%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : GRP656-10 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 : Unsatisfiable 0.27s 0.28s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 40 ( 40 unt; 0 typ; 0 def)
% Number of atoms : 104 ( 64 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 231 ( 7 ~; 0 |; 0 &; 224 @)
% ( 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 : 9 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 64 ( 0 ^; 64 !; 0 ?; 64 :)
% 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_tuple,type,
tuple: $i > $i > $i ).
thf(tp_x1,type,
x1: $i > $i ).
thf(tp_x1_2,type,
x1_2: $i > $i ).
thf(1,axiom,
! [A: $i,B: $i,C: $i] :
( ( mult @ ( mult @ A @ B ) @ ( mult @ C @ A ) )
= ( mult @ ( mult @ A @ ( mult @ B @ C ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f05) ).
thf(2,axiom,
! [A: $i,B: $i] :
( ( rd @ ( mult @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f04) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( mult @ ( rd @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f03) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ld @ A @ ( mult @ A @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f02) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( mult @ A @ ( ld @ A @ B ) )
= B ),
file('/export/starexec/sandbox2/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,
! [X0: $i] :
( ( tuple @ ( mult @ X0 @ ( x1 @ X0 ) ) @ ( mult @ ( x1_2 @ X0 ) @ X0 ) )
!= ( tuple @ ( x1 @ X0 ) @ ( x1_2 @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
thf(9,plain,
$false = $false,
inference(unfold_def,[status(thm)],[7]) ).
thf(10,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( mult @ ( mult @ A @ B ) @ ( mult @ C @ A ) )
= ( mult @ ( mult @ A @ ( mult @ B @ C ) ) @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(11,plain,
( ( ! [A: $i,B: $i] :
( ( rd @ ( mult @ A @ B ) @ B )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(12,plain,
( ( ! [A: $i,B: $i] :
( ( mult @ ( rd @ A @ B ) @ B )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(13,plain,
( ( ! [A: $i,B: $i] :
( ( ld @ A @ ( mult @ A @ B ) )
= B ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(14,plain,
( ( ! [A: $i,B: $i] :
( ( mult @ A @ ( ld @ A @ B ) )
= B ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(15,plain,
( ( ! [X0: $i] :
( ( tuple @ ( mult @ X0 @ ( x1 @ X0 ) ) @ ( mult @ ( x1_2 @ X0 ) @ X0 ) )
!= ( tuple @ ( x1 @ X0 ) @ ( x1_2 @ X0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(16,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(17,plain,
( ( ! [X0: $i] :
( ( tuple @ ( mult @ X0 @ ( x1 @ X0 ) ) @ ( mult @ ( x1_2 @ X0 ) @ X0 ) )
!= ( tuple @ ( x1 @ X0 ) @ ( x1_2 @ X0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(18,plain,
( ( ! [A: $i,B: $i] :
( ( mult @ A @ ( ld @ A @ B ) )
= B ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(19,plain,
( ( ! [A: $i,B: $i] :
( ( ld @ A @ ( mult @ A @ B ) )
= B ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(20,plain,
( ( ! [A: $i,B: $i] :
( ( mult @ ( rd @ A @ B ) @ B )
= A ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(21,plain,
( ( ! [A: $i,B: $i] :
( ( rd @ ( mult @ A @ B ) @ B )
= A ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(22,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( mult @ ( mult @ A @ B ) @ ( mult @ C @ A ) )
= ( mult @ ( mult @ A @ ( mult @ B @ C ) ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(23,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[16]) ).
thf(24,plain,
( ( ! [SX0: $i] :
( ( tuple @ ( mult @ SX0 @ ( x1 @ SX0 ) ) @ ( mult @ ( x1_2 @ SX0 ) @ SX0 ) )
!= ( tuple @ ( x1 @ SX0 ) @ ( x1_2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(25,plain,
! [SV1: $i] :
( ( ! [SY12: $i] :
( ( mult @ SV1 @ ( ld @ SV1 @ SY12 ) )
= SY12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(26,plain,
! [SV2: $i] :
( ( ! [SY13: $i] :
( ( ld @ SV2 @ ( mult @ SV2 @ SY13 ) )
= SY13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(27,plain,
! [SV3: $i] :
( ( ! [SY14: $i] :
( ( mult @ ( rd @ SV3 @ SY14 ) @ SY14 )
= SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(28,plain,
! [SV4: $i] :
( ( ! [SY15: $i] :
( ( rd @ ( mult @ SV4 @ SY15 ) @ SY15 )
= SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(29,plain,
! [SV5: $i] :
( ( ! [SY16: $i,SY17: $i] :
( ( mult @ ( mult @ SV5 @ SY16 ) @ ( mult @ SY17 @ SV5 ) )
= ( mult @ ( mult @ SV5 @ ( mult @ SY16 @ SY17 ) ) @ SV5 ) ) )
= $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] :
( ( ( tuple @ ( mult @ SV6 @ ( x1 @ SV6 ) ) @ ( mult @ ( x1_2 @ SV6 ) @ SV6 ) )
!= ( tuple @ ( x1 @ SV6 ) @ ( x1_2 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(32,plain,
! [SV7: $i,SV1: $i] :
( ( ( mult @ SV1 @ ( ld @ SV1 @ SV7 ) )
= SV7 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(33,plain,
! [SV8: $i,SV2: $i] :
( ( ( ld @ SV2 @ ( mult @ SV2 @ SV8 ) )
= SV8 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(34,plain,
! [SV9: $i,SV3: $i] :
( ( ( mult @ ( rd @ SV3 @ SV9 ) @ SV9 )
= SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(35,plain,
! [SV10: $i,SV4: $i] :
( ( ( rd @ ( mult @ SV4 @ SV10 ) @ SV10 )
= SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(36,plain,
! [SV11: $i,SV5: $i] :
( ( ! [SY18: $i] :
( ( mult @ ( mult @ SV5 @ SV11 ) @ ( mult @ SY18 @ SV5 ) )
= ( mult @ ( mult @ SV5 @ ( mult @ SV11 @ SY18 ) ) @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(37,plain,
! [SV6: $i] :
( ( ( tuple @ ( mult @ SV6 @ ( x1 @ SV6 ) ) @ ( mult @ ( x1_2 @ SV6 ) @ SV6 ) )
= ( tuple @ ( x1 @ SV6 ) @ ( x1_2 @ SV6 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(38,plain,
! [SV12: $i,SV11: $i,SV5: $i] :
( ( ( mult @ ( mult @ SV5 @ SV11 ) @ ( mult @ SV12 @ SV5 ) )
= ( mult @ ( mult @ SV5 @ ( mult @ SV11 @ SV12 ) ) @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(39,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[30,38,37,35,34,33,32]) ).
thf(40,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP656-10 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.19 % Computer : n018.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Oct 6 10:51:06 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.27/0.28
% 0.27/0.28 No.of.Axioms: 6
% 0.27/0.28
% 0.27/0.28 Length.of.Defs: 0
% 0.27/0.28
% 0.27/0.28 Contains.Choice.Funs: false
% 0.27/0.28
% 0.27/0.28 ********************************
% 0.27/0.28 * All subproblems solved! *
% 0.27/0.28 ********************************
% 0.27/0.28 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:6,ps:3,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:39,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.27/0.28
% 0.27/0.28 %**** Beginning of derivation protocol ****
% 0.27/0.28 % SZS output start CNFRefutation
% See solution above
% 0.27/0.28
% 0.27/0.28 %**** End of derivation protocol ****
% 0.27/0.28 %**** no. of clauses in derivation: 40 ****
% 0.27/0.28 %**** clause counter: 39 ****
% 0.27/0.28
% 0.27/0.28 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:6,ps:3,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:39,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------