%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWX221+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 : n013.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 03:32:52 PM UTC 2026
% Result : Theorem 7.32s 3.35s
% Output : CNFRefutation 7.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 11
% Syntax : Number of formulae : 70 ( 24 unt; 0 def)
% Number of atoms : 162 ( 40 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 176 ( 84 ~; 67 |; 16 &)
% ( 7 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-3 aty)
% Number of variables : 174 ( 0 sgn 172 !; 2 ?; 77 :)
% Comments :
%------------------------------------------------------------------------------
fof(f21,axiom,
! [X0,X1,X2,X3] : app(X0,X1,X2) != lam(X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_021) ).
fof(f23,axiom,
! [X0,X1] : lam(X0) != var(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_023) ).
fof(f24,axiom,
! [X0,X1,X2] :
( X0 != lam(proj1Lam(X0))
=> ( nf(app(X0,X1,X2))
<=> ( nf(X1)
& nf(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_024) ).
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(f30,axiom,
! [X0,X1,X2] : index(cons(X0,X1),suc(X2)) = index(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_030) ).
fof(f31,axiom,
! [X0,X1,X2,X3,X4] :
( tc(X0,app(X2,X3,X4),X1)
<=> ( tc(X0,X3,X4)
& tc(X0,X2,arr(X4,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_031) ).
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(arr(a,arr(b,c)),arr(b,arr(a,c))))
& nf(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal_036) ).
fof(f37,negated_conjecture,
~ ? [X0] :
( tc(nil,X0,arr(arr(a,arr(b,c)),arr(b,arr(a,c))))
& nf(X0) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f38,plain,
! [X0,X1,X2] :
( lam(proj1Lam(X0)) = X0
| ( nf(app(X0,X1,X2))
<=> ( nf(X1)
& nf(X0) ) ) ),
inference(ennf_transformation,[],[f24]) ).
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(arr(a,arr(b,c)),arr(b,arr(a,c))))
| ~ nf(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f43,plain,
! [X0,X1,X2] :
( lam(proj1Lam(X0)) = X0
| ( ( ~ nf(app(X0,X1,X2))
| ( nf(X1)
& nf(X0) ) )
& ( ~ nf(X1)
| ~ nf(X0)
| nf(app(X0,X1,X2)) ) ) ),
inference(nnf_transformation,[],[f38]) ).
fof(f44,plain,
! [X0,X1,X2] :
( lam(proj1Lam(X0)) = X0
| ( ( ~ nf(app(X0,X1,X2))
| ( nf(X1)
& nf(X0) ) )
& ( ~ nf(X1)
| ~ nf(X0)
| nf(app(X0,X1,X2)) ) ) ),
inference(flattening,[],[f43]) ).
fof(f45,plain,
! [X0] :
( ( ~ nf(lam(X0))
| nf(X0) )
& ( ~ nf(X0)
| nf(lam(X0)) ) ),
inference(nnf_transformation,[],[f26]) ).
fof(f46,plain,
! [X0,X1,X2,X3,X4] :
( ( ~ tc(X0,app(X2,X3,X4),X1)
| ( tc(X0,X3,X4)
& tc(X0,X2,arr(X4,X1)) ) )
& ( ~ tc(X0,X3,X4)
| ~ tc(X0,X2,arr(X4,X1))
| tc(X0,app(X2,X3,X4),X1) ) ),
inference(nnf_transformation,[],[f31]) ).
fof(f47,plain,
! [X0,X1,X2,X3,X4] :
( ( ~ tc(X0,app(X2,X3,X4),X1)
| ( tc(X0,X3,X4)
& tc(X0,X2,arr(X4,X1)) ) )
& ( ~ tc(X0,X3,X4)
| ~ tc(X0,X2,arr(X4,X1))
| tc(X0,app(X2,X3,X4),X1) ) ),
inference(flattening,[],[f46]) ).
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(f70,plain,
! [X2,X3,X0,X1] : app(X0,X1,X2) != lam(X3),
inference(cnf_transformation,[],[f21]) ).
fof(f72,plain,
! [X0,X1] : lam(X0) != var(X1),
inference(cnf_transformation,[],[f23]) ).
fof(f75,plain,
! [X2,X0,X1] :
( lam(proj1Lam(X0)) = X0
| ~ nf(X1)
| ~ nf(X0)
| nf(app(X0,X1,X2)) ),
inference(cnf_transformation,[],[f44]) ).
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(f82,plain,
! [X2,X0,X1] : index(cons(X0,X1),suc(X2)) = index(X1,X2),
inference(cnf_transformation,[],[f30]) ).
fof(f85,plain,
! [X2,X3,X0,X1,X4] :
( ~ tc(X0,X3,X4)
| ~ tc(X0,X2,arr(X4,X1))
| tc(X0,app(X2,X3,X4),X1) ),
inference(cnf_transformation,[],[f47]) ).
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(arr(a,arr(b,c)),arr(b,arr(a,c))))
| ~ 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_69,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : app(X0,X1,X2) != lam(X3),
inference(cnf_transformation,[],[f70]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] : lam(X0) != var(X1),
inference(cnf_transformation,[],[f72]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i] :
( nf(app(X0,X1,X2))
| ( lam(proj1Lam(X0)) = X0 )
| ~ nf(X1)
| ~ nf(X0) ),
inference(cnf_transformation,[],[f75]) ).
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_81,plain,
! [X0: $i,X1: $i,X2: $i] : index(cons(X0,X1),suc(X2)) = index(X1,X2),
inference(cnf_transformation,[],[f82]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( tc(X0,app(X1,X4,X2),X3)
| ~ tc(X0,X4,X2)
| ~ tc(X0,X1,arr(X2,X3)) ),
inference(cnf_transformation,[],[f85]) ).
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(arr(a,arr(b,c)),arr(b,arr(a,c)))) ),
inference(cnf_transformation,[],[f92]) ).
tcf(c_1258,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_1259,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( tc(cons(X3,X0),var(suc(X1)),X2)
| ( index(X0,X1) != just(X2) ) ),
inference(superposition,[status(thm)],[c_81,c_89]) ).
tcf(c_1269,plain,
! [X0: $i] :
( ~ nf(lam(X0))
| ~ tc(cons(arr(a,arr(b,c)),nil),X0,arr(b,arr(a,c))) ),
inference(superposition,[status(thm)],[c_86,c_91]) ).
tcf(c_1278,plain,
! [X0: $i] :
( ~ nf(lam(lam(X0)))
| ~ tc(cons(b,cons(arr(a,arr(b,c)),nil)),X0,arr(a,c)) ),
inference(superposition,[status(thm)],[c_86,c_1269]) ).
tcf(c_1292,plain,
! [X0: $i,X1: $i] : tc(cons(X0,X1),var(zero),X0),
inference(equality_resolution,[status(thm)],[c_1258]) ).
tcf(c_1301,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( tc(cons(X2,cons(X0,X3)),var(suc(zero)),X1)
| ( just(X0) != just(X1) ) ),
inference(superposition,[status(thm)],[c_80,c_1259]) ).
tcf(c_1302,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( tc(cons(X3,cons(X4,X0)),var(suc(suc(X1))),X2)
| ( index(X0,X1) != just(X2) ) ),
inference(superposition,[status(thm)],[c_81,c_1259]) ).
tcf(c_1305,plain,
! [X0: $i,X1: $i,X2: $i] : tc(cons(X0,cons(X1,X2)),var(suc(zero)),X1),
inference(equality_resolution,[status(thm)],[c_1301]) ).
tcf(c_1309,plain,
! [X0: $i] :
( ~ nf(lam(lam(lam(X0))))
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X0,c) ),
inference(superposition,[status(thm)],[c_86,c_1278]) ).
tcf(c_1343,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ nf(lam(lam(lam(app(X0,X2,X1)))))
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X2,X1)
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X0,arr(X1,c)) ),
inference(superposition,[status(thm)],[c_82,c_1309]) ).
tcf(c_1422,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( tc(cons(X2,cons(X3,cons(X0,X4))),var(suc(suc(zero))),X1)
| ( just(X0) != just(X1) ) ),
inference(superposition,[status(thm)],[c_80,c_1302]) ).
tcf(c_1426,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : tc(cons(X0,cons(X1,cons(X2,X3))),var(suc(suc(zero))),X2),
inference(equality_resolution,[status(thm)],[c_1422]) ).
tcf(c_1446,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ nf(lam(lam(lam(app(app(X0,X3,X1),X4,X2)))))
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X4,X2)
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X3,X1)
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X0,arr(X1,arr(X2,c))) ),
inference(superposition,[status(thm)],[c_82,c_1343]) ).
tcf(c_1700,plain,
! [X0: $i,X1: $i] :
( ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X1,b)
| ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X0,a)
| ~ nf(lam(lam(lam(app(app(var(suc(suc(zero))),X0,a),X1,b))))) ),
inference(superposition,[status(thm)],[c_1426,c_1446]) ).
tcf(c_2491,plain,
! [X0: $i] :
( ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X0,b)
| ~ nf(lam(lam(lam(app(app(var(suc(suc(zero))),var(zero),a),X0,b))))) ),
inference(superposition,[status(thm)],[c_1292,c_1700]) ).
tcf(c_2592,plain,
! [X0: $i] :
( ~ tc(cons(a,cons(b,cons(arr(a,arr(b,c)),nil))),X0,b)
| ~ nf(lam(lam(app(app(var(suc(suc(zero))),var(zero),a),X0,b)))) ),
inference(superposition,[status(thm)],[c_76,c_2491]) ).
tcf(c_2599,plain,
~ nf(lam(lam(app(app(var(suc(suc(zero))),var(zero),a),var(suc(zero)),b)))),
inference(superposition,[status(thm)],[c_1305,c_2592]) ).
tcf(c_2600,plain,
~ nf(lam(app(app(var(suc(suc(zero))),var(zero),a),var(suc(zero)),b))),
inference(superposition,[status(thm)],[c_76,c_2599]) ).
tcf(c_2601,plain,
~ nf(app(app(var(suc(suc(zero))),var(zero),a),var(suc(zero)),b)),
inference(superposition,[status(thm)],[c_76,c_2600]) ).
tcf(c_2605,plain,
( ( lam(proj1Lam(app(var(suc(suc(zero))),var(zero),a))) = app(var(suc(suc(zero))),var(zero),a) )
| ~ nf(var(suc(zero)))
| ~ nf(app(var(suc(suc(zero))),var(zero),a)) ),
inference(superposition,[status(thm)],[c_72,c_2601]) ).
tcf(c_2606,plain,
( ( lam(proj1Lam(app(var(suc(suc(zero))),var(zero),a))) = app(var(suc(suc(zero))),var(zero),a) )
| ~ nf(app(var(suc(suc(zero))),var(zero),a)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2605,c_78]) ).
tcf(c_2609,plain,
( ( lam(proj1Lam(var(suc(suc(zero))))) = var(suc(suc(zero))) )
| ( lam(proj1Lam(app(var(suc(suc(zero))),var(zero),a))) = app(var(suc(suc(zero))),var(zero),a) )
| ~ nf(var(zero))
| ~ nf(var(suc(suc(zero)))) ),
inference(superposition,[status(thm)],[c_72,c_2606]) ).
tcf(c_2610,plain,
lam(proj1Lam(app(var(suc(suc(zero))),var(zero),a))) = app(var(suc(suc(zero))),var(zero),a),
inference(forward_subsumption_resolution,[status(thm)],[c_2609,c_71,c_78,c_78]) ).
tcf(c_2803,plain,
! [X0: $i,X1: $i,X2: $i] : app(var(suc(suc(zero))),var(zero),a) != app(X0,X1,X2),
inference(superposition,[status(thm)],[c_2610,c_69]) ).
tcf(c_2813,plain,
$false,
inference(equality_resolution,[status(thm)],[c_2803]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWX221+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.38 % Computer : n013.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Thu Sep 24 23:42:38 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 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
% 0.13/0.44
% 0.13/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.44
% 0.13/0.44 % Detected problem language: tptp
% 0.13/0.46 % Proving...
% 7.32/3.35 % SZS status Started for theBenchmark.p
% 7.32/3.35 % SZS status Theorem for theBenchmark.p
% 7.32/3.35
% 7.32/3.35 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.32/3.35
% 7.32/3.35 % ------ iProver source info
% 7.32/3.35
% 7.32/3.35 % git: date: 2026-07-19 20:42:38 +0200
% 7.32/3.35 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.32/3.35 % git: non_committed_changes: false
% 7.32/3.35
% 7.32/3.35 % ------ Parsing...
% 7.32/3.35 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 7.32/3.35
% 7.32/3.35 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 7.32/3.35
% 7.32/3.35 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 7.32/3.35
% 7.32/3.35 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.32/3.35 % ------ Proving...
% 7.32/3.35 % ------ Problem Properties
% 7.32/3.35
% 7.32/3.35 %
% 7.32/3.35 % clauses 43
% 7.32/3.35 % conjectures 1
% 7.32/3.35 % EPR 3
% 7.32/3.35 % Horn 40
% 7.32/3.35 % unary 28
% 7.32/3.35 % binary 10
% 7.32/3.35 % lits 64
% 7.32/3.35 % lits eq 34
% 7.32/3.35 % fd_pure 0
% 7.32/3.35 % fd_pseudo 0
% 7.32/3.35 % fd_cond 0
% 7.32/3.35 % fd_pseudo_cond 1
% 7.32/3.35 % AC symbols 0
% 7.32/3.35
% 7.32/3.35 % ------ Input Options Time Limit: Unbounded
% 7.32/3.35
% 7.32/3.35
% 7.32/3.35 % ------
% 7.32/3.35 % Current options:
% 7.32/3.35 % ------
% 7.32/3.35
% 7.32/3.35
% 7.32/3.35 %
% 7.32/3.35
% 7.32/3.35 % ------ Proving...
% 7.32/3.35 %
% 7.32/3.35
% 7.32/3.35 % SZS status Theorem for theBenchmark.p
% 7.32/3.35
% 7.32/3.35 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.32/3.36
% 7.32/3.36
%------------------------------------------------------------------------------