%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWX224+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 : 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 03:32:53 PM UTC 2026
% Result : Theorem 3.33s 1.18s
% Output : CNFRefutation 3.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 38 ( 17 unt; 0 def)
% Number of atoms : 79 ( 20 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 80 ( 39 ~; 29 |; 7 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 112 ( 0 sgn 110 !; 2 ?; 47 :)
% Comments :
%------------------------------------------------------------------------------
fof(f25,axiom,
! [X0,X1] : index(cons(X0,X1),zero) = just(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_025) ).
fof(f26,axiom,
! [X0,X1,X2] : index(cons(X0,X1),suc(X2)) = index(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_026) ).
fof(f27,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_027) ).
fof(f29,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_029) ).
fof(f31,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_031) ).
fof(f32,conjecture,
? [X0] : tc(nil,X0,arr(arr(a,arr(a,b)),arr(a,b))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal_032) ).
fof(f33,negated_conjecture,
~ ? [X0] : tc(nil,X0,arr(arr(a,arr(a,b)),arr(a,b))),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f36,plain,
! [X0,X1,X2,X3] :
( index(X0,X2) != just(X3)
| ( tc(X0,var(X2),X1)
<=> X3 = X1 ) ),
inference(ennf_transformation,[],[f31]) ).
fof(f37,plain,
! [X0] : ~ tc(nil,X0,arr(arr(a,arr(a,b)),arr(a,b))),
inference(ennf_transformation,[],[f33]) ).
fof(f38,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,[],[f27]) ).
fof(f39,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,[],[f38]) ).
fof(f40,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,[],[f29]) ).
fof(f41,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,[],[f36]) ).
fof(f66,plain,
! [X0,X1] : just(X0) = index(cons(X0,X1),zero),
inference(cnf_transformation,[],[f25]) ).
fof(f67,plain,
! [X2,X0,X1] : index(cons(X0,X1),suc(X2)) = index(X1,X2),
inference(cnf_transformation,[],[f26]) ).
fof(f70,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,[],[f39]) ).
fof(f73,plain,
! [X2,X3,X0,X1] :
( ~ tc(cons(X2,X0),X1,X3)
| tc(X0,lam(X1),arr(X2,X3)) ),
inference(cnf_transformation,[],[f40]) ).
fof(f76,plain,
! [X2,X3,X0,X1] :
( index(X0,X2) != just(X3)
| X1 != X3
| tc(X0,var(X2),X1) ),
inference(cnf_transformation,[],[f41]) ).
fof(f77,plain,
! [X0] : ~ tc(nil,X0,arr(arr(a,arr(a,b)),arr(a,b))),
inference(cnf_transformation,[],[f37]) ).
fof(f78,plain,
! [X2,X3,X0] :
( index(X0,X2) != just(X3)
| tc(X0,var(X2),X3) ),
inference(equality_resolution,[],[f76]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] : index(cons(X0,X1),zero) = just(X0),
inference(cnf_transformation,[],[f66]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i] : index(cons(X0,X1),suc(X2)) = index(X1,X2),
inference(cnf_transformation,[],[f67]) ).
tcf(c_75,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,[],[f70]) ).
tcf(c_79,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,[],[f73]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i,X2: $i] :
( tc(X0,var(X1),X2)
| ( index(X0,X1) != just(X2) ) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_84,negated_conjecture,
! [X0: $i] : ~ tc(nil,X0,arr(arr(a,arr(a,b)),arr(a,b))),
inference(cnf_transformation,[],[f77]) ).
tcf(c_342,plain,
! [X0: $i,X1: $i,X2: $i] :
( tc(cons(X0,X2),var(zero),X1)
| ( just(X0) != just(X1) ) ),
inference(superposition,[status(thm)],[c_73,c_82]) ).
tcf(c_343,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_74,c_82]) ).
tcf(c_370,plain,
! [X0: $i] : ~ tc(cons(arr(a,arr(a,b)),nil),X0,arr(a,b)),
inference(superposition,[status(thm)],[c_79,c_84]) ).
tcf(c_439,plain,
! [X0: $i,X1: $i] : tc(cons(X0,X1),var(zero),X0),
inference(equality_resolution,[status(thm)],[c_342]) ).
tcf(c_444,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_73,c_343]) ).
tcf(c_468,plain,
! [X0: $i] : ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X0,b),
inference(superposition,[status(thm)],[c_79,c_370]) ).
tcf(c_515,plain,
! [X0: $i,X1: $i,X2: $i] : tc(cons(X0,cons(X1,X2)),var(suc(zero)),X1),
inference(equality_resolution,[status(thm)],[c_444]) ).
tcf(c_543,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X2,X1)
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X0,arr(X1,b)) ),
inference(superposition,[status(thm)],[c_75,c_468]) ).
tcf(c_680,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X4,X2)
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X3,X1)
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X0,arr(X1,arr(X2,b))) ),
inference(superposition,[status(thm)],[c_75,c_543]) ).
tcf(c_973,plain,
! [X0: $i,X1: $i] :
( ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X1,a)
| ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X0,a) ),
inference(superposition,[status(thm)],[c_515,c_680]) ).
tcf(c_1568,plain,
! [X0: $i] : ~ tc(cons(a,cons(arr(a,arr(a,b)),nil)),X0,a),
inference(superposition,[status(thm)],[c_439,c_973]) ).
tcf(c_2904,plain,
$false,
inference(superposition,[status(thm)],[c_439,c_1568]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX224+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n005.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 23:43:32 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.41
% 0.10/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.41
% 0.10/0.41 % Detected problem language: tptp
% 0.10/0.42 % Proving...
% 3.33/1.18 % SZS status Started for theBenchmark.p
% 3.33/1.18 % SZS status Theorem for theBenchmark.p
% 3.33/1.18
% 3.33/1.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.33/1.18
% 3.33/1.18 % ------ iProver source info
% 3.33/1.18
% 3.33/1.18 % git: date: 2026-07-19 20:42:38 +0200
% 3.33/1.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.33/1.18 % git: non_committed_changes: false
% 3.33/1.18
% 3.33/1.18 % ------ Parsing...
% 3.33/1.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.33/1.18
% 3.33/1.18 % ------ Preprocessing... sup_sim: 0 pe_s pe_e %
% 3.33/1.18
% 3.33/1.18 % ------ Preprocessing... gs_s sp: 0 0s gs_e scvd_s sp: 0 0s scvd_e snvd_s sp: 0 0s snvd_e %
% 3.33/1.18
% 3.33/1.18 % ------ Preprocessing...
% 3.33/1.18 % ------ Proving...
% 3.33/1.18 % ------ Problem Properties
% 3.33/1.18
% 3.33/1.18 %
% 3.33/1.18 % clauses 37
% 3.33/1.18 % conjectures 1
% 3.33/1.18 % EPR 3
% 3.33/1.18 % Horn 37
% 3.33/1.18 % unary 27
% 3.33/1.18 % binary 8
% 3.33/1.18 % lits 49
% 3.33/1.18 % lits eq 33
% 3.33/1.18 % fd_pure 0
% 3.33/1.18 % fd_pseudo 0
% 3.33/1.18 % fd_cond 0
% 3.33/1.18 % fd_pseudo_cond 1
% 3.33/1.18 % AC symbols 0
% 3.33/1.18
% 3.33/1.18 % ------ Input Options Time Limit: Unbounded
% 3.33/1.18
% 3.33/1.18
% 3.33/1.18 % ------
% 3.33/1.18 % Current options:
% 3.33/1.18 % ------
% 3.33/1.18
% 3.33/1.18
% 3.33/1.18 %
% 3.33/1.18
% 3.33/1.18 % ------ Proving...
% 3.33/1.18 %
% 3.33/1.18
% 3.33/1.18 % SZS status Theorem for theBenchmark.p
% 3.33/1.18
% 3.33/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.33/1.18
% 3.33/1.18
%------------------------------------------------------------------------------