%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : GRP660+2 : 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/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 10:21:41 AM UTC 2026
% Result : Theorem 168.38s 28.35s
% Output : CNFRefutation 168.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 58 ( 57 unt; 0 typ; 0 def)
% Number of atoms : 165 ( 111 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 329 ( 4 ~; 0 |; 5 &; 320 @)
% ( 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; 4 con; 0-2 aty)
% Number of variables : 101 ( 0 ^; 101 !; 0 ?; 101 :)
% 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_X0,type,
sK1_X0: $i ).
thf(tp_sK2_SY13,type,
sK2_SY13: $i ).
thf(1,axiom,
! [C: $i,B: $i,A: $i] :
( ( mult @ ( mult @ ( mult @ A @ B ) @ C ) @ A )
= ( mult @ A @ ( mult @ B @ ( mult @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f05) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( rd @ ( mult @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f04) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( mult @ ( rd @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f03) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( ld @ A @ ( mult @ A @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f02) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( mult @ A @ ( ld @ A @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f01) ).
thf(6,conjecture,
! [X0: $i,X1: $i] :
( ( ( mult @ X0 @ ( rd @ X1 @ X1 ) )
= X0 )
& ( ( mult @ ( rd @ X1 @ X1 ) @ X0 )
= X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
thf(7,negated_conjecture,
( ( ! [X0: $i,X1: $i] :
( ( ( mult @ X0 @ ( rd @ X1 @ X1 ) )
= X0 )
& ( ( mult @ ( rd @ X1 @ X1 ) @ X0 )
= X0 ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[6]) ).
thf(8,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( mult @ X0 @ ( rd @ X1 @ X1 ) )
= X0 )
& ( ( mult @ ( rd @ X1 @ X1 ) @ X0 )
= X0 ) ) )
= $false ),
inference(unfold_def,[status(thm)],[7]) ).
thf(9,plain,
( ( ! [C: $i,B: $i,A: $i] :
( ( mult @ ( mult @ ( mult @ A @ B ) @ C ) @ A )
= ( mult @ A @ ( mult @ B @ ( mult @ 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,
( ( ! [SY13: $i] :
( ( ( mult @ sK1_X0 @ ( rd @ SY13 @ SY13 ) )
= sK1_X0 )
& ( ( mult @ ( rd @ SY13 @ SY13 ) @ sK1_X0 )
= sK1_X0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[8]) ).
thf(15,plain,
( ( ( ( mult @ sK1_X0 @ ( rd @ sK2_SY13 @ sK2_SY13 ) )
= sK1_X0 )
& ( ( mult @ ( rd @ sK2_SY13 @ sK2_SY13 ) @ sK1_X0 )
= sK1_X0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[14]) ).
thf(16,plain,
( ( ( mult @ sK1_X0 @ ( rd @ sK2_SY13 @ sK2_SY13 ) )
= sK1_X0 )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[15]) ).
thf(17,plain,
( ( ( mult @ ( rd @ sK2_SY13 @ sK2_SY13 ) @ sK1_X0 )
= sK1_X0 )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[15]) ).
thf(18,plain,
( ( ( mult @ sK1_X0 @ ( rd @ sK2_SY13 @ sK2_SY13 ) )
!= sK1_X0 )
= $true ),
inference(polarity_switch,[status(thm)],[16]) ).
thf(19,plain,
( ( ( mult @ ( rd @ sK2_SY13 @ sK2_SY13 ) @ sK1_X0 )
!= sK1_X0 )
= $true ),
inference(polarity_switch,[status(thm)],[17]) ).
thf(20,plain,
( ( ! [B: $i,A: $i] :
( ( mult @ A @ ( ld @ A @ B ) )
= B ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(21,plain,
( ( ! [B: $i,A: $i] :
( ( ld @ A @ ( mult @ A @ B ) )
= B ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(22,plain,
( ( ! [B: $i,A: $i] :
( ( mult @ ( rd @ A @ B ) @ B )
= A ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(23,plain,
( ( ! [B: $i,A: $i] :
( ( rd @ ( mult @ A @ B ) @ B )
= A ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(24,plain,
( ( ! [C: $i,B: $i,A: $i] :
( ( mult @ ( mult @ ( mult @ A @ B ) @ C ) @ A )
= ( mult @ A @ ( mult @ B @ ( mult @ C @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(25,plain,
( ( ( mult @ sK1_X0 @ ( rd @ sK2_SY13 @ sK2_SY13 ) )
!= sK1_X0 )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(26,plain,
! [SV1: $i] :
( ( ! [SY14: $i] :
( ( mult @ SY14 @ ( ld @ SY14 @ SV1 ) )
= SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(27,plain,
! [SV2: $i] :
( ( ! [SY15: $i] :
( ( ld @ SY15 @ ( mult @ SY15 @ SV2 ) )
= SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(28,plain,
! [SV3: $i] :
( ( ! [SY16: $i] :
( ( mult @ ( rd @ SY16 @ SV3 ) @ SV3 )
= SY16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(29,plain,
! [SV4: $i] :
( ( ! [SY17: $i] :
( ( rd @ ( mult @ SY17 @ SV4 ) @ SV4 )
= SY17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(30,plain,
! [SV5: $i] :
( ( ! [SY18: $i,SY19: $i] :
( ( mult @ ( mult @ ( mult @ SY19 @ SY18 ) @ SV5 ) @ SY19 )
= ( mult @ SY19 @ ( mult @ SY18 @ ( mult @ SV5 @ SY19 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(31,plain,
( ( ( mult @ sK1_X0 @ ( rd @ sK2_SY13 @ sK2_SY13 ) )
= sK1_X0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(32,plain,
! [SV1: $i,SV6: $i] :
( ( ( mult @ SV6 @ ( ld @ SV6 @ SV1 ) )
= SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(33,plain,
! [SV2: $i,SV7: $i] :
( ( ( ld @ SV7 @ ( mult @ SV7 @ SV2 ) )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(34,plain,
! [SV3: $i,SV8: $i] :
( ( ( mult @ ( rd @ SV8 @ SV3 ) @ SV3 )
= SV8 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(35,plain,
! [SV4: $i,SV9: $i] :
( ( ( rd @ ( mult @ SV9 @ SV4 ) @ SV4 )
= SV9 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(36,plain,
! [SV5: $i,SV10: $i] :
( ( ! [SY20: $i] :
( ( mult @ ( mult @ ( mult @ SY20 @ SV10 ) @ SV5 ) @ SY20 )
= ( mult @ SY20 @ ( mult @ SV10 @ ( mult @ SV5 @ SY20 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(37,plain,
! [SV5: $i,SV10: $i,SV11: $i] :
( ( ( mult @ ( mult @ ( mult @ SV11 @ SV10 ) @ SV5 ) @ SV11 )
= ( mult @ SV11 @ ( mult @ SV10 @ ( mult @ SV5 @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(38,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[31,37,35,34,33,32]) ).
thf(39,plain,
( ( ! [B: $i,A: $i] :
( ( mult @ A @ ( ld @ A @ B ) )
= B ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(40,plain,
( ( ! [B: $i,A: $i] :
( ( ld @ A @ ( mult @ A @ B ) )
= B ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(41,plain,
( ( ! [B: $i,A: $i] :
( ( mult @ ( rd @ A @ B ) @ B )
= A ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(42,plain,
( ( ! [B: $i,A: $i] :
( ( rd @ ( mult @ A @ B ) @ B )
= A ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(43,plain,
( ( ! [C: $i,B: $i,A: $i] :
( ( mult @ ( mult @ ( mult @ A @ B ) @ C ) @ A )
= ( mult @ A @ ( mult @ B @ ( mult @ C @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(44,plain,
( ( ( mult @ ( rd @ sK2_SY13 @ sK2_SY13 ) @ sK1_X0 )
!= sK1_X0 )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(45,plain,
! [SV12: $i] :
( ( ! [SY21: $i] :
( ( mult @ SY21 @ ( ld @ SY21 @ SV12 ) )
= SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(46,plain,
! [SV13: $i] :
( ( ! [SY22: $i] :
( ( ld @ SY22 @ ( mult @ SY22 @ SV13 ) )
= SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(47,plain,
! [SV14: $i] :
( ( ! [SY23: $i] :
( ( mult @ ( rd @ SY23 @ SV14 ) @ SV14 )
= SY23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(48,plain,
! [SV15: $i] :
( ( ! [SY24: $i] :
( ( rd @ ( mult @ SY24 @ SV15 ) @ SV15 )
= SY24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(49,plain,
! [SV16: $i] :
( ( ! [SY25: $i,SY26: $i] :
( ( mult @ ( mult @ ( mult @ SY26 @ SY25 ) @ SV16 ) @ SY26 )
= ( mult @ SY26 @ ( mult @ SY25 @ ( mult @ SV16 @ SY26 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(50,plain,
( ( ( mult @ ( rd @ sK2_SY13 @ sK2_SY13 ) @ sK1_X0 )
= sK1_X0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(51,plain,
! [SV12: $i,SV17: $i] :
( ( ( mult @ SV17 @ ( ld @ SV17 @ SV12 ) )
= SV12 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(52,plain,
! [SV13: $i,SV18: $i] :
( ( ( ld @ SV18 @ ( mult @ SV18 @ SV13 ) )
= SV13 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(53,plain,
! [SV14: $i,SV19: $i] :
( ( ( mult @ ( rd @ SV19 @ SV14 ) @ SV14 )
= SV19 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(54,plain,
! [SV15: $i,SV20: $i] :
( ( ( rd @ ( mult @ SV20 @ SV15 ) @ SV15 )
= SV20 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(55,plain,
! [SV16: $i,SV21: $i] :
( ( ! [SY27: $i] :
( ( mult @ ( mult @ ( mult @ SY27 @ SV21 ) @ SV16 ) @ SY27 )
= ( mult @ SY27 @ ( mult @ SV21 @ ( mult @ SV16 @ SY27 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(56,plain,
! [SV16: $i,SV21: $i,SV22: $i] :
( ( ( mult @ ( mult @ ( mult @ SV22 @ SV21 ) @ SV16 ) @ SV22 )
= ( mult @ SV22 @ ( mult @ SV21 @ ( mult @ SV16 @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(57,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[50,56,54,53,52,51]) ).
thf(58,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[57,38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP660+2 : 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/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 10:51:22 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
% 168.38/28.35
% 168.38/28.35 No.of.Axioms: 5
% 168.38/28.35
% 168.38/28.35 Length.of.Defs: 0
% 168.38/28.35
% 168.38/28.35 Contains.Choice.Funs: false
% 168.38/28.35 .
% 168.38/28.35
% 168.38/28.35 ********************************
% 168.38/28.35 * All subproblems solved! *
% 168.38/28.35 ********************************
% 168.38/28.35 % SZS status Theorem for /export/starexec/sandbox2/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:285,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:57,loop_count:0,foatp_calls:1,translation:fof_full)
% 168.38/28.35
% 168.38/28.35 %**** Beginning of derivation protocol ****
% 168.38/28.35 % SZS output start CNFRefutation
% See solution above
% 168.38/28.35
% 168.38/28.35 %**** End of derivation protocol ****
% 168.38/28.35 %**** no. of clauses in derivation: 58 ****
% 168.38/28.35 %**** clause counter: 57 ****
% 168.38/28.35
% 168.38/28.35 % SZS status Theorem for /export/starexec/sandbox2/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:285,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:57,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------