%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : GRP657+1 : TPTP v9.3.1. Released v4.0.0.
% 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 : n019.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 10:21:39 AM UTC 2026
% Result : Theorem 0.08s 0.23s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 43 ( 39 unt; 0 typ; 0 def)
% Number of atoms : 136 ( 95 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 279 ( 32 ~; 10 |; 5 &; 232 @)
% ( 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 : 7 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 83 ( 0 ^; 78 !; 5 ?; 83 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_ld,type,
ld: $i > $i > $i ).
thf(tp_mult,type,
mult: $i > $i > $i ).
thf(tp_rd,type,
rd: $i > $i > $i ).
thf(tp_sK1_SY20,type,
sK1_SY20: $i > $i ).
thf(1,axiom,
! [C: $i,B: $i,A: $i] :
( ( mult @ ( mult @ A @ B ) @ ( mult @ C @ A ) )
= ( mult @ A @ ( mult @ ( mult @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( rd @ ( mult @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f04) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( mult @ ( rd @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f03) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( ld @ A @ ( mult @ A @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( mult @ A @ ( ld @ A @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f01) ).
thf(6,conjecture,
? [X0: $i] :
! [X1: $i] :
( ( ( mult @ X1 @ X0 )
= X1 )
& ( ( mult @ X0 @ X1 )
= X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(7,negated_conjecture,
( ( ? [X0: $i] :
! [X1: $i] :
( ( ( mult @ X1 @ X0 )
= X1 )
& ( ( mult @ X0 @ X1 )
= X1 ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[6]) ).
thf(8,plain,
( ( ? [X0: $i] :
! [X1: $i] :
( ( ( mult @ X1 @ X0 )
= X1 )
& ( ( mult @ X0 @ X1 )
= X1 ) ) )
= $false ),
inference(unfold_def,[status(thm)],[7]) ).
thf(9,plain,
( ( ! [C: $i,B: $i,A: $i] :
( ( mult @ ( mult @ A @ B ) @ ( mult @ C @ A ) )
= ( mult @ A @ ( mult @ ( mult @ B @ C ) @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(10,plain,
( ( ! [B: $i,A: $i] :
( ( rd @ ( mult @ A @ B ) @ B )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(11,plain,
( ( ! [B: $i,A: $i] :
( ( mult @ ( rd @ A @ B ) @ B )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(12,plain,
( ( ! [B: $i,A: $i] :
( ( ld @ A @ ( mult @ A @ B ) )
= B ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(13,plain,
( ( ! [B: $i,A: $i] :
( ( mult @ A @ ( ld @ A @ B ) )
= B ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(14,plain,
( ( ~ ? [X0: $i] :
! [X1: $i] :
( ( ( mult @ X1 @ X0 )
= X1 )
& ( ( mult @ X0 @ X1 )
= X1 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(15,plain,
( ( ! [B: $i,A: $i] :
( ( mult @ A @ ( ld @ A @ B ) )
= B ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(16,plain,
( ( ! [B: $i,A: $i] :
( ( ld @ A @ ( mult @ A @ B ) )
= B ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(17,plain,
( ( ! [B: $i,A: $i] :
( ( mult @ ( rd @ A @ B ) @ B )
= A ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(18,plain,
( ( ! [B: $i,A: $i] :
( ( rd @ ( mult @ A @ B ) @ B )
= A ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(19,plain,
( ( ! [C: $i,B: $i,A: $i] :
( ( mult @ ( mult @ A @ B ) @ ( mult @ C @ A ) )
= ( mult @ A @ ( mult @ ( mult @ B @ C ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(20,plain,
( ( ~ ? [X0: $i] :
! [X1: $i] :
( ( ( mult @ X1 @ X0 )
= X1 )
& ( ( mult @ X0 @ X1 )
= X1 ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(21,plain,
( ( ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] :
~ ( ( ( mult @ SX1 @ SX0 )
!= SX1 )
| ( ( mult @ SX0 @ SX1 )
!= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(22,plain,
! [SV1: $i] :
( ( ! [SY13: $i] :
( ( mult @ SY13 @ ( ld @ SY13 @ SV1 ) )
= SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(23,plain,
! [SV2: $i] :
( ( ! [SY14: $i] :
( ( ld @ SY14 @ ( mult @ SY14 @ SV2 ) )
= SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(24,plain,
! [SV3: $i] :
( ( ! [SY15: $i] :
( ( mult @ ( rd @ SY15 @ SV3 ) @ SV3 )
= SY15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(25,plain,
! [SV4: $i] :
( ( ! [SY16: $i] :
( ( rd @ ( mult @ SY16 @ SV4 ) @ SV4 )
= SY16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(26,plain,
! [SV5: $i] :
( ( ! [SY17: $i,SY18: $i] :
( ( mult @ ( mult @ SY18 @ SY17 ) @ ( mult @ SV5 @ SY18 ) )
= ( mult @ SY18 @ ( mult @ ( mult @ SY17 @ SV5 ) @ SY18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(27,plain,
( ( ~ ! [SX0: $i] :
~ ! [SX1: $i] :
~ ( ( ( mult @ SX1 @ SX0 )
!= SX1 )
| ( ( mult @ SX0 @ SX1 )
!= SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(28,plain,
! [SV1: $i,SV6: $i] :
( ( ( mult @ SV6 @ ( ld @ SV6 @ SV1 ) )
= SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(29,plain,
! [SV2: $i,SV7: $i] :
( ( ( ld @ SV7 @ ( mult @ SV7 @ SV2 ) )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(30,plain,
! [SV3: $i,SV8: $i] :
( ( ( mult @ ( rd @ SV8 @ SV3 ) @ SV3 )
= SV8 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(31,plain,
! [SV4: $i,SV9: $i] :
( ( ( rd @ ( mult @ SV9 @ SV4 ) @ SV4 )
= SV9 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(32,plain,
! [SV5: $i,SV10: $i] :
( ( ! [SY19: $i] :
( ( mult @ ( mult @ SY19 @ SV10 ) @ ( mult @ SV5 @ SY19 ) )
= ( mult @ SY19 @ ( mult @ ( mult @ SV10 @ SV5 ) @ SY19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(33,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ( ( ( mult @ SX1 @ SX0 )
!= SX1 )
| ( ( mult @ SX0 @ SX1 )
!= SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[27]) ).
thf(34,plain,
! [SV5: $i,SV10: $i,SV11: $i] :
( ( ( mult @ ( mult @ SV11 @ SV10 ) @ ( mult @ SV5 @ SV11 ) )
= ( mult @ SV11 @ ( mult @ ( mult @ SV10 @ SV5 ) @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(35,plain,
! [SV12: $i] :
( ( ~ ! [SY20: $i] :
~ ( ( ( mult @ SY20 @ SV12 )
!= SY20 )
| ( ( mult @ SV12 @ SY20 )
!= SY20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(36,plain,
! [SV12: $i] :
( ( ! [SY20: $i] :
~ ( ( ( mult @ SY20 @ SV12 )
!= SY20 )
| ( ( mult @ SV12 @ SY20 )
!= SY20 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(37,plain,
! [SV12: $i] :
( ( ~ ( ( ( mult @ ( sK1_SY20 @ SV12 ) @ SV12 )
!= ( sK1_SY20 @ SV12 ) )
| ( ( mult @ SV12 @ ( sK1_SY20 @ SV12 ) )
!= ( sK1_SY20 @ SV12 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[36]) ).
thf(38,plain,
! [SV12: $i] :
( ( ( ( mult @ ( sK1_SY20 @ SV12 ) @ SV12 )
!= ( sK1_SY20 @ SV12 ) )
| ( ( mult @ SV12 @ ( sK1_SY20 @ SV12 ) )
!= ( sK1_SY20 @ SV12 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[37]) ).
thf(39,plain,
! [SV12: $i] :
( ( ( ( mult @ ( sK1_SY20 @ SV12 ) @ SV12 )
!= ( sK1_SY20 @ SV12 ) )
= $true )
| ( ( ( mult @ SV12 @ ( sK1_SY20 @ SV12 ) )
!= ( sK1_SY20 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[38]) ).
thf(40,plain,
! [SV12: $i] :
( ( ( ( mult @ ( sK1_SY20 @ SV12 ) @ SV12 )
= ( sK1_SY20 @ SV12 ) )
= $false )
| ( ( ( mult @ SV12 @ ( sK1_SY20 @ SV12 ) )
!= ( sK1_SY20 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(41,plain,
! [SV12: $i] :
( ( ( ( mult @ SV12 @ ( sK1_SY20 @ SV12 ) )
= ( sK1_SY20 @ SV12 ) )
= $false )
| ( ( ( mult @ ( sK1_SY20 @ SV12 ) @ SV12 )
= ( sK1_SY20 @ SV12 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(42,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[28,41,34,31,30,29]) ).
thf(43,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP657+1 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.08/0.18 % Computer : n019.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Oct 6 10:48:31 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.23
% 0.08/0.23 No.of.Axioms: 5
% 0.08/0.23
% 0.08/0.23 Length.of.Defs: 0
% 0.08/0.23
% 0.08/0.23 Contains.Choice.Funs: false
% 0.08/0.23 .
% 0.08/0.23
% 0.08/0.23 ********************************
% 0.08/0.23 * All subproblems solved! *
% 0.08/0.23 ********************************
% 0.08/0.23 % SZS status Theorem 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:42,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.23
% 0.08/0.23 %**** Beginning of derivation protocol ****
% 0.08/0.23 % SZS output start CNFRefutation
% See solution above
% 0.08/0.23
% 0.08/0.23 %**** End of derivation protocol ****
% 0.08/0.23 %**** no. of clauses in derivation: 43 ****
% 0.08/0.23 %**** clause counter: 42 ****
% 0.08/0.23
% 0.08/0.23 % SZS status Theorem 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:42,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------