%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU104+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 : n005.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 4.29s 1.54s
% Output : CNFRefutation 4.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 67 ( 23 unt; 0 def)
% Number of atoms : 181 ( 14 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 193 ( 79 ~; 74 |; 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; 2 con; 0-2 aty)
% Number of variables : 93 ( 1 sgn 87 !; 6 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f17,axiom,
! [X0,X1] : set_union2(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
fof(f28,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/sandbox/benchmark/theBenchmark.p',t10_finsub_1) ).
fof(f29,conjecture,
! [X0] :
( ~ empty(X0)
=> ( ! [X1] :
( element(X1,X0)
=> ! [X2] :
( element(X2,X0)
=> ( in(set_difference(X1,X2),X0)
& in(symmetric_difference(X1,X2),X0) ) ) )
=> preboolean(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_finsub_1) ).
fof(f30,negated_conjecture,
~ ! [X0] :
( ~ empty(X0)
=> ( ! [X1] :
( element(X1,X0)
=> ! [X2] :
( element(X2,X0)
=> ( in(set_difference(X1,X2),X0)
& in(symmetric_difference(X1,X2),X0) ) ) )
=> preboolean(X0) ) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f32,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(f34,axiom,
! [X0] : set_difference(X0,empty_set) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
fof(f43,axiom,
! [X0,X1] : set_union2(X0,X1) = symmetric_difference(X0,set_difference(X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t98_xboole_1) ).
fof(f44,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(rectify,[],[f17]) ).
fof(f71,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,[],[f28]) ).
fof(f72,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,[],[f71]) ).
fof(f73,plain,
? [X0] :
( ~ empty(X0)
& ! [X1] :
( ~ element(X1,X0)
| ! [X2] :
( ~ element(X2,X0)
| ( in(set_difference(X1,X2),X0)
& in(symmetric_difference(X1,X2),X0) ) ) )
& ~ preboolean(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f74,plain,
? [X0] :
( ~ empty(X0)
& ! [X1] :
( ~ element(X1,X0)
| ! [X2] :
( ~ element(X2,X0)
| ( in(set_difference(X1,X2),X0)
& in(symmetric_difference(X1,X2),X0) ) ) )
& ~ preboolean(X0) ),
inference(flattening,[],[f73]) ).
fof(f75,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(ennf_transformation,[],[f32]) ).
fof(f95,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,[],[f72]) ).
fof(f96,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,[],[f95]) ).
fof(f97,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))],[f96]) ).
fof(f98,plain,
( ~ empty(sK12)
& ! [X1] :
( ~ element(X1,sK12)
| ! [X2] :
( ~ element(X2,sK12)
| ( in(set_difference(X1,X2),sK12)
& in(symmetric_difference(X1,X2),sK12) ) ) )
& ~ preboolean(sK12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X0,sK12)],[f74]) ).
fof(f105,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f116,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(cnf_transformation,[],[f44]) ).
fof(f141,plain,
! [X0] :
( in(sK11(X0),X0)
| preboolean(X0) ),
inference(cnf_transformation,[],[f97]) ).
fof(f142,plain,
! [X0] :
( in(sK10(X0),X0)
| preboolean(X0) ),
inference(cnf_transformation,[],[f97]) ).
fof(f143,plain,
! [X0] :
( ~ in(set_difference(sK10(X0),sK11(X0)),X0)
| ~ in(set_union2(sK10(X0),sK11(X0)),X0)
| preboolean(X0) ),
inference(cnf_transformation,[],[f97]) ).
fof(f145,plain,
! [X2,X1] :
( ~ element(X1,sK12)
| ~ element(X2,sK12)
| in(set_difference(X1,X2),sK12) ),
inference(cnf_transformation,[],[f98]) ).
fof(f146,plain,
! [X2,X1] :
( ~ element(X1,sK12)
| ~ element(X2,sK12)
| in(symmetric_difference(X1,X2),sK12) ),
inference(cnf_transformation,[],[f98]) ).
fof(f147,plain,
~ preboolean(sK12),
inference(cnf_transformation,[],[f98]) ).
fof(f149,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f151,plain,
! [X0] : set_difference(X0,empty_set) = X0,
inference(cnf_transformation,[],[f34]) ).
fof(f160,plain,
! [X0,X1] : set_union2(X0,X1) = symmetric_difference(X0,set_difference(X1,X0)),
inference(cnf_transformation,[],[f43]) ).
fof(f162,plain,
! [X0,X1] : symmetric_difference(X0,set_difference(X1,X0)) = symmetric_difference(X1,set_difference(X0,X1)),
inference(definition_unfolding,[],[f105,f160,f160]) ).
fof(f166,plain,
! [X0] : symmetric_difference(X0,set_difference(X0,X0)) = X0,
inference(definition_unfolding,[],[f116,f160]) ).
fof(f167,plain,
! [X0] :
( ~ in(set_difference(sK10(X0),sK11(X0)),X0)
| ~ in(symmetric_difference(sK10(X0),set_difference(sK11(X0),sK10(X0))),X0)
| preboolean(X0) ),
inference(definition_unfolding,[],[f143,f160]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] : symmetric_difference(X0,set_difference(X1,X0)) = symmetric_difference(X1,set_difference(X0,X1)),
inference(cnf_transformation,[],[f162]) ).
tcf(c_66,plain,
! [X0: $i] : symmetric_difference(X0,set_difference(X0,X0)) = X0,
inference(cnf_transformation,[],[f166]) ).
tcf(c_89,plain,
! [X0: $i] :
( preboolean(X0)
| ~ in(set_difference(sK10(X0),sK11(X0)),X0)
| ~ in(symmetric_difference(sK10(X0),set_difference(sK11(X0),sK10(X0))),X0) ),
inference(cnf_transformation,[],[f167]) ).
tcf(c_90,plain,
! [X0: $i] :
( preboolean(X0)
| in(sK10(X0),X0) ),
inference(cnf_transformation,[],[f142]) ).
tcf(c_91,plain,
! [X0: $i] :
( preboolean(X0)
| in(sK11(X0),X0) ),
inference(cnf_transformation,[],[f141]) ).
tcf(c_94,negated_conjecture,
~ preboolean(sK12),
inference(cnf_transformation,[],[f147]) ).
tcf(c_95,negated_conjecture,
! [X0: $i,X1: $i] :
( in(symmetric_difference(X0,X1),sK12)
| ~ element(X1,sK12)
| ~ element(X0,sK12) ),
inference(cnf_transformation,[],[f146]) ).
tcf(c_96,negated_conjecture,
! [X0: $i,X1: $i] :
( in(set_difference(X0,X1),sK12)
| ~ element(X1,sK12)
| ~ element(X0,sK12) ),
inference(cnf_transformation,[],[f145]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f149]) ).
tcf(c_101,plain,
! [X0: $i] : set_difference(X0,empty_set) = X0,
inference(cnf_transformation,[],[f151]) ).
tcf(c_123,plain,
( preboolean(sK12)
| in(sK11(sK12),sK12) ),
inference(instantiation,[status(thm)],[c_91]) ).
tcf(c_124,plain,
( preboolean(sK12)
| in(sK10(sK12),sK12) ),
inference(instantiation,[status(thm)],[c_90]) ).
tcf(c_1180,negated_conjecture,
! [X0: $i,X1: $i] :
( in(set_difference(X0,X1),sK12)
| ~ element(X1,sK12)
| ~ element(X0,sK12) ),
inference(demodulation,[status(thm)],[c_96]) ).
tcf(c_1181,negated_conjecture,
! [X0: $i,X1: $i] :
( in(symmetric_difference(X0,X1),sK12)
| ~ element(X1,sK12)
| ~ element(X0,sK12) ),
inference(demodulation,[status(thm)],[c_95]) ).
tcf(c_1182,negated_conjecture,
~ preboolean(sK12),
inference(demodulation,[status(thm)],[c_94]) ).
tcf(c_1638,plain,
! [X0: $i] :
( in(X0,sK12)
| ~ element(empty_set,sK12)
| ~ element(X0,sK12) ),
inference(superposition,[status(thm)],[c_101,c_1180]) ).
tcf(c_1692,plain,
! [X0: $i] :
( preboolean(X0)
| element(sK10(X0),X0) ),
inference(superposition,[status(thm)],[c_90,c_99]) ).
tcf(c_1693,plain,
! [X0: $i] :
( preboolean(X0)
| element(sK11(X0),X0) ),
inference(superposition,[status(thm)],[c_91,c_99]) ).
tcf(c_1695,plain,
! [X0: $i,X1: $i] :
( element(set_difference(X0,X1),sK12)
| ~ element(X1,sK12)
| ~ element(X0,sK12) ),
inference(superposition,[status(thm)],[c_1180,c_99]) ).
tcf(c_1715,plain,
( preboolean(sK12)
| in(sK10(sK12),sK12)
| ~ element(empty_set,sK12) ),
inference(superposition,[status(thm)],[c_1692,c_1638]) ).
tcf(c_1716,plain,
( in(sK10(sK12),sK12)
| ~ element(empty_set,sK12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1715,c_1182]) ).
tcf(c_1723,plain,
( preboolean(sK12)
| in(sK11(sK12),sK12)
| ~ element(empty_set,sK12) ),
inference(superposition,[status(thm)],[c_1693,c_1638]) ).
tcf(c_1724,plain,
( in(sK11(sK12),sK12)
| ~ element(empty_set,sK12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1723,c_1182]) ).
tcf(c_1727,plain,
in(sK10(sK12),sK12),
inference(global_subsumption_just,[status(thm)],[c_1716,c_94,c_124]) ).
tcf(c_1729,plain,
element(sK10(sK12),sK12),
inference(superposition,[status(thm)],[c_1727,c_99]) ).
tcf(c_1730,plain,
in(sK11(sK12),sK12),
inference(global_subsumption_just,[status(thm)],[c_1724,c_94,c_123]) ).
tcf(c_1732,plain,
element(sK11(sK12),sK12),
inference(superposition,[status(thm)],[c_1730,c_99]) ).
tcf(c_1940,plain,
! [X0: $i] :
( in(X0,sK12)
| ~ element(X0,sK12)
| ~ element(set_difference(X0,X0),sK12) ),
inference(superposition,[status(thm)],[c_66,c_1181]) ).
tcf(c_2040,plain,
! [X0: $i] :
( in(X0,sK12)
| ~ element(X0,sK12) ),
inference(superposition,[status(thm)],[c_1695,c_1940]) ).
tcf(c_2148,plain,
! [X0: $i,X1: $i] :
( in(symmetric_difference(X0,set_difference(X1,X0)),sK12)
| ~ element(X1,sK12)
| ~ element(set_difference(X0,X1),sK12) ),
inference(superposition,[status(thm)],[c_56,c_1181]) ).
tcf(c_2455,plain,
( preboolean(sK12)
| ~ element(sK11(sK12),sK12)
| ~ element(set_difference(sK10(sK12),sK11(sK12)),sK12)
| ~ in(set_difference(sK10(sK12),sK11(sK12)),sK12) ),
inference(superposition,[status(thm)],[c_2148,c_89]) ).
tcf(c_2456,plain,
( ~ element(set_difference(sK10(sK12),sK11(sK12)),sK12)
| ~ in(set_difference(sK10(sK12),sK11(sK12)),sK12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2455,c_1182,c_1732]) ).
tcf(c_2548,plain,
~ element(set_difference(sK10(sK12),sK11(sK12)),sK12),
inference(forward_subsumption_resolution,[status(thm)],[c_2456,c_2040]) ).
tcf(c_2549,plain,
( ~ element(sK11(sK12),sK12)
| ~ element(sK10(sK12),sK12) ),
inference(superposition,[status(thm)],[c_1695,c_2548]) ).
tcf(c_2550,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2549,c_1732,c_1729]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU104+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.20/0.45 % Computer : n005.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % OS : Linux 6.8.0-71-generic
% 0.20/0.45 % CPULimit : 300
% 0.20/0.45 % WCLimit : 300
% 0.20/0.45 % DateTime : Thu Sep 24 12:45:18 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.46 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.23/0.51 Running first-order theorem proving
% 0.23/0.51 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
% 0.23/0.53
% 0.23/0.53 % ======== iProver multi-core TPTP/SMT =========
% 0.23/0.53
% 0.23/0.53 % Detected problem language: tptp
% 0.23/0.54 % Proving...
% 4.29/1.54 % SZS status Started for theBenchmark.p
% 4.29/1.54 % SZS status Theorem for theBenchmark.p
% 4.29/1.54
% 4.29/1.54 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.29/1.54
% 4.29/1.54 % ------ iProver source info
% 4.29/1.54
% 4.29/1.54 % git: date: 2026-07-19 20:42:38 +0200
% 4.29/1.54 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.29/1.54 % git: non_committed_changes: false
% 4.29/1.54
% 4.29/1.54 % ------ Parsing...
% 4.29/1.54 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.29/1.54
% 4.29/1.54 % ------ Preprocessing... sup_sim: 1 sf_s rm: 11 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 %
% 4.29/1.54
% 4.29/1.54 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.29/1.54
% 4.29/1.54 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.29/1.54 % ------ Proving...
% 4.29/1.54 % ------ Problem Properties
% 4.29/1.54
% 4.29/1.54 %
% 4.29/1.54 % clauses 45
% 4.29/1.54 % conjectures 4
% 4.29/1.54 % EPR 14
% 4.29/1.54 % Horn 39
% 4.29/1.54 % unary 22
% 4.29/1.54 % binary 14
% 4.29/1.54 % lits 79
% 4.29/1.54 % lits eq 9
% 4.29/1.54 % fd_pure 0
% 4.29/1.54 % fd_pseudo 0
% 4.29/1.54 % fd_cond 1
% 4.29/1.54 % fd_pseudo_cond 1
% 4.29/1.54 % AC symbols 0
% 4.29/1.54
% 4.29/1.54 % ------ Schedule dynamic 5 is on
% 4.29/1.54
% 4.29/1.54 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.29/1.54
% 4.29/1.54
% 4.29/1.54 % ------
% 4.29/1.54 % Current options:
% 4.29/1.54 % ------
% 4.29/1.54
% 4.29/1.54
% 4.29/1.54 %
% 4.29/1.54
% 4.29/1.54 % ------ Proving...
% 4.29/1.54 %
% 4.29/1.54
% 4.29/1.54 % SZS status Theorem for theBenchmark.p
% 4.29/1.54
% 4.29/1.54 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.29/1.54
% 4.29/1.54
%------------------------------------------------------------------------------