%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWV411+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n011.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 03:17:34 PM UTC 2026
% Result : Theorem 2.79s 1.27s
% Output : CNFRefutation 2.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 42 ( 16 unt; 2 def)
% Number of atoms : 119 ( 26 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 105 ( 41 ~; 39 |; 17 &)
% ( 2 <=>; 6 =>; 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; 3 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 107 ( 0 sgn 93 !; 14 ?; 27 :)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X0,X1,X2,X3] :
( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
<=> ( X1 = X2
| contains_slb(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+2.ax',ax21) ).
fof(f11,axiom,
! [X0,X1,X2,X3,X4] :
( pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
<=> ( ( X3 = X4
& X1 = X2 )
| pair_in_list(X0,X2,X4) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+2.ax',ax23) ).
fof(f19,conjecture,
! [X0] :
( ! [X1] :
( contains_slb(X0,X1)
=> ? [X2] : pair_in_list(X0,X1,X2) )
=> ! [X3,X4,X5] :
( contains_slb(insert_slb(X0,pair(X4,X5)),X3)
=> ? [X6] : pair_in_list(insert_slb(X0,pair(X4,X5)),X3,X6) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l47_co) ).
fof(f20,negated_conjecture,
~ ! [X0] :
( ! [X1] :
( contains_slb(X0,X1)
=> ? [X2] : pair_in_list(X0,X1,X2) )
=> ! [X3,X4,X5] :
( contains_slb(insert_slb(X0,pair(X4,X5)),X3)
=> ? [X6] : pair_in_list(insert_slb(X0,pair(X4,X5)),X3,X6) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f32,plain,
? [X0] :
( ! [X1] :
( ~ contains_slb(X0,X1)
| ? [X2] : pair_in_list(X0,X1,X2) )
& ? [X3,X4,X5] :
( contains_slb(insert_slb(X0,pair(X4,X5)),X3)
& ! [X6] : ~ pair_in_list(insert_slb(X0,pair(X4,X5)),X3,X6) ) ),
inference(ennf_transformation,[],[f20]) ).
fof(f33,plain,
! [X0,X1,X2,X3] :
( ( ~ contains_slb(insert_slb(X0,pair(X1,X3)),X2)
| X1 = X2
| contains_slb(X0,X2) )
& ( ( X1 != X2
& ~ contains_slb(X0,X2) )
| contains_slb(insert_slb(X0,pair(X1,X3)),X2) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f34,plain,
! [X0,X1,X2,X3] :
( ( ~ contains_slb(insert_slb(X0,pair(X1,X3)),X2)
| X1 = X2
| contains_slb(X0,X2) )
& ( ( X1 != X2
& ~ contains_slb(X0,X2) )
| contains_slb(insert_slb(X0,pair(X1,X3)),X2) ) ),
inference(flattening,[],[f33]) ).
fof(f35,plain,
! [X0,X1,X2,X3,X4] :
( ( ~ pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
| ( X3 = X4
& X1 = X2 )
| pair_in_list(X0,X2,X4) )
& ( ( ( X3 != X4
| X1 != X2 )
& ~ pair_in_list(X0,X2,X4) )
| pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f36,plain,
! [X0,X1,X2,X3,X4] :
( ( ~ pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
| ( X3 = X4
& X1 = X2 )
| pair_in_list(X0,X2,X4) )
& ( ( ( X3 != X4
| X1 != X2 )
& ~ pair_in_list(X0,X2,X4) )
| pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4) ) ),
inference(flattening,[],[f35]) ).
fof(f37,plain,
? [X0] :
( ! [X5] :
( ~ contains_slb(X0,X5)
| ? [X6] : pair_in_list(X0,X5,X6) )
& ? [X1,X2,X3] :
( contains_slb(insert_slb(X0,pair(X2,X3)),X1)
& ! [X4] : ~ pair_in_list(insert_slb(X0,pair(X2,X3)),X1,X4) ) ),
inference(rectify,[],[f32]) ).
fof(f38,plain,
( ! [X5] :
( ~ contains_slb(sK0,X5)
| pair_in_list(sK0,X5,sK4(X5)) )
& contains_slb(insert_slb(sK0,pair(sK2,sK3)),sK1)
& ! [X4] : ~ pair_in_list(insert_slb(sK0,pair(sK2,sK3)),sK1,X4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X6,sK4(X5))],[f37]) ).
fof(f47,plain,
! [X2,X3,X0,X1] :
( ~ contains_slb(insert_slb(X0,pair(X1,X3)),X2)
| X1 = X2
| contains_slb(X0,X2) ),
inference(cnf_transformation,[],[f34]) ).
fof(f53,plain,
! [X2,X3,X0,X1,X4] :
( X3 != X4
| X1 != X2
| pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4) ),
inference(cnf_transformation,[],[f36]) ).
fof(f54,plain,
! [X2,X3,X0,X1,X4] :
( ~ pair_in_list(X0,X2,X4)
| pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4) ),
inference(cnf_transformation,[],[f36]) ).
fof(f62,plain,
! [X5] :
( ~ contains_slb(sK0,X5)
| pair_in_list(sK0,X5,sK4(X5)) ),
inference(cnf_transformation,[],[f38]) ).
fof(f63,plain,
contains_slb(insert_slb(sK0,pair(sK2,sK3)),sK1),
inference(cnf_transformation,[],[f38]) ).
fof(f64,plain,
! [X4] : ~ pair_in_list(insert_slb(sK0,pair(sK2,sK3)),sK1,X4),
inference(cnf_transformation,[],[f38]) ).
fof(f66,plain,
! [X2,X3,X0,X4] :
( X3 != X4
| pair_in_list(insert_slb(X0,pair(X2,X3)),X2,X4) ),
inference(equality_resolution,[],[f53]) ).
fof(f67,plain,
! [X2,X0,X4] : pair_in_list(insert_slb(X0,pair(X2,X4)),X2,X4),
inference(equality_resolution,[],[f66]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( contains_slb(X0,X3)
| ( X1 = X3 )
| ~ contains_slb(insert_slb(X0,pair(X1,X2)),X3) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( pair_in_list(insert_slb(X0,pair(X3,X4)),X1,X2)
| ~ pair_in_list(X0,X1,X2) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] : pair_in_list(insert_slb(X0,pair(X1,X2)),X1,X2),
inference(cnf_transformation,[],[f67]) ).
tcf(c_72,negated_conjecture,
! [X0: $i] : ~ pair_in_list(insert_slb(sK0,pair(sK2,sK3)),sK1,X0),
inference(cnf_transformation,[],[f64]) ).
tcf(c_73,negated_conjecture,
contains_slb(insert_slb(sK0,pair(sK2,sK3)),sK1),
inference(cnf_transformation,[],[f63]) ).
tcf(c_74,negated_conjecture,
! [X0: $i] :
( pair_in_list(sK0,X0,sK4(X0))
| ~ contains_slb(sK0,X0) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_426,definition,
iPr_def_10 = pair(sK2,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_427,definition,
iPr_def_11 = insert_slb(sK0,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_428,negated_conjecture,
! [X0: $i] :
( pair_in_list(sK0,X0,sK4(X0))
| ~ contains_slb(sK0,X0) ),
inference(demodulation,[status(thm)],[c_74]) ).
tcf(c_429,negated_conjecture,
contains_slb(iPr_def_11,sK1),
inference(demodulation,[status(thm)],[c_73,c_426,c_427]) ).
tcf(c_430,negated_conjecture,
! [X0: $i] : ~ pair_in_list(iPr_def_11,sK1,X0),
inference(demodulation,[status(thm)],[c_72]) ).
tcf(c_753,plain,
! [X0: $i] : pair_in_list(insert_slb(X0,iPr_def_10),sK2,sK3),
inference(superposition,[status(thm)],[c_426,c_62]) ).
tcf(c_755,plain,
pair_in_list(iPr_def_11,sK2,sK3),
inference(superposition,[status(thm)],[c_427,c_753]) ).
tcf(c_787,plain,
! [X0: $i,X1: $i,X2: $i] :
( pair_in_list(insert_slb(X0,iPr_def_10),X1,X2)
| ~ pair_in_list(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_426,c_61]) ).
tcf(c_798,plain,
! [X0: $i,X1: $i] :
( contains_slb(X0,X1)
| ( X1 = sK2 )
| ~ contains_slb(insert_slb(X0,iPr_def_10),X1) ),
inference(superposition,[status(thm)],[c_426,c_59]) ).
tcf(c_858,plain,
! [X0: $i,X1: $i] :
( pair_in_list(iPr_def_11,X0,X1)
| ~ pair_in_list(sK0,X0,X1) ),
inference(superposition,[status(thm)],[c_427,c_787]) ).
tcf(c_866,plain,
! [X0: $i] :
( pair_in_list(iPr_def_11,X0,sK4(X0))
| ~ contains_slb(sK0,X0) ),
inference(superposition,[status(thm)],[c_428,c_858]) ).
tcf(c_874,plain,
~ contains_slb(sK0,sK1),
inference(superposition,[status(thm)],[c_866,c_430]) ).
tcf(c_926,plain,
! [X0: $i] :
( contains_slb(sK0,X0)
| ( X0 = sK2 )
| ~ contains_slb(iPr_def_11,X0) ),
inference(superposition,[status(thm)],[c_427,c_798]) ).
tcf(c_937,plain,
( contains_slb(sK0,sK1)
| ( sK2 = sK1 ) ),
inference(superposition,[status(thm)],[c_429,c_926]) ).
tcf(c_939,plain,
sK2 = sK1,
inference(forward_subsumption_resolution,[status(thm)],[c_937,c_874]) ).
tcf(c_941,plain,
! [X0: $i] : ~ pair_in_list(iPr_def_11,sK2,X0),
inference(demodulation,[status(thm)],[c_430,c_939]) ).
tcf(c_943,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_755,c_941]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV411+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n011.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 19:30:57 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 0.11/0.41
% 0.11/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.41
% 0.11/0.41 % Detected problem language: tptp
% 0.11/0.42 % Proving...
% 2.79/1.27 % SZS status Started for theBenchmark.p
% 2.79/1.27 % SZS status Theorem for theBenchmark.p
% 2.79/1.27
% 2.79/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.79/1.27
% 2.79/1.27 % ------ iProver source info
% 2.79/1.27
% 2.79/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 2.79/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.79/1.27 % git: non_committed_changes: false
% 2.79/1.27
% 2.79/1.27 % ------ Parsing...
% 2.79/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.79/1.27
% 2.79/1.27 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 2.79/1.27
% 2.79/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.79/1.27
% 2.79/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.79/1.27 % ------ Proving...
% 2.79/1.27 % ------ Problem Properties
% 2.79/1.27
% 2.79/1.27 %
% 2.79/1.27 % clauses 26
% 2.79/1.27 % conjectures 3
% 2.79/1.27 % EPR 8
% 2.79/1.27 % Horn 19
% 2.79/1.27 % unary 14
% 2.79/1.27 % binary 6
% 2.79/1.27 % lits 44
% 2.79/1.27 % lits eq 15
% 2.79/1.27 % fd_pure 0
% 2.79/1.27 % fd_pseudo 0
% 2.79/1.27 % fd_cond 0
% 2.79/1.27 % fd_pseudo_cond 5
% 2.79/1.27 % AC symbols 0
% 2.79/1.27
% 2.79/1.27 % ------ Schedule dynamic 5 is on
% 2.79/1.27
% 2.79/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.79/1.27
% 2.79/1.27
% 2.79/1.27 % ------
% 2.79/1.27 % Current options:
% 2.79/1.27 % ------
% 2.79/1.27
% 2.79/1.27
% 2.79/1.27 %
% 2.79/1.27
% 2.79/1.27 % ------ Proving...
% 2.79/1.27 %
% 2.79/1.27
% 2.79/1.27 % SZS status Theorem for theBenchmark.p
% 2.79/1.27
% 2.79/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.79/1.27
% 2.79/1.27
%------------------------------------------------------------------------------