%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : LAT394-1 : TPTP v9.3.1. Released v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 10:27:44 AM UTC 2026
% Result : Unsatisfiable 6.74s 1.35s
% Output : CNFRefutation 6.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 34 ( 34 unt; 0 typ; 0 def)
% Number of atoms : 88 ( 53 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 278 ( 6 ~; 0 |; 0 &; 272 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 52 ( 0 ^; 52 !; 0 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_and,type,
and: $i > $i > $i ).
thf(tp_f,type,
f: $i > $i > $i ).
thf(tp_neg,type,
neg: $i > $i ).
thf(tp_or,type,
or: $i > $i > $i ).
thf(tp_x0,type,
x0: $i ).
thf(tp_x1,type,
x1: $i ).
thf(1,axiom,
! [A: $i] :
( ( neg @ A )
= ( f @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_003) ).
thf(2,axiom,
! [A: $i,B: $i] :
( ( and @ A @ B )
= ( f @ ( f @ A @ B ) @ ( f @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_002) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( or @ A @ B )
= ( f @ ( f @ A @ A ) @ ( f @ B @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_001) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( f @ ( f @ ( f @ ( f @ A @ B ) @ ( f @ B @ C ) ) @ D ) @ ( f @ B @ ( f @ ( f @ B @ ( f @ ( f @ A @ A ) @ A ) ) @ C ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos) ).
thf(5,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(6,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[5]) ).
thf(7,negated_conjecture,
( ( f @ x0 @ ( f @ x0 @ x0 ) )
!= ( f @ x1 @ ( f @ x1 @ x1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(8,plain,
$false = $false,
inference(unfold_def,[status(thm)],[6]) ).
thf(9,plain,
( ( ! [A: $i] :
( ( neg @ A )
= ( f @ A @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(10,plain,
( ( ! [A: $i,B: $i] :
( ( and @ A @ B )
= ( f @ ( f @ A @ B ) @ ( f @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(11,plain,
( ( ! [A: $i,B: $i] :
( ( or @ A @ B )
= ( f @ ( f @ A @ A ) @ ( f @ B @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(12,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( f @ ( f @ ( f @ ( f @ A @ B ) @ ( f @ B @ C ) ) @ D ) @ ( f @ B @ ( f @ ( f @ B @ ( f @ ( f @ A @ A ) @ A ) ) @ C ) ) )
= B ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(13,plain,
( ( ( f @ x0 @ ( f @ x0 @ x0 ) )
!= ( f @ x1 @ ( f @ x1 @ x1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(14,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(15,plain,
( ( ( f @ x0 @ ( f @ x0 @ x0 ) )
!= ( f @ x1 @ ( f @ x1 @ x1 ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(16,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( f @ ( f @ ( f @ ( f @ A @ B ) @ ( f @ B @ C ) ) @ D ) @ ( f @ B @ ( f @ ( f @ B @ ( f @ ( f @ A @ A ) @ A ) ) @ C ) ) )
= B ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(17,plain,
( ( ! [A: $i,B: $i] :
( ( or @ A @ B )
= ( f @ ( f @ A @ A ) @ ( f @ B @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(18,plain,
( ( ! [A: $i,B: $i] :
( ( and @ A @ B )
= ( f @ ( f @ A @ B ) @ ( f @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(19,plain,
( ( ! [A: $i] :
( ( neg @ A )
= ( f @ A @ A ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(20,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[14]) ).
thf(21,plain,
( ( ( f @ x0 @ ( f @ x0 @ x0 ) )
!= ( f @ x1 @ ( f @ x1 @ x1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(22,plain,
! [SV1: $i] :
( ( ! [SY9: $i,SY10: $i,SY11: $i] :
( ( f @ ( f @ ( f @ ( f @ SV1 @ SY9 ) @ ( f @ SY9 @ SY10 ) ) @ SY11 ) @ ( f @ SY9 @ ( f @ ( f @ SY9 @ ( f @ ( f @ SV1 @ SV1 ) @ SV1 ) ) @ SY10 ) ) )
= SY9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(23,plain,
! [SV2: $i] :
( ( ! [SY12: $i] :
( ( or @ SV2 @ SY12 )
= ( f @ ( f @ SV2 @ SV2 ) @ ( f @ SY12 @ SY12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(24,plain,
! [SV3: $i] :
( ( ! [SY13: $i] :
( ( and @ SV3 @ SY13 )
= ( f @ ( f @ SV3 @ SY13 ) @ ( f @ SV3 @ SY13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(25,plain,
! [SV4: $i] :
( ( ( neg @ SV4 )
= ( f @ SV4 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(26,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(27,plain,
( ( ( f @ x0 @ ( f @ x0 @ x0 ) )
= ( f @ x1 @ ( f @ x1 @ x1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(28,plain,
! [SV5: $i,SV1: $i] :
( ( ! [SY14: $i,SY15: $i] :
( ( f @ ( f @ ( f @ ( f @ SV1 @ SV5 ) @ ( f @ SV5 @ SY14 ) ) @ SY15 ) @ ( f @ SV5 @ ( f @ ( f @ SV5 @ ( f @ ( f @ SV1 @ SV1 ) @ SV1 ) ) @ SY14 ) ) )
= SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(29,plain,
! [SV6: $i,SV2: $i] :
( ( ( or @ SV2 @ SV6 )
= ( f @ ( f @ SV2 @ SV2 ) @ ( f @ SV6 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(30,plain,
! [SV7: $i,SV3: $i] :
( ( ( and @ SV3 @ SV7 )
= ( f @ ( f @ SV3 @ SV7 ) @ ( f @ SV3 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(31,plain,
! [SV8: $i,SV5: $i,SV1: $i] :
( ( ! [SY16: $i] :
( ( f @ ( f @ ( f @ ( f @ SV1 @ SV5 ) @ ( f @ SV5 @ SV8 ) ) @ SY16 ) @ ( f @ SV5 @ ( f @ ( f @ SV5 @ ( f @ ( f @ SV1 @ SV1 ) @ SV1 ) ) @ SV8 ) ) )
= SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(32,plain,
! [SV9: $i,SV8: $i,SV5: $i,SV1: $i] :
( ( ( f @ ( f @ ( f @ ( f @ SV1 @ SV5 ) @ ( f @ SV5 @ SV8 ) ) @ SV9 ) @ ( f @ SV5 @ ( f @ ( f @ SV5 @ ( f @ ( f @ SV1 @ SV1 ) @ SV1 ) ) @ SV8 ) ) )
= SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(33,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[25,32,30,29,27,26]) ).
thf(34,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT394-1 : TPTP v9.3.1. Released v5.4.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.17 % Computer : n002.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Oct 6 12:08:12 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.74/1.35
% 6.74/1.35 No.of.Axioms: 5
% 6.74/1.35
% 6.74/1.35 Length.of.Defs: 0
% 6.74/1.35
% 6.74/1.35 Contains.Choice.Funs: false
% 6.74/1.35
% 6.74/1.35 ********************************
% 6.74/1.35 * All subproblems solved! *
% 6.74/1.35 ********************************
% 6.74/1.35 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:5,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:33,loop_count:0,foatp_calls:1,translation:fof_full)
% 6.74/1.35
% 6.74/1.35 %**** Beginning of derivation protocol ****
% 6.74/1.35 % SZS output start CNFRefutation
% See solution above
% 6.74/1.35
% 6.74/1.35 %**** End of derivation protocol ****
% 6.74/1.35 %**** no. of clauses in derivation: 34 ****
% 6.74/1.35 %**** clause counter: 33 ****
% 6.74/1.35
% 6.74/1.35 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:5,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:33,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------