%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : GRP777+1 : TPTP v9.3.1. Released v4.1.0.
% 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 : n012.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 10:21:55 AM UTC 2026
% Result : Theorem 7.49s 1.44s
% Output : CNFRefutation 7.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 54 ( 54 unt; 0 typ; 0 def)
% Number of atoms : 140 ( 95 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 344 ( 2 ~; 0 |; 0 &; 342 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 6 con; 0-3 aty)
% Number of variables : 103 ( 0 ^; 103 !; 0 ?; 103 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_b,type,
b: $i ).
thf(tp_bigC,type,
bigC: $i > $i > $i > $i ).
thf(tp_c,type,
c: $i ).
thf(tp_difference,type,
difference: $i > $i > $i ).
thf(tp_product,type,
product: $i > $i > $i ).
thf(tp_quotient,type,
quotient: $i > $i > $i ).
thf(tp_sK1_X0,type,
sK1_X0: $i ).
thf(1,axiom,
( ( product @ ( product @ a @ c ) @ ( product @ c @ b ) )
= ( product @ a @ b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos09) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( bigC @ A @ B @ C )
= ( product @ ( product @ A @ B ) @ ( product @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos08) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( product @ ( product @ ( product @ A @ B ) @ B ) @ ( product @ B @ ( product @ B @ A ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos07) ).
thf(4,axiom,
! [A: $i] :
( ( product @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos06) ).
thf(5,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( product @ ( product @ A @ B ) @ ( product @ C @ D ) )
= ( product @ ( product @ A @ C ) @ ( product @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos05) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( product @ ( quotient @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos04) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( quotient @ ( product @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos03) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( product @ A @ ( difference @ A @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos02) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( difference @ A @ ( product @ A @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos01) ).
thf(10,conjecture,
! [X0: $i] :
( ( bigC @ a @ b @ X0 )
= ( bigC @ c @ c @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(11,negated_conjecture,
( ( ! [X0: $i] :
( ( bigC @ a @ b @ X0 )
= ( bigC @ c @ c @ X0 ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[10]) ).
thf(12,plain,
( ( ! [X0: $i] :
( ( bigC @ a @ b @ X0 )
= ( bigC @ c @ c @ X0 ) ) )
= $false ),
inference(unfold_def,[status(thm)],[11]) ).
thf(13,plain,
( ( ( product @ ( product @ a @ c ) @ ( product @ c @ b ) )
= ( product @ a @ b ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(14,plain,
( ( ! [C: $i,B: $i,A: $i] :
( ( bigC @ A @ B @ C )
= ( product @ ( product @ A @ B ) @ ( product @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(15,plain,
( ( ! [B: $i,A: $i] :
( ( product @ ( product @ ( product @ A @ B ) @ B ) @ ( product @ B @ ( product @ B @ A ) ) )
= B ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(16,plain,
( ( ! [A: $i] :
( ( product @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(17,plain,
( ( ! [D: $i,C: $i,B: $i,A: $i] :
( ( product @ ( product @ A @ B ) @ ( product @ C @ D ) )
= ( product @ ( product @ A @ C ) @ ( product @ B @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(18,plain,
( ( ! [B: $i,A: $i] :
( ( product @ ( quotient @ A @ B ) @ B )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(19,plain,
( ( ! [B: $i,A: $i] :
( ( quotient @ ( product @ A @ B ) @ B )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(20,plain,
( ( ! [B: $i,A: $i] :
( ( product @ A @ ( difference @ A @ B ) )
= B ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(21,plain,
( ( ! [B: $i,A: $i] :
( ( difference @ A @ ( product @ A @ B ) )
= B ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(22,plain,
( ( ( bigC @ a @ b @ sK1_X0 )
= ( bigC @ c @ c @ sK1_X0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[12]) ).
thf(23,plain,
( ( ( bigC @ a @ b @ sK1_X0 )
!= ( bigC @ c @ c @ sK1_X0 ) )
= $true ),
inference(polarity_switch,[status(thm)],[22]) ).
thf(24,plain,
( ( ! [B: $i,A: $i] :
( ( difference @ A @ ( product @ A @ B ) )
= B ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(25,plain,
( ( ! [B: $i,A: $i] :
( ( product @ A @ ( difference @ A @ B ) )
= B ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(26,plain,
( ( ! [B: $i,A: $i] :
( ( quotient @ ( product @ A @ B ) @ B )
= A ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(27,plain,
( ( ! [B: $i,A: $i] :
( ( product @ ( quotient @ A @ B ) @ B )
= A ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(28,plain,
( ( ! [D: $i,C: $i,B: $i,A: $i] :
( ( product @ ( product @ A @ B ) @ ( product @ C @ D ) )
= ( product @ ( product @ A @ C ) @ ( product @ B @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(29,plain,
( ( ! [A: $i] :
( ( product @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(30,plain,
( ( ! [B: $i,A: $i] :
( ( product @ ( product @ ( product @ A @ B ) @ B ) @ ( product @ B @ ( product @ B @ A ) ) )
= B ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(31,plain,
( ( ! [C: $i,B: $i,A: $i] :
( ( bigC @ A @ B @ C )
= ( product @ ( product @ A @ B ) @ ( product @ C @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(32,plain,
( ( ( product @ ( product @ a @ c ) @ ( product @ c @ b ) )
= ( product @ a @ b ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(33,plain,
( ( ( bigC @ a @ b @ sK1_X0 )
!= ( bigC @ c @ c @ sK1_X0 ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(34,plain,
! [SV1: $i] :
( ( ! [SY19: $i] :
( ( difference @ SY19 @ ( product @ SY19 @ SV1 ) )
= SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(35,plain,
! [SV2: $i] :
( ( ! [SY20: $i] :
( ( product @ SY20 @ ( difference @ SY20 @ SV2 ) )
= SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(36,plain,
! [SV3: $i] :
( ( ! [SY21: $i] :
( ( quotient @ ( product @ SY21 @ SV3 ) @ SV3 )
= SY21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(37,plain,
! [SV4: $i] :
( ( ! [SY22: $i] :
( ( product @ ( quotient @ SY22 @ SV4 ) @ SV4 )
= SY22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(38,plain,
! [SV5: $i] :
( ( ! [SY23: $i,SY24: $i,SY25: $i] :
( ( product @ ( product @ SY25 @ SY24 ) @ ( product @ SY23 @ SV5 ) )
= ( product @ ( product @ SY25 @ SY23 ) @ ( product @ SY24 @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(39,plain,
! [SV6: $i] :
( ( ( product @ SV6 @ SV6 )
= SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(40,plain,
! [SV7: $i] :
( ( ! [SY26: $i] :
( ( product @ ( product @ ( product @ SY26 @ SV7 ) @ SV7 ) @ ( product @ SV7 @ ( product @ SV7 @ SY26 ) ) )
= SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(41,plain,
! [SV8: $i] :
( ( ! [SY27: $i,SY28: $i] :
( ( bigC @ SY28 @ SY27 @ SV8 )
= ( product @ ( product @ SY28 @ SY27 ) @ ( product @ SV8 @ SY28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(42,plain,
( ( ( bigC @ a @ b @ sK1_X0 )
= ( bigC @ c @ c @ sK1_X0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(43,plain,
! [SV1: $i,SV9: $i] :
( ( ( difference @ SV9 @ ( product @ SV9 @ SV1 ) )
= SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(44,plain,
! [SV2: $i,SV10: $i] :
( ( ( product @ SV10 @ ( difference @ SV10 @ SV2 ) )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(45,plain,
! [SV3: $i,SV11: $i] :
( ( ( quotient @ ( product @ SV11 @ SV3 ) @ SV3 )
= SV11 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(46,plain,
! [SV4: $i,SV12: $i] :
( ( ( product @ ( quotient @ SV12 @ SV4 ) @ SV4 )
= SV12 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(47,plain,
! [SV5: $i,SV13: $i] :
( ( ! [SY29: $i,SY30: $i] :
( ( product @ ( product @ SY30 @ SY29 ) @ ( product @ SV13 @ SV5 ) )
= ( product @ ( product @ SY30 @ SV13 ) @ ( product @ SY29 @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(48,plain,
! [SV7: $i,SV14: $i] :
( ( ( product @ ( product @ ( product @ SV14 @ SV7 ) @ SV7 ) @ ( product @ SV7 @ ( product @ SV7 @ SV14 ) ) )
= SV7 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(49,plain,
! [SV8: $i,SV15: $i] :
( ( ! [SY31: $i] :
( ( bigC @ SY31 @ SV15 @ SV8 )
= ( product @ ( product @ SY31 @ SV15 ) @ ( product @ SV8 @ SY31 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(50,plain,
! [SV5: $i,SV13: $i,SV16: $i] :
( ( ! [SY32: $i] :
( ( product @ ( product @ SY32 @ SV16 ) @ ( product @ SV13 @ SV5 ) )
= ( product @ ( product @ SY32 @ SV13 ) @ ( product @ SV16 @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(51,plain,
! [SV8: $i,SV15: $i,SV17: $i] :
( ( ( bigC @ SV17 @ SV15 @ SV8 )
= ( product @ ( product @ SV17 @ SV15 ) @ ( product @ SV8 @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(52,plain,
! [SV5: $i,SV13: $i,SV16: $i,SV18: $i] :
( ( ( product @ ( product @ SV18 @ SV16 ) @ ( product @ SV13 @ SV5 ) )
= ( product @ ( product @ SV18 @ SV13 ) @ ( product @ SV16 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(53,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[32,52,51,48,46,45,44,43,42,39]) ).
thf(54,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP777+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.02 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Tue Oct 6 10:53:46 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.49/1.44
% 7.49/1.44 No.of.Axioms: 9
% 7.49/1.44
% 7.49/1.44 Length.of.Defs: 0
% 7.49/1.44
% 7.49/1.44 Contains.Choice.Funs: false
% 7.49/1.44 .
% 7.49/1.44
% 7.49/1.44 ********************************
% 7.49/1.44 * All subproblems solved! *
% 7.49/1.44 ********************************
% 7.49/1.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:9,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:53,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 7.49/1.44
% 7.49/1.44 %**** Beginning of derivation protocol ****
% 7.49/1.44 % SZS output start CNFRefutation
% See solution above
% 7.49/1.44
% 7.49/1.44 %**** End of derivation protocol ****
% 7.49/1.44 %**** no. of clauses in derivation: 54 ****
% 7.49/1.44 %**** clause counter: 53 ****
% 7.49/1.44
% 7.49/1.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:9,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:53,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------