%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWV378+1 : TPTP v9.3.1. Released v3.3.0.
% 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 03:17:30 PM UTC 2026
% Result : Theorem 7.56s 1.97s
% Output : CNFRefutation 7.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 8
% Syntax : Number of formulae : 56 ( 14 unt; 0 def)
% Number of atoms : 121 ( 36 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 110 ( 45 ~; 50 |; 6 &)
% ( 2 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 155 ( 0 sgn 151 !; 4 ?; 68 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( less_than(X1,X0)
| less_than(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax',totality) ).
fof(f4,axiom,
! [X0,X1] :
( strictly_less_than(X0,X1)
<=> ( ~ less_than(X1,X0)
& less_than(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax',stricly_smaller_definition) ).
fof(f28,axiom,
! [X0,X1] :
( ok(triple(X0,X1,bad))
<=> $false ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax40) ).
fof(f29,axiom,
! [X0,X1,X2] :
( ~ ok(triple(X0,X1,X2))
=> X2 = bad ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax41) ).
fof(f31,axiom,
! [X0,X1,X2,X3] :
( ~ contains_slb(X1,X3)
=> remove_cpq(triple(X0,X1,X2),X3) = triple(X0,X1,bad) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax43) ).
fof(f32,axiom,
! [X0,X1,X2,X3] :
( ( less_than(lookup_slb(X1,X3),X3)
& contains_slb(X1,X3) )
=> remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax44) ).
fof(f33,axiom,
! [X0,X1,X2,X3] :
( ( strictly_less_than(X3,lookup_slb(X1,X3))
& contains_slb(X1,X3) )
=> remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),bad) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax45) ).
fof(f42,conjecture,
! [X0,X1,X2,X3] :
( ~ ok(triple(X0,X1,X2))
=> ~ ok(remove_cpq(triple(X0,X1,X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l14_co) ).
fof(f43,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ~ ok(triple(X0,X1,X2))
=> ~ ok(remove_cpq(triple(X0,X1,X2),X3)) ),
inference(negated_conjecture,[status(cth)],[f42]) ).
fof(f46,plain,
! [X0,X1] : ~ ok(triple(X0,X1,bad)),
inference(true_and_false_elimination,[],[f28]) ).
fof(f47,plain,
! [X0,X1] : ~ ok(triple(X0,X1,bad)),
inference(flattening,[],[f46]) ).
fof(f52,plain,
! [X0,X1] :
( ( ~ less_than(X1,X0)
& less_than(X0,X1) )
=> strictly_less_than(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f55,plain,
! [X0,X1] :
( less_than(X1,X0)
| ~ less_than(X0,X1)
| strictly_less_than(X0,X1) ),
inference(ennf_transformation,[],[f52]) ).
fof(f56,plain,
! [X0,X1] :
( less_than(X1,X0)
| ~ less_than(X0,X1)
| strictly_less_than(X0,X1) ),
inference(flattening,[],[f55]) ).
fof(f69,plain,
! [X0,X1,X2] :
( ok(triple(X0,X1,X2))
| X2 = bad ),
inference(ennf_transformation,[],[f29]) ).
fof(f70,plain,
! [X0,X1,X2,X3] :
( contains_slb(X1,X3)
| remove_cpq(triple(X0,X1,X2),X3) = triple(X0,X1,bad) ),
inference(ennf_transformation,[],[f31]) ).
fof(f71,plain,
! [X0,X1,X2,X3] :
( ~ less_than(lookup_slb(X1,X3),X3)
| ~ contains_slb(X1,X3)
| remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),X2) ),
inference(ennf_transformation,[],[f32]) ).
fof(f72,plain,
! [X0,X1,X2,X3] :
( ~ less_than(lookup_slb(X1,X3),X3)
| ~ contains_slb(X1,X3)
| remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),X2) ),
inference(flattening,[],[f71]) ).
fof(f73,plain,
! [X0,X1,X2,X3] :
( ~ strictly_less_than(X3,lookup_slb(X1,X3))
| ~ contains_slb(X1,X3)
| remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),bad) ),
inference(ennf_transformation,[],[f33]) ).
fof(f74,plain,
! [X0,X1,X2,X3] :
( ~ strictly_less_than(X3,lookup_slb(X1,X3))
| ~ contains_slb(X1,X3)
| remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),bad) ),
inference(flattening,[],[f73]) ).
fof(f82,plain,
? [X0,X1,X2,X3] :
( ~ ok(triple(X0,X1,X2))
& ok(remove_cpq(triple(X0,X1,X2),X3)) ),
inference(ennf_transformation,[],[f43]) ).
fof(f89,plain,
( ~ ok(triple(sK0,sK1,sK2))
& ok(remove_cpq(triple(sK0,sK1,sK2),sK3)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f82]) ).
fof(f91,plain,
! [X0,X1] :
( less_than(X1,X0)
| less_than(X0,X1) ),
inference(cnf_transformation,[],[f2]) ).
fof(f93,plain,
! [X0,X1] :
( less_than(X1,X0)
| ~ less_than(X0,X1)
| strictly_less_than(X0,X1) ),
inference(cnf_transformation,[],[f56]) ).
fof(f124,plain,
! [X0,X1] : ~ ok(triple(X0,X1,bad)),
inference(cnf_transformation,[],[f47]) ).
fof(f125,plain,
! [X2,X0,X1] :
( ok(triple(X0,X1,X2))
| bad = X2 ),
inference(cnf_transformation,[],[f69]) ).
fof(f127,plain,
! [X2,X3,X0,X1] :
( contains_slb(X1,X3)
| triple(X0,X1,bad) = remove_cpq(triple(X0,X1,X2),X3) ),
inference(cnf_transformation,[],[f70]) ).
fof(f128,plain,
! [X2,X3,X0,X1] :
( ~ less_than(lookup_slb(X1,X3),X3)
| ~ contains_slb(X1,X3)
| remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),X2) ),
inference(cnf_transformation,[],[f72]) ).
fof(f129,plain,
! [X2,X3,X0,X1] :
( ~ strictly_less_than(X3,lookup_slb(X1,X3))
| ~ contains_slb(X1,X3)
| remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),bad) ),
inference(cnf_transformation,[],[f74]) ).
fof(f138,plain,
~ ok(triple(sK0,sK1,sK2)),
inference(cnf_transformation,[],[f89]) ).
fof(f139,plain,
ok(remove_cpq(triple(sK0,sK1,sK2),sK3)),
inference(cnf_transformation,[],[f89]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( less_than(X1,X0)
| less_than(X0,X1) ),
inference(cnf_transformation,[],[f91]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( strictly_less_than(X0,X1)
| less_than(X1,X0)
| ~ less_than(X0,X1) ),
inference(cnf_transformation,[],[f93]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i] : ~ ok(triple(X0,X1,bad)),
inference(cnf_transformation,[],[f124]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i,X2: $i] :
( ok(triple(X1,X2,X0))
| ( X0 = bad ) ),
inference(cnf_transformation,[],[f125]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( contains_slb(X1,X3)
| ( remove_cpq(triple(X0,X1,X2),X3) = triple(X0,X1,bad) ) ),
inference(cnf_transformation,[],[f127]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( triple(remove_pqp(X2,X1),remove_slb(X0,X1),X3) = remove_cpq(triple(X2,X0,X3),X1) )
| ~ contains_slb(X0,X1)
| ~ less_than(lookup_slb(X0,X1),X1) ),
inference(cnf_transformation,[],[f128]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( triple(remove_pqp(X2,X0),remove_slb(X1,X0),bad) = remove_cpq(triple(X2,X1,X3),X0) )
| ~ contains_slb(X1,X0)
| ~ strictly_less_than(X0,lookup_slb(X1,X0)) ),
inference(cnf_transformation,[],[f129]) ).
tcf(c_95,negated_conjecture,
ok(remove_cpq(triple(sK0,sK1,sK2),sK3)),
inference(cnf_transformation,[],[f139]) ).
tcf(c_96,negated_conjecture,
~ ok(triple(sK0,sK1,sK2)),
inference(cnf_transformation,[],[f138]) ).
tcf(c_130,plain,
! [X0: $i,X1: $i] :
( strictly_less_than(X0,X1)
| less_than(X1,X0) ),
inference(global_subsumption_just,[status(thm)],[c_52,c_50,c_52]) ).
tcf(c_131,plain,
! [X0: $i,X1: $i] :
( strictly_less_than(X1,X0)
| less_than(X0,X1) ),
inference(renaming,[status(thm)],[c_130]) ).
tcf(c_406,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( less_than(X2,X3)
| ( triple(remove_pqp(X4,X1),remove_slb(X0,X1),bad) = remove_cpq(triple(X4,X0,X5),X1) )
| ~ contains_slb(X0,X1)
| ( X1 != X3 )
| ( lookup_slb(X0,X1) != X2 ) ),
inference(resolution_lifted,[status(thm)],[c_88,c_131]) ).
tcf(c_407,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( less_than(lookup_slb(X0,X1),X1)
| ( triple(remove_pqp(X2,X1),remove_slb(X0,X1),bad) = remove_cpq(triple(X2,X0,X3),X1) )
| ~ contains_slb(X0,X1) ),
inference(unflattening,[status(thm)],[c_406]) ).
tcf(c_1203,plain,
bad = sK2,
inference(superposition,[status(thm)],[c_84,c_96]) ).
tcf(c_1204,plain,
~ ok(triple(sK0,sK1,bad)),
inference(superposition,[status(thm)],[c_1203,c_96]) ).
tcf(c_1205,plain,
ok(remove_cpq(triple(sK0,sK1,bad),sK3)),
inference(superposition,[status(thm)],[c_1203,c_95]) ).
tcf(c_1221,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( triple(remove_pqp(X4,X1),remove_slb(X0,X1),bad) = remove_cpq(triple(X4,X0,X5),X1) )
| ( triple(remove_pqp(X2,X1),remove_slb(X0,X1),X3) = remove_cpq(triple(X2,X0,X3),X1) )
| ~ contains_slb(X0,X1) ),
inference(superposition,[status(thm)],[c_407,c_87]) ).
tcf(c_1289,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( ( remove_cpq(triple(X6,X2,X7),X1) = triple(X6,X2,bad) )
| ( triple(remove_pqp(X4,X1),remove_slb(X2,X1),bad) = remove_cpq(triple(X4,X2,X5),X1) )
| ( triple(remove_pqp(X0,X1),remove_slb(X2,X1),X3) = remove_cpq(triple(X0,X2,X3),X1) ) ),
inference(superposition,[status(thm)],[c_86,c_1221]) ).
tcf(c_1444,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ok(triple(sK0,sK1,bad))
| ( triple(remove_pqp(X2,sK3),remove_slb(sK1,sK3),bad) = remove_cpq(triple(X2,sK1,X3),sK3) )
| ( triple(remove_pqp(X0,sK3),remove_slb(sK1,sK3),X1) = remove_cpq(triple(X0,sK1,X1),sK3) ) ),
inference(superposition,[status(thm)],[c_1289,c_95]) ).
tcf(c_1473,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( triple(remove_pqp(X0,sK3),remove_slb(sK1,sK3),X1) = remove_cpq(triple(X0,sK1,X1),sK3) )
| ( triple(remove_pqp(X2,sK3),remove_slb(sK1,sK3),bad) = remove_cpq(triple(X2,sK1,X3),sK3) ) ),
inference(global_subsumption_just,[status(thm)],[c_1444,c_1204,c_1444]) ).
tcf(c_1474,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( triple(remove_pqp(X2,sK3),remove_slb(sK1,sK3),bad) = remove_cpq(triple(X2,sK1,X3),sK3) )
| ( triple(remove_pqp(X0,sK3),remove_slb(sK1,sK3),X1) = remove_cpq(triple(X0,sK1,X1),sK3) ) ),
inference(renaming,[status(thm)],[c_1473]) ).
tcf(c_1623,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( triple(remove_pqp(X2,sK3),remove_slb(sK1,sK3),X3) = remove_cpq(triple(X2,sK1,X3),sK3) )
| ~ ok(remove_cpq(triple(X0,sK1,X1),sK3)) ),
inference(superposition,[status(thm)],[c_1474,c_83]) ).
tcf(c_1747,plain,
! [X0: $i,X1: $i] : triple(remove_pqp(X0,sK3),remove_slb(sK1,sK3),X1) = remove_cpq(triple(X0,sK1,X1),sK3),
inference(superposition,[status(thm)],[c_95,c_1623]) ).
tcf(c_1780,plain,
! [X0: $i] : ~ ok(remove_cpq(triple(X0,sK1,bad),sK3)),
inference(superposition,[status(thm)],[c_1747,c_83]) ).
tcf(c_1805,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_1205,c_1780]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWV378+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.18/0.42 % Computer : n026.cluster.edu
% 0.18/0.42 % Model : x86_64 x86_64
% 0.18/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.42 % Memory : 8046.5625MB
% 0.18/0.42 % OS : Linux 6.8.0-71-generic
% 0.18/0.42 % CPULimit : 300
% 0.18/0.42 % WCLimit : 300
% 0.18/0.42 % DateTime : Thu Sep 24 19:28:09 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.43 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.24/0.49 Running first-order theorem proving
% 0.24/0.49 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
% 0.24/0.50
% 0.24/0.50 % ======== iProver multi-core TPTP/SMT =========
% 0.24/0.50
% 0.24/0.50 % Detected problem language: tptp
% 0.24/0.52 % Proving...
% 7.56/1.97 % SZS status Started for theBenchmark.p
% 7.56/1.97 % SZS status Theorem for theBenchmark.p
% 7.56/1.97
% 7.56/1.97 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.56/1.97
% 7.56/1.97 % ------ iProver source info
% 7.56/1.97
% 7.56/1.97 % git: date: 2026-07-19 20:42:38 +0200
% 7.56/1.97 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.56/1.97 % git: non_committed_changes: false
% 7.56/1.97
% 7.56/1.97 % ------ Parsing...
% 7.56/1.97 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 7.56/1.97
% 7.56/1.97 % ------ Preprocessing... sup_sim: 0 sf_s rm: 7 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 %
% 7.56/1.97
% 7.56/1.97 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 7.56/1.97
% 7.56/1.97 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.56/1.97 % ------ Proving...
% 7.56/1.97 % ------ Problem Properties
% 7.56/1.97
% 7.56/1.97 %
% 7.56/1.97 % clauses 41
% 7.56/1.97 % conjectures 2
% 7.56/1.97 % EPR 6
% 7.56/1.97 % Horn 27
% 7.56/1.97 % unary 17
% 7.56/1.97 % binary 12
% 7.56/1.97 % lits 78
% 7.56/1.97 % lits eq 28
% 7.56/1.97 % fd_pure 0
% 7.56/1.97 % fd_pseudo 0
% 7.56/1.97 % fd_cond 5
% 7.56/1.97 % fd_pseudo_cond 5
% 7.56/1.97 % AC symbols 0
% 7.56/1.97
% 7.56/1.97 % ------ Input Options Time Limit: Unbounded
% 7.56/1.97
% 7.56/1.97
% 7.56/1.97 % ------
% 7.56/1.97 % Current options:
% 7.56/1.97 % ------
% 7.56/1.97
% 7.56/1.97
% 7.56/1.97 %
% 7.56/1.97
% 7.56/1.97 % ------ Proving...
% 7.56/1.97 %
% 7.56/1.97
% 7.56/1.97 % SZS status Theorem for theBenchmark.p
% 7.56/1.97
% 7.56/1.97 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.56/1.97
% 7.56/1.97
%------------------------------------------------------------------------------