%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : GRP688-1 : 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 : 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 10:21:45 AM UTC 2026
% Result : Unsatisfiable 34.11s 6.04s
% Output : CNFRefutation 34.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 13
% Syntax : Number of formulae : 63 ( 63 unt; 0 typ; 0 def)
% Number of atoms : 161 ( 104 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 284 ( 6 ~; 0 |; 0 &; 278 @)
% ( 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 : 10 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 86 ( 0 ^; 86 !; 0 ?; 86 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_i,type,
i: $i > $i ).
thf(tp_ld,type,
ld: $i > $i > $i ).
thf(tp_mult,type,
mult: $i > $i > $i ).
thf(tp_op_c,type,
op_c: $i ).
thf(tp_op_d,type,
op_d: $i ).
thf(tp_rd,type,
rd: $i > $i > $i ).
thf(tp_unit,type,
unit: $i ).
thf(1,axiom,
( ( mult @ op_d @ ( mult @ op_d @ op_d ) )
= unit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c11) ).
thf(2,axiom,
( ( mult @ op_c @ ( mult @ op_c @ ( mult @ op_c @ op_c ) ) )
= unit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c10) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( i @ ( mult @ A @ B ) )
= ( mult @ ( i @ A ) @ ( i @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c09) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( mult @ ( i @ A ) @ ( mult @ A @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c08) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( mult @ A @ ( mult @ B @ ( mult @ A @ C ) ) )
= ( mult @ ( mult @ A @ ( mult @ B @ A ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c07) ).
thf(6,axiom,
! [A: $i] :
( ( mult @ unit @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c06) ).
thf(7,axiom,
! [A: $i] :
( ( mult @ A @ unit )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c05) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( rd @ ( mult @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c04) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( mult @ ( rd @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c03) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( ld @ A @ ( mult @ A @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c02) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( mult @ A @ ( ld @ A @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c01) ).
thf(12,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(13,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[12]) ).
thf(14,negated_conjecture,
( ( mult @ op_c @ op_d )
!= ( mult @ op_d @ op_c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(15,plain,
$false = $false,
inference(unfold_def,[status(thm)],[13]) ).
thf(16,plain,
( ( ( mult @ op_d @ ( mult @ op_d @ op_d ) )
= unit )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(17,plain,
( ( ( mult @ op_c @ ( mult @ op_c @ ( mult @ op_c @ op_c ) ) )
= unit )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(18,plain,
( ( ! [A: $i,B: $i] :
( ( i @ ( mult @ A @ B ) )
= ( mult @ ( i @ A ) @ ( i @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(19,plain,
( ( ! [A: $i,B: $i] :
( ( mult @ ( i @ A ) @ ( mult @ A @ B ) )
= B ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(20,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( mult @ A @ ( mult @ B @ ( mult @ A @ C ) ) )
= ( mult @ ( mult @ A @ ( mult @ B @ A ) ) @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(21,plain,
( ( ! [A: $i] :
( ( mult @ unit @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(22,plain,
( ( ! [A: $i] :
( ( mult @ A @ unit )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(23,plain,
( ( ! [A: $i,B: $i] :
( ( rd @ ( mult @ A @ B ) @ B )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(24,plain,
( ( ! [A: $i,B: $i] :
( ( mult @ ( rd @ A @ B ) @ B )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(25,plain,
( ( ! [A: $i,B: $i] :
( ( ld @ A @ ( mult @ A @ B ) )
= B ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(26,plain,
( ( ! [A: $i,B: $i] :
( ( mult @ A @ ( ld @ A @ B ) )
= B ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(27,plain,
( ( ( mult @ op_c @ op_d )
!= ( mult @ op_d @ op_c ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(28,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[15]) ).
thf(29,plain,
( ( ( mult @ op_c @ op_d )
!= ( mult @ op_d @ op_c ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(30,plain,
( ( ! [A: $i,B: $i] :
( ( mult @ A @ ( ld @ A @ B ) )
= B ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(31,plain,
( ( ! [A: $i,B: $i] :
( ( ld @ A @ ( mult @ A @ B ) )
= B ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(32,plain,
( ( ! [A: $i,B: $i] :
( ( mult @ ( rd @ A @ B ) @ B )
= A ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(33,plain,
( ( ! [A: $i,B: $i] :
( ( rd @ ( mult @ A @ B ) @ B )
= A ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(34,plain,
( ( ! [A: $i] :
( ( mult @ A @ unit )
= A ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(35,plain,
( ( ! [A: $i] :
( ( mult @ unit @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(36,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( mult @ A @ ( mult @ B @ ( mult @ A @ C ) ) )
= ( mult @ ( mult @ A @ ( mult @ B @ A ) ) @ C ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(37,plain,
( ( ! [A: $i,B: $i] :
( ( mult @ ( i @ A ) @ ( mult @ A @ B ) )
= B ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(38,plain,
( ( ! [A: $i,B: $i] :
( ( i @ ( mult @ A @ B ) )
= ( mult @ ( i @ A ) @ ( i @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(39,plain,
( ( ( mult @ op_c @ ( mult @ op_c @ ( mult @ op_c @ op_c ) ) )
= unit )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(40,plain,
( ( ( mult @ op_d @ ( mult @ op_d @ op_d ) )
= unit )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(41,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[28]) ).
thf(42,plain,
( ( ( mult @ op_c @ op_d )
!= ( mult @ op_d @ op_c ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(43,plain,
! [SV1: $i] :
( ( ! [SY17: $i] :
( ( mult @ SV1 @ ( ld @ SV1 @ SY17 ) )
= SY17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(44,plain,
! [SV2: $i] :
( ( ! [SY18: $i] :
( ( ld @ SV2 @ ( mult @ SV2 @ SY18 ) )
= SY18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(45,plain,
! [SV3: $i] :
( ( ! [SY19: $i] :
( ( mult @ ( rd @ SV3 @ SY19 ) @ SY19 )
= SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(46,plain,
! [SV4: $i] :
( ( ! [SY20: $i] :
( ( rd @ ( mult @ SV4 @ SY20 ) @ SY20 )
= SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(47,plain,
! [SV5: $i] :
( ( ( mult @ SV5 @ unit )
= SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(48,plain,
! [SV6: $i] :
( ( ( mult @ unit @ SV6 )
= SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(49,plain,
! [SV7: $i] :
( ( ! [SY21: $i,SY22: $i] :
( ( mult @ SV7 @ ( mult @ SY21 @ ( mult @ SV7 @ SY22 ) ) )
= ( mult @ ( mult @ SV7 @ ( mult @ SY21 @ SV7 ) ) @ SY22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(50,plain,
! [SV8: $i] :
( ( ! [SY23: $i] :
( ( mult @ ( i @ SV8 ) @ ( mult @ SV8 @ SY23 ) )
= SY23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(51,plain,
! [SV9: $i] :
( ( ! [SY24: $i] :
( ( i @ ( mult @ SV9 @ SY24 ) )
= ( mult @ ( i @ SV9 ) @ ( i @ SY24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(52,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(53,plain,
( ( ( mult @ op_c @ op_d )
= ( mult @ op_d @ op_c ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(54,plain,
! [SV10: $i,SV1: $i] :
( ( ( mult @ SV1 @ ( ld @ SV1 @ SV10 ) )
= SV10 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(55,plain,
! [SV11: $i,SV2: $i] :
( ( ( ld @ SV2 @ ( mult @ SV2 @ SV11 ) )
= SV11 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(56,plain,
! [SV12: $i,SV3: $i] :
( ( ( mult @ ( rd @ SV3 @ SV12 ) @ SV12 )
= SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(57,plain,
! [SV13: $i,SV4: $i] :
( ( ( rd @ ( mult @ SV4 @ SV13 ) @ SV13 )
= SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(58,plain,
! [SV14: $i,SV7: $i] :
( ( ! [SY25: $i] :
( ( mult @ SV7 @ ( mult @ SV14 @ ( mult @ SV7 @ SY25 ) ) )
= ( mult @ ( mult @ SV7 @ ( mult @ SV14 @ SV7 ) ) @ SY25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(59,plain,
! [SV15: $i,SV8: $i] :
( ( ( mult @ ( i @ SV8 ) @ ( mult @ SV8 @ SV15 ) )
= SV15 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(60,plain,
! [SV16: $i,SV9: $i] :
( ( ( i @ ( mult @ SV9 @ SV16 ) )
= ( mult @ ( i @ SV9 ) @ ( i @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(61,plain,
! [SV17: $i,SV14: $i,SV7: $i] :
( ( ( mult @ SV7 @ ( mult @ SV14 @ ( mult @ SV7 @ SV17 ) ) )
= ( mult @ ( mult @ SV7 @ ( mult @ SV14 @ SV7 ) ) @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(62,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[39,61,60,59,57,56,55,54,53,52,48,47,40]) ).
thf(63,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP688-1 : 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
% 0.07/0.17 % Computer : n011.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 10:50:51 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
% 34.11/6.04
% 34.11/6.04 No.of.Axioms: 12
% 34.11/6.04
% 34.11/6.04 Length.of.Defs: 0
% 34.11/6.04
% 34.11/6.04 Contains.Choice.Funs: false
% 34.11/6.04 .
% 34.11/6.04
% 34.11/6.04 ********************************
% 34.11/6.04 * All subproblems solved! *
% 34.11/6.04 ********************************
% 34.11/6.04 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:12,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:62,loop_count:0,foatp_calls:1,translation:fof_full)
% 34.11/6.04
% 34.11/6.04 %**** Beginning of derivation protocol ****
% 34.11/6.04 % SZS output start CNFRefutation
% See solution above
% 34.11/6.04
% 34.11/6.04 %**** End of derivation protocol ****
% 34.11/6.04 %**** no. of clauses in derivation: 63 ****
% 34.11/6.04 %**** clause counter: 62 ****
% 34.11/6.04
% 34.11/6.04 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:12,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:62,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------