%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : GRP710-10 : TPTP v9.3.1. Released v8.1.0.
% 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 : n011.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 10:21:49 AM UTC 2026
% Result : Unsatisfiable 0.08s 0.25s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 36 ( 36 unt; 0 typ; 0 def)
% Number of atoms : 92 ( 56 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 131 ( 7 ~; 0 |; 0 &; 124 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 5 con; 0-2 aty)
% Number of variables : 40 ( 0 ^; 40 !; 0 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_i,type,
i: $i > $i ).
thf(tp_mult,type,
mult: $i > $i > $i ).
thf(tp_unit,type,
unit: $i ).
thf(tp_x0,type,
x0: $i ).
thf(tp_x1,type,
x1: $i ).
thf(1,axiom,
! [A: $i] :
( ( mult @ ( i @ A ) @ A )
= unit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).
thf(2,axiom,
! [A: $i] :
( ( mult @ A @ ( i @ A ) )
= unit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f04) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( mult @ A @ ( mult @ B @ ( mult @ B @ C ) ) )
= ( mult @ ( mult @ ( mult @ A @ B ) @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f03) ).
thf(4,axiom,
! [A: $i] :
( ( mult @ unit @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).
thf(5,axiom,
! [A: $i] :
( ( mult @ A @ unit )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f01) ).
thf(6,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(7,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[6]) ).
thf(8,negated_conjecture,
! [X2: $i] :
( ( mult @ x0 @ X2 )
!= x1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
thf(9,plain,
$false = $false,
inference(unfold_def,[status(thm)],[7]) ).
thf(10,plain,
( ( ! [A: $i] :
( ( mult @ ( i @ A ) @ A )
= unit ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(11,plain,
( ( ! [A: $i] :
( ( mult @ A @ ( i @ A ) )
= unit ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(12,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( mult @ A @ ( mult @ B @ ( mult @ B @ C ) ) )
= ( mult @ ( mult @ ( mult @ A @ B ) @ B ) @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(13,plain,
( ( ! [A: $i] :
( ( mult @ unit @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(14,plain,
( ( ! [A: $i] :
( ( mult @ A @ unit )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(15,plain,
( ( ! [X2: $i] :
( ( mult @ x0 @ X2 )
!= x1 ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(16,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(17,plain,
( ( ! [X2: $i] :
( ( mult @ x0 @ X2 )
!= x1 ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(18,plain,
( ( ! [A: $i] :
( ( mult @ A @ unit )
= A ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(19,plain,
( ( ! [A: $i] :
( ( mult @ unit @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(20,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( mult @ A @ ( mult @ B @ ( mult @ B @ C ) ) )
= ( mult @ ( mult @ ( mult @ A @ B ) @ B ) @ C ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(21,plain,
( ( ! [A: $i] :
( ( mult @ A @ ( i @ A ) )
= unit ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(22,plain,
( ( ! [A: $i] :
( ( mult @ ( i @ A ) @ A )
= unit ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(23,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[16]) ).
thf(24,plain,
( ( ! [SX0: $i] :
( ( mult @ x0 @ SX0 )
!= x1 ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(25,plain,
! [SV1: $i] :
( ( ( mult @ SV1 @ unit )
= SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(26,plain,
! [SV2: $i] :
( ( ( mult @ unit @ SV2 )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(27,plain,
! [SV3: $i] :
( ( ! [SY8: $i,SY9: $i] :
( ( mult @ SV3 @ ( mult @ SY8 @ ( mult @ SY8 @ SY9 ) ) )
= ( mult @ ( mult @ ( mult @ SV3 @ SY8 ) @ SY8 ) @ SY9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(28,plain,
! [SV4: $i] :
( ( ( mult @ SV4 @ ( i @ SV4 ) )
= unit )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(29,plain,
! [SV5: $i] :
( ( ( mult @ ( i @ SV5 ) @ SV5 )
= unit )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(30,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(31,plain,
! [SV6: $i] :
( ( ( mult @ x0 @ SV6 )
!= x1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(32,plain,
! [SV7: $i,SV3: $i] :
( ( ! [SY10: $i] :
( ( mult @ SV3 @ ( mult @ SV7 @ ( mult @ SV7 @ SY10 ) ) )
= ( mult @ ( mult @ ( mult @ SV3 @ SV7 ) @ SV7 ) @ SY10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(33,plain,
! [SV6: $i] :
( ( ( mult @ x0 @ SV6 )
= x1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(34,plain,
! [SV8: $i,SV7: $i,SV3: $i] :
( ( ( mult @ SV3 @ ( mult @ SV7 @ ( mult @ SV7 @ SV8 ) ) )
= ( mult @ ( mult @ ( mult @ SV3 @ SV7 ) @ SV7 ) @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(35,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[25,34,33,30,29,28,26]) ).
thf(36,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP710-10 : TPTP v9.3.1. Released v8.1.0.
% 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
% 0.08/0.17 % Computer : n011.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Oct 6 10:52:32 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.25
% 0.08/0.25 No.of.Axioms: 6
% 0.08/0.25
% 0.08/0.25 Length.of.Defs: 0
% 0.08/0.25
% 0.08/0.25 Contains.Choice.Funs: false
% 0.08/0.25
% 0.08/0.25 ********************************
% 0.08/0.25 * All subproblems solved! *
% 0.08/0.25 ********************************
% 0.08/0.25 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:6,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:35,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.25
% 0.08/0.25 %**** Beginning of derivation protocol ****
% 0.08/0.25 % SZS output start CNFRefutation
% See solution above
% 0.08/0.26
% 0.08/0.26 %**** End of derivation protocol ****
% 0.08/0.26 %**** no. of clauses in derivation: 36 ****
% 0.08/0.26 %**** clause counter: 35 ****
% 0.08/0.26
% 0.08/0.26 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:6,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:35,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------