%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : LDA007-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 : Wed Oct 7 10:31:13 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.20s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 34 ( 34 unt; 0 typ; 0 def)
% Number of atoms : 84 ( 51 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 116 ( 6 ~; 0 |; 0 &; 110 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 10 con; 0-2 aty)
% Number of variables : 18 ( 0 ^; 18 !; 0 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_f,type,
f: $i > $i > $i ).
thf(tp_k,type,
k: $i ).
thf(tp_s,type,
s: $i ).
thf(tp_t,type,
t: $i ).
thf(tp_tk,type,
tk: $i ).
thf(tp_ts,type,
ts: $i ).
thf(tp_tsk,type,
tsk: $i ).
thf(tp_tt,type,
tt: $i ).
thf(tp_tt_ts,type,
tt_ts: $i ).
thf(1,axiom,
( tsk
= ( f @ ts @ k ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_5) ).
thf(2,axiom,
( tk
= ( f @ t @ k ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_4) ).
thf(3,axiom,
( tt_ts
= ( f @ tt @ ts ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3) ).
thf(4,axiom,
( ts
= ( f @ t @ s ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2) ).
thf(5,axiom,
( tt
= ( f @ t @ t ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1) ).
thf(6,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( f @ X @ ( f @ Y @ Z ) )
= ( f @ ( f @ X @ Y ) @ ( f @ X @ Z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1) ).
thf(7,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(8,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[7]) ).
thf(9,negated_conjecture,
( ( f @ t @ tsk )
!= ( f @ tt_ts @ tk ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equation) ).
thf(10,plain,
$false = $false,
inference(unfold_def,[status(thm)],[8]) ).
thf(11,plain,
( ( tsk
= ( f @ ts @ k ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(12,plain,
( ( tk
= ( f @ t @ k ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(13,plain,
( ( tt_ts
= ( f @ tt @ ts ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(14,plain,
( ( ts
= ( f @ t @ s ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(15,plain,
( ( tt
= ( f @ t @ t ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(16,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( f @ X @ ( f @ Y @ Z ) )
= ( f @ ( f @ X @ Y ) @ ( f @ X @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(17,plain,
( ( ( f @ t @ tsk )
!= ( f @ tt_ts @ tk ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(18,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[10]) ).
thf(19,plain,
( ( ( f @ t @ tsk )
!= ( f @ tt_ts @ tk ) )
= $true ),
inference(extcnf_combined,[status(esa)],[17]) ).
thf(20,plain,
( ( ( f @ t @ tsk )
!= ( f @ tt_ts @ tk ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(21,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( f @ X @ ( f @ Y @ Z ) )
= ( f @ ( f @ X @ Y ) @ ( f @ X @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(22,plain,
( ( tt
= ( f @ t @ t ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(23,plain,
( ( ts
= ( f @ t @ s ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(24,plain,
( ( tt_ts
= ( f @ tt @ ts ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(25,plain,
( ( tk
= ( f @ t @ k ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(26,plain,
( ( tsk
= ( f @ ts @ k ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(27,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[18]) ).
thf(28,plain,
( ( ( f @ t @ tsk )
= ( f @ tt_ts @ tk ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(29,plain,
! [SV1: $i] :
( ( ! [SY3: $i,SY4: $i] :
( ( f @ SV1 @ ( f @ SY3 @ SY4 ) )
= ( f @ ( f @ SV1 @ SY3 ) @ ( f @ SV1 @ SY4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(30,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(31,plain,
! [SV2: $i,SV1: $i] :
( ( ! [SY5: $i] :
( ( f @ SV1 @ ( f @ SV2 @ SY5 ) )
= ( f @ ( f @ SV1 @ SV2 ) @ ( f @ SV1 @ SY5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(32,plain,
! [SV3: $i,SV2: $i,SV1: $i] :
( ( ( f @ SV1 @ ( f @ SV2 @ SV3 ) )
= ( f @ ( f @ SV1 @ SV2 ) @ ( f @ SV1 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(33,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[22,32,30,28,26,25,24,23]) ).
thf(34,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LDA007-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.15 % Computer : n016.cluster.edu
% 0.10/0.15 % Model : x86_64 x86_64
% 0.10/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.15 % Memory : 8046.5625MB
% 0.10/0.15 % OS : Linux 6.8.0-71-generic
% 0.10/0.15 % CPULimit : 300
% 0.10/0.15 % WCLimit : 300
% 0.10/0.15 % DateTime : Tue Oct 6 12:43:29 UTC 2026
% 0.10/0.15 % CPUTime :
% 0.10/0.15 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.20
% 0.10/0.20 No.of.Axioms: 7
% 0.10/0.20
% 0.10/0.20 Length.of.Defs: 0
% 0.10/0.20
% 0.10/0.20 Contains.Choice.Funs: false
% 0.10/0.20
% 0.10/0.20 ********************************
% 0.10/0.20 * All subproblems solved! *
% 0.10/0.20 ********************************
% 0.10/0.20 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:7,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:33,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.10/0.20
% 0.10/0.20 %**** Beginning of derivation protocol ****
% 0.10/0.20 % SZS output start CNFRefutation
% See solution above
% 0.10/0.20
% 0.10/0.20 %**** End of derivation protocol ****
% 0.10/0.20 %**** no. of clauses in derivation: 34 ****
% 0.10/0.20 %**** clause counter: 33 ****
% 0.10/0.20
% 0.10/0.20 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:7,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:33,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------