%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWX222+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n010.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 03:32:53 PM UTC 2026
% Result : Theorem 3.23s 1.28s
% Output : CNFRefutation 3.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 38 ( 15 unt; 2 def)
% Number of atoms : 80 ( 17 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 64 ( 31 ~; 23 |; 5 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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; 3 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 68 ( 0 sgn 66 !; 2 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
fof(f26,axiom,
! [X0] :
( nf(lam(X0))
<=> nf(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_026) ).
fof(f27,axiom,
! [X0] : nf(var(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_027) ).
fof(f29,axiom,
! [X0,X1] : index(cons(X0,X1),zero) = just(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_029) ).
fof(f33,axiom,
! [X0,X1,X2,X3] :
( tc(X0,lam(X1),arr(X2,X3))
<=> tc(cons(X2,X0),X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_033) ).
fof(f35,axiom,
! [X0,X1,X2,X3] :
( index(X0,X2) = just(X3)
=> ( tc(X0,var(X2),X1)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_035) ).
fof(f36,conjecture,
? [X0] :
( tc(nil,X0,arr(a,arr(b,b)))
& nf(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal_036) ).
fof(f37,negated_conjecture,
~ ? [X0] :
( tc(nil,X0,arr(a,arr(b,b)))
& nf(X0) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f41,plain,
! [X0,X1,X2,X3] :
( index(X0,X2) != just(X3)
| ( tc(X0,var(X2),X1)
<=> X3 = X1 ) ),
inference(ennf_transformation,[],[f35]) ).
fof(f42,plain,
! [X0] :
( ~ tc(nil,X0,arr(a,arr(b,b)))
| ~ nf(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f45,plain,
! [X0] :
( ( ~ nf(lam(X0))
| nf(X0) )
& ( ~ nf(X0)
| nf(lam(X0)) ) ),
inference(nnf_transformation,[],[f26]) ).
fof(f48,plain,
! [X0,X1,X2,X3] :
( ( ~ tc(X0,lam(X1),arr(X2,X3))
| tc(cons(X2,X0),X1,X3) )
& ( ~ tc(cons(X2,X0),X1,X3)
| tc(X0,lam(X1),arr(X2,X3)) ) ),
inference(nnf_transformation,[],[f33]) ).
fof(f49,plain,
! [X0,X1,X2,X3] :
( index(X0,X2) != just(X3)
| ( ( ~ tc(X0,var(X2),X1)
| X3 = X1 )
& ( X1 != X3
| tc(X0,var(X2),X1) ) ) ),
inference(nnf_transformation,[],[f41]) ).
fof(f78,plain,
! [X0] :
( ~ nf(X0)
| nf(lam(X0)) ),
inference(cnf_transformation,[],[f45]) ).
fof(f79,plain,
! [X0] : nf(var(X0)),
inference(cnf_transformation,[],[f27]) ).
fof(f81,plain,
! [X0,X1] : just(X0) = index(cons(X0,X1),zero),
inference(cnf_transformation,[],[f29]) ).
fof(f88,plain,
! [X2,X3,X0,X1] :
( ~ tc(cons(X2,X0),X1,X3)
| tc(X0,lam(X1),arr(X2,X3)) ),
inference(cnf_transformation,[],[f48]) ).
fof(f91,plain,
! [X2,X3,X0,X1] :
( index(X0,X2) != just(X3)
| X1 != X3
| tc(X0,var(X2),X1) ),
inference(cnf_transformation,[],[f49]) ).
fof(f92,plain,
! [X0] :
( ~ tc(nil,X0,arr(a,arr(b,b)))
| ~ nf(X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f93,plain,
! [X2,X3,X0] :
( index(X0,X2) != just(X3)
| tc(X0,var(X2),X3) ),
inference(equality_resolution,[],[f91]) ).
tcf(c_76,plain,
! [X0: $i] :
( nf(lam(X0))
| ~ nf(X0) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_78,plain,
! [X0: $i] : nf(var(X0)),
inference(cnf_transformation,[],[f79]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i] : index(cons(X0,X1),zero) = just(X0),
inference(cnf_transformation,[],[f81]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( tc(X1,lam(X2),arr(X0,X3))
| ~ tc(cons(X0,X1),X2,X3) ),
inference(cnf_transformation,[],[f88]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i,X2: $i] :
( tc(X0,var(X1),X2)
| ( index(X0,X1) != just(X2) ) ),
inference(cnf_transformation,[],[f93]) ).
tcf(c_91,negated_conjecture,
! [X0: $i] :
( ~ nf(X0)
| ~ tc(nil,X0,arr(a,arr(b,b))) ),
inference(cnf_transformation,[],[f92]) ).
tcf(c_443,definition,
iPr_def_10 = arr(b,b),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_444,definition,
iPr_def_11 = arr(a,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_445,negated_conjecture,
! [X0: $i] :
( ~ nf(X0)
| ~ tc(nil,X0,iPr_def_11) ),
inference(demodulation,[status(thm)],[c_91,c_443,c_444]) ).
tcf(c_1310,plain,
! [X0: $i,X1: $i,X2: $i] :
( tc(cons(X0,X2),var(zero),X1)
| ( just(X0) != just(X1) ) ),
inference(superposition,[status(thm)],[c_80,c_89]) ).
tcf(c_1342,plain,
! [X0: $i,X1: $i] :
( tc(X0,lam(X1),iPr_def_10)
| ~ tc(cons(b,X0),X1,b) ),
inference(superposition,[status(thm)],[c_443,c_86]) ).
tcf(c_1343,plain,
! [X0: $i,X1: $i] :
( tc(X0,lam(X1),iPr_def_11)
| ~ tc(cons(a,X0),X1,iPr_def_10) ),
inference(superposition,[status(thm)],[c_444,c_86]) ).
tcf(c_1470,plain,
! [X0: $i,X1: $i] : tc(cons(X0,X1),var(zero),X0),
inference(equality_resolution,[status(thm)],[c_1310]) ).
tcf(c_1472,plain,
! [X0: $i] : tc(X0,lam(var(zero)),iPr_def_10),
inference(superposition,[status(thm)],[c_1470,c_1342]) ).
tcf(c_1475,plain,
! [X0: $i] : tc(X0,lam(lam(var(zero))),iPr_def_11),
inference(superposition,[status(thm)],[c_1472,c_1343]) ).
tcf(c_1479,plain,
~ nf(lam(lam(var(zero)))),
inference(superposition,[status(thm)],[c_1475,c_445]) ).
tcf(c_1481,plain,
~ nf(lam(var(zero))),
inference(superposition,[status(thm)],[c_76,c_1479]) ).
tcf(c_1495,plain,
~ nf(var(zero)),
inference(superposition,[status(thm)],[c_76,c_1481]) ).
tcf(c_1496,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1495,c_78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX222+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n010.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 23:43:43 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 3.23/1.28 % SZS status Started for theBenchmark.p
% 3.23/1.28 % SZS status Theorem for theBenchmark.p
% 3.23/1.28
% 3.23/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.23/1.28
% 3.23/1.28 % ------ iProver source info
% 3.23/1.28
% 3.23/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 3.23/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.23/1.28 % git: non_committed_changes: false
% 3.23/1.28
% 3.23/1.28 % ------ Parsing...
% 3.23/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.23/1.28
% 3.23/1.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.23/1.28
% 3.23/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.23/1.28
% 3.23/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.23/1.28 % ------ Proving...
% 3.23/1.28 % ------ Problem Properties
% 3.23/1.28
% 3.23/1.28 %
% 3.23/1.28 % clauses 45
% 3.23/1.28 % conjectures 1
% 3.23/1.28 % EPR 4
% 3.23/1.28 % Horn 42
% 3.23/1.28 % unary 30
% 3.23/1.28 % binary 10
% 3.23/1.28 % lits 66
% 3.23/1.28 % lits eq 36
% 3.23/1.28 % fd_pure 0
% 3.23/1.28 % fd_pseudo 0
% 3.23/1.28 % fd_cond 0
% 3.23/1.28 % fd_pseudo_cond 1
% 3.23/1.28 % AC symbols 0
% 3.23/1.28
% 3.23/1.28 % ------ Schedule dynamic 5 is on
% 3.23/1.28
% 3.23/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.23/1.28
% 3.23/1.28
% 3.23/1.28 % ------
% 3.23/1.28 % Current options:
% 3.23/1.28 % ------
% 3.23/1.28
% 3.23/1.28
% 3.23/1.28 %
% 3.23/1.28
% 3.23/1.28 % ------ Proving...
% 3.23/1.28 %
% 3.23/1.28
% 3.23/1.28 % SZS status Theorem for theBenchmark.p
% 3.23/1.28
% 3.23/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.23/1.28
% 3.23/1.28
%------------------------------------------------------------------------------