87 !; 3 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
fof(f6,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(f7,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f20,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(f21,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f22,conjecture,
! [X0] :
( ( preboolean(X0)
& ~ empty(X0) )
=> in(empty_set,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_finsub_1) ).
fof(f23,negated_conjecture,
~ ! [X0] :
( ( preboolean(X0)
& ~ empty(X0) )
=> in(empty_set,X0) ),
inference(negated_conjecture,[status(cth)],[f22]) ).
fof(f25,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f26,axiom,
! [X0,X1] :
( set_difference(X0,X1) = empty_set
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).
fof(f35,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f21]) ).
fof(f50,plain,
! [X0,X1,X2] :
( ~ element(X2,X0)
| ~ element(X1,X0)
| ~ preboolean(X0)
| empty(X0)
| element(prebool_difference(X0,X1,X2),X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ~ element(X2,X0)
| ~ element(X1,X0)
| ~ preboolean(X0)
| empty(X0)
| element(prebool_difference(X0,X1,X2),X0) ),
inference(flattening,[],[f50]) ).
fof(f56,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,[],[f20]) ).
fof(f57,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,[],[f56]) ).
fof(f58,plain,
? [X0] :
( preboolean(X0)
& ~ empty(X0)
& ~ in(empty_set,X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f59,plain,
? [X0] :
( preboolean(X0)
& ~ empty(X0)
& ~ in(empty_set,X0) ),
inference(flattening,[],[f58]) ).
fof(f61,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(ennf_transformation,[],[f25]) ).
fof(f62,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(flattening,[],[f61]) ).
fof(f69,plain,
! [X0] : element(sK0(X0),X0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f7]) ).
fof(f79,plain,
( preboolean(sK10)
& ~ empty(sK10)
& ~ in(empty_set,sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X0,sK10)],[f59]) ).
fof(f80,plain,
! [X0,X1] :
( ( set_difference(X0,X1) != empty_set
| subset(X0,X1) )
& ( ~ subset(X0,X1)
| set_difference(X0,X1) = empty_set ) ),
inference(nnf_transformation,[],[f26]) ).
fof(f88,plain,
! [X2,X0,X1] :
( ~ element(X2,X0)
| ~ element(X1,X0)
| ~ preboolean(X0)
| empty(X0)
| element(prebool_difference(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f89,plain,
! [X0] : element(sK0(X0),X0),
inference(cnf_transformation,[],[f69]) ).
fof(f114,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,[],[f57]) ).
fof(f115,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f35]) ).
fof(f116,plain,
preboolean(sK10),
inference(cnf_transformation,[],[f79]) ).
fof(f117,plain,
~ empty(sK10),
inference(cnf_transformation,[],[f79]) ).
fof(f118,plain,
~ in(empty_set,sK10),
inference(cnf_transformation,[],[f79]) ).
fof(f120,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f62]) ).
fof(f122,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_difference(X0,X1) = empty_set ),
inference(cnf_transformation,[],[f80]) ).
tcf(c_55,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,[],[f88]) ).
tcf(c_56,plain,
! [X0: $i] : element(sK0(X0),X0),
inference(cnf_transformation,[],[f89]) ).
tcf(c_81,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,[],[f114]) ).
tcf(c_82,plain,
! [X0: $i] : subset(X0,X0),
inference(cnf_transformation,[],[f115]) ).
tcf(c_83,negated_conjecture,
~ in(empty_set,sK10),
inference(cnf_transformation,[],[f118]) ).
tcf(c_84,negated_conjecture,
~ empty(sK10),
inference(cnf_transformation,[],[f117]) ).
tcf(c_85,negated_conjecture,
preboolean(sK10),
inference(cnf_transformation,[],[f116]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f120]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,X1) = empty_set )
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f122]) ).
tcf(c_619,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 != sK10 ) ),
inference(resolution_lifted,[status(thm)],[c_81,c_85]) ).
tcf(c_620,plain,
! [X0: $i,X1: $i] :
( empty(sK10)
| ( prebool_difference(sK10,X0,X1) = set_difference(X0,X1) )
| ~ element(X1,sK10)
| ~ element(X0,sK10) ),
inference(unflattening,[status(thm)],[c_619]) ).
tcf(c_622,plain,
! [X0: $i,X1: $i] :
( ~ element(X0,sK10)
| ~ element(X1,sK10)
| ( prebool_difference(sK10,X0,X1) = set_difference(X0,X1) ) ),
inference(global_subsumption_just,[status(thm)],[c_620,c_84,c_620]) ).
tcf(c_623,plain,
! [X0: $i,X1: $i] :
( ( prebool_difference(sK10,X0,X1) = set_difference(X0,X1) )
| ~ element(X1,sK10)
| ~ element(X0,sK10) ),
inference(renaming,[status(thm)],[c_622]) ).
tcf(c_634,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty(X0)
| element(prebool_difference(X0,X1,X2),X0)
| ~ element(X2,X0)
| ~ element(X1,X0)
| ( X0 != sK10 ) ),
inference(resolution_lifted,[status(thm)],[c_55,c_85]) ).
tcf(c_635,plain,
! [X0: $i,X1: $i] :
( empty(sK10)
| element(prebool_difference(sK10,X0,X1),sK10)
| ~ element(X1,sK10)
| ~ element(X0,sK10) ),
inference(unflattening,[status(thm)],[c_634]) ).
tcf(c_637,plain,
! [X0: $i,X1: $i] :
( ~ element(X0,sK10)
| ~ element(X1,sK10)
| element(prebool_difference(sK10,X0,X1),sK10) ),
inference(global_subsumption_just,[status(thm)],[c_635,c_84,c_635]) ).
tcf(c_638,plain,
! [X0: $i,X1: $i] :
( element(prebool_difference(sK10,X0,X1),sK10)
| ~ element(X1,sK10)
| ~ element(X0,sK10) ),
inference(renaming,[status(thm)],[c_637]) ).
tcf(c_1203,plain,
! [X0: $i,X1: $i] :
( element(prebool_difference(sK10,X0,X1),sK10)
| ~ element(X1,sK10)
| ~ element(X0,sK10) ),
inference(demodulation,[status(thm)],[c_638]) ).
tcf(c_1204,plain,
! [X0: $i,X1: $i] :
( ( prebool_difference(sK10,X0,X1) = set_difference(X0,X1) )
| ~ element(X1,sK10)
| ~ element(X0,sK10) ),
inference(demodulation,[status(thm)],[c_623]) ).
tcf(c_1205,negated_conjecture,
~ empty(sK10),
inference(demodulation,[status(thm)],[c_84]) ).
tcf(c_1206,negated_conjecture,
~ in(empty_set,sK10),
inference(demodulation,[status(thm)],[c_83]) ).
tcf(c_2211,plain,
! [X0: $i] :
( ( prebool_difference(sK10,X0,sK0(sK10)) = set_difference(X0,sK0(sK10)) )
| ~ element(X0,sK10) ),
inference(superposition,[status(thm)],[c_56,c_1204]) ).
tcf(c_2349,plain,
prebool_difference(sK10,sK0(sK10),sK0(sK10)) = set_difference(sK0(sK10),sK0(sK10)),
inference(superposition,[status(thm)],[c_56,c_2211]) ).
tcf(c_3104,plain,
! [X0: $i,X1: $i] :
( empty(sK10)
| in(prebool_difference(sK10,X0,X1),sK10)
| ~ element(X1,sK10)
| ~ element(X0,sK10) ),
inference(superposition,[status(thm)],[c_1203,c_87]) ).
tcf(c_3121,plain,
! [X0: $i,X1: $i] :
( in(prebool_difference(sK10,X0,X1),sK10)
| ~ element(X1,sK10)
| ~ element(X0,sK10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3104,c_1205]) ).
tcf(c_3143,plain,
( in(set_difference(sK0(sK10),sK0(sK10)),sK10)
| ~ element(sK0(sK10),sK10) ),
inference(superposition,[status(thm)],[c_2349,c_3121]) ).
tcf(c_3147,plain,
in(set_difference(sK0(sK10),sK0(sK10)),sK10),
inference(forward_subsumption_resolution,[status(thm)],[c_3143,c_56]) ).
tcf(c_3549,plain,
! [X0: $i] : set_difference(X0,X0) = empty_set,
inference(superposition,[status(thm)],[c_82,c_88]) ).
tcf(c_3553,plain,
in(empty_set,sK10),
inference(demodulation,[status(thm)],[c_3147,c_3549]) ).
tcf(c_3555,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3553,c_1206]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU107+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n026.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 12:48:54 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 0.90/1.30 % SZS status Started for theBenchmark.p
% 0.90/1.30 % SZS status Theorem for theBenchmark.p
% 0.90/1.30
% 0.90/1.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.90/1.30
% 0.90/1.30 % ------ iProver source info
% 0.90/1.30
% 0.90/1.30 % git: date: 2026-07-19 20:42:38 +0200
% 0.90/1.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.90/1.30 % git: non_committed_changes: false
% 0.90/1.30
% 0.90/1.30 % ------ Parsing...
% 0.90/1.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.90/1.30
% 0.90/1.30 % ------ Preprocessing... sup_sim: 0 sf_s rm: 9 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 5 0s sf_e pe_s pe_e %
% 0.90/1.30
% 0.90/1.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.90/1.30
% 0.90/1.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.90/1.30 % ------ Proving...
% 0.90/1.30 % ------ Problem Properties
% 0.90/1.30
% 0.90/1.30 %
% 0.90/1.30 % clauses 38
% 0.90/1.30 % conjectures 2
% 0.90/1.30 % EPR 16
% 0.90/1.30 % Horn 34
% 0.90/1.30 % unary 16
% 0.90/1.30 % binary 14
% 0.90/1.30 % lits 68
% 0.90/1.30 % lits eq 8
% 0.90/1.30 % fd_pure 0
% 0.90/1.30 % fd_pseudo 0
% 0.90/1.30 % fd_cond 1
% 0.90/1.30 % fd_pseudo_cond 1
% 0.90/1.30 % AC symbols 0
% 0.90/1.30
% 0.90/1.30 % ------ Schedule dynamic 5 is on
% 0.90/1.30
% 0.90/1.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.90/1.30
% 0.90/1.30
% 0.90/1.30 % ------
% 0.90/1.30 % Current options:
% 0.90/1.30 % ------
% 0.90/1.30
% 0.90/1.30
% 0.90/1.30 %
% 0.90/1.30
% 0.90/1.30 % ------ Proving...
% 0.90/1.30 %
% 0.90/1.30
% 0.90/1.30 % SZS status Theorem for theBenchmark.p
% 0.90/1.30
% 0.90/1.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.90/1.30
% 0.90/1.30
%------------------------------------------------------------------------------