%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : GRP715+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 : 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 10:21:50 AM UTC 2026
% Result : Theorem 12.30s 2.40s
% Output : CNFRefutation 12.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 63 ( 62 unt; 0 typ; 0 def)
% Number of atoms : 175 ( 118 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 396 ( 4 ~; 0 |; 4 &; 388 @)
% ( 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 : 11 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 91 ( 0 ^; 91 !; 0 ?; 91 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_minus,type,
minus: $i > $i ).
thf(tp_mult,type,
mult: $i > $i > $i ).
thf(tp_op_0,type,
op_0: $i ).
thf(tp_op_a,type,
op_a: $i ).
thf(tp_op_b,type,
op_b: $i ).
thf(tp_plus,type,
plus: $i > $i > $i ).
thf(tp_sK1_X0,type,
sK1_X0: $i ).
thf(tp_unit,type,
unit: $i ).
thf(1,axiom,
( ( mult @ op_b @ op_a )
= unit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f11) ).
thf(2,axiom,
( ( mult @ op_a @ op_b )
= unit ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f10) ).
thf(3,axiom,
! [A: $i] :
( ( mult @ unit @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f09) ).
thf(4,axiom,
! [A: $i] :
( ( mult @ A @ unit )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f08) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( mult @ A @ ( mult @ B @ B ) )
= ( mult @ ( mult @ A @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f07) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( mult @ ( mult @ ( mult @ A @ B ) @ C ) @ B )
= ( mult @ A @ ( mult @ ( mult @ B @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f06) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( mult @ A @ ( plus @ B @ C ) )
= ( plus @ ( mult @ A @ B ) @ ( mult @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).
thf(12,conjecture,
! [X0: $i] :
( ( ( mult @ ( mult @ X0 @ op_a ) @ op_b )
= X0 )
& ( ( mult @ ( mult @ X0 @ op_b ) @ op_a )
= X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(13,negated_conjecture,
( ( ! [X0: $i] :
( ( ( mult @ ( mult @ X0 @ op_a ) @ op_b )
= X0 )
& ( ( mult @ ( mult @ X0 @ op_b ) @ op_a )
= X0 ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[12]) ).
thf(14,plain,
( ( ! [X0: $i] :
( ( ( mult @ ( mult @ X0 @ op_a ) @ op_b )
= X0 )
& ( ( mult @ ( mult @ X0 @ op_b ) @ op_a )
= X0 ) ) )
= $false ),
inference(unfold_def,[status(thm)],[13]) ).
thf(15,plain,
( ( ( mult @ op_b @ op_a )
= unit )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(16,plain,
( ( ( mult @ op_a @ op_b )
= unit )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(17,plain,
( ( ! [A: $i] :
( ( mult @ unit @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(18,plain,
( ( ! [A: $i] :
( ( mult @ A @ unit )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(19,plain,
( ( ! [B: $i,A: $i] :
( ( mult @ A @ ( mult @ B @ B ) )
= ( mult @ ( mult @ A @ B ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(20,plain,
( ( ! [C: $i,B: $i,A: $i] :
( ( mult @ ( mult @ ( mult @ A @ B ) @ C ) @ B )
= ( mult @ A @ ( mult @ ( mult @ B @ C ) @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(21,plain,
( ( ! [C: $i,B: $i,A: $i] :
( ( mult @ A @ ( plus @ B @ C ) )
= ( plus @ ( mult @ A @ B ) @ ( mult @ A @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(22,plain,
( ( ( ( mult @ ( mult @ sK1_X0 @ op_a ) @ op_b )
= sK1_X0 )
& ( ( mult @ ( mult @ sK1_X0 @ op_b ) @ op_a )
= sK1_X0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[14]) ).
thf(23,plain,
( ( ( mult @ ( mult @ sK1_X0 @ op_a ) @ op_b )
= sK1_X0 )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[22]) ).
thf(24,plain,
( ( ( mult @ ( mult @ sK1_X0 @ op_b ) @ op_a )
= sK1_X0 )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[22]) ).
thf(25,plain,
( ( ( mult @ ( mult @ sK1_X0 @ op_a ) @ op_b )
!= sK1_X0 )
= $true ),
inference(polarity_switch,[status(thm)],[23]) ).
thf(26,plain,
( ( ( mult @ ( mult @ sK1_X0 @ op_b ) @ op_a )
!= sK1_X0 )
= $true ),
inference(polarity_switch,[status(thm)],[24]) ).
thf(27,plain,
( ( ! [C: $i,B: $i,A: $i] :
( ( mult @ A @ ( plus @ B @ C ) )
= ( plus @ ( mult @ A @ B ) @ ( mult @ A @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(28,plain,
( ( ! [C: $i,B: $i,A: $i] :
( ( mult @ ( mult @ ( mult @ A @ B ) @ C ) @ B )
= ( mult @ A @ ( mult @ ( mult @ B @ C ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(29,plain,
( ( ! [B: $i,A: $i] :
( ( mult @ A @ ( mult @ B @ B ) )
= ( mult @ ( mult @ A @ B ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(30,plain,
( ( ! [A: $i] :
( ( mult @ A @ unit )
= A ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(31,plain,
( ( ! [A: $i] :
( ( mult @ unit @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(32,plain,
( ( ( mult @ op_a @ op_b )
= unit )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(33,plain,
( ( ( mult @ op_b @ op_a )
= unit )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(34,plain,
( ( ( mult @ ( mult @ sK1_X0 @ op_a ) @ op_b )
!= sK1_X0 )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(35,plain,
! [SV1: $i] :
( ( ! [SY11: $i,SY12: $i] :
( ( mult @ SY12 @ ( plus @ SY11 @ SV1 ) )
= ( plus @ ( mult @ SY12 @ SY11 ) @ ( mult @ SY12 @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(36,plain,
! [SV2: $i] :
( ( ! [SY13: $i,SY14: $i] :
( ( mult @ ( mult @ ( mult @ SY14 @ SY13 ) @ SV2 ) @ SY13 )
= ( mult @ SY14 @ ( mult @ ( mult @ SY13 @ SV2 ) @ SY13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(37,plain,
! [SV3: $i] :
( ( ! [SY15: $i] :
( ( mult @ SY15 @ ( mult @ SV3 @ SV3 ) )
= ( mult @ ( mult @ SY15 @ SV3 ) @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(38,plain,
! [SV4: $i] :
( ( ( mult @ SV4 @ unit )
= SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(39,plain,
! [SV5: $i] :
( ( ( mult @ unit @ SV5 )
= SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(40,plain,
( ( ( mult @ ( mult @ sK1_X0 @ op_a ) @ op_b )
= sK1_X0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(41,plain,
! [SV1: $i,SV6: $i] :
( ( ! [SY16: $i] :
( ( mult @ SY16 @ ( plus @ SV6 @ SV1 ) )
= ( plus @ ( mult @ SY16 @ SV6 ) @ ( mult @ SY16 @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(42,plain,
! [SV2: $i,SV7: $i] :
( ( ! [SY17: $i] :
( ( mult @ ( mult @ ( mult @ SY17 @ SV7 ) @ SV2 ) @ SV7 )
= ( mult @ SY17 @ ( mult @ ( mult @ SV7 @ SV2 ) @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(43,plain,
! [SV3: $i,SV8: $i] :
( ( ( mult @ SV8 @ ( mult @ SV3 @ SV3 ) )
= ( mult @ ( mult @ SV8 @ SV3 ) @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(44,plain,
! [SV1: $i,SV6: $i,SV9: $i] :
( ( ( mult @ SV9 @ ( plus @ SV6 @ SV1 ) )
= ( plus @ ( mult @ SV9 @ SV6 ) @ ( mult @ SV9 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(45,plain,
! [SV2: $i,SV7: $i,SV10: $i] :
( ( ( mult @ ( mult @ ( mult @ SV10 @ SV7 ) @ SV2 ) @ SV7 )
= ( mult @ SV10 @ ( mult @ ( mult @ SV7 @ SV2 ) @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(46,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[32,45,44,43,40,39,38,33]) ).
thf(47,plain,
( ( ! [C: $i,B: $i,A: $i] :
( ( mult @ A @ ( plus @ B @ C ) )
= ( plus @ ( mult @ A @ B ) @ ( mult @ A @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(48,plain,
( ( ! [C: $i,B: $i,A: $i] :
( ( mult @ ( mult @ ( mult @ A @ B ) @ C ) @ B )
= ( mult @ A @ ( mult @ ( mult @ B @ C ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(49,plain,
( ( ! [B: $i,A: $i] :
( ( mult @ A @ ( mult @ B @ B ) )
= ( mult @ ( mult @ A @ B ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(50,plain,
( ( ! [A: $i] :
( ( mult @ A @ unit )
= A ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(51,plain,
( ( ! [A: $i] :
( ( mult @ unit @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(52,plain,
( ( ( mult @ op_a @ op_b )
= unit )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(53,plain,
( ( ( mult @ op_b @ op_a )
= unit )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(54,plain,
( ( ( mult @ ( mult @ sK1_X0 @ op_b ) @ op_a )
!= sK1_X0 )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(55,plain,
! [SV11: $i] :
( ( ! [SY18: $i,SY19: $i] :
( ( mult @ SY19 @ ( plus @ SY18 @ SV11 ) )
= ( plus @ ( mult @ SY19 @ SY18 ) @ ( mult @ SY19 @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(56,plain,
! [SV12: $i] :
( ( ! [SY20: $i,SY21: $i] :
( ( mult @ ( mult @ ( mult @ SY21 @ SY20 ) @ SV12 ) @ SY20 )
= ( mult @ SY21 @ ( mult @ ( mult @ SY20 @ SV12 ) @ SY20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(57,plain,
! [SV13: $i] :
( ( ! [SY22: $i] :
( ( mult @ SY22 @ ( mult @ SV13 @ SV13 ) )
= ( mult @ ( mult @ SY22 @ SV13 ) @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(58,plain,
! [SV14: $i] :
( ( ( mult @ SV14 @ unit )
= SV14 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(59,plain,
! [SV15: $i] :
( ( ( mult @ unit @ SV15 )
= SV15 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(60,plain,
( ( ( mult @ ( mult @ sK1_X0 @ op_b ) @ op_a )
= sK1_X0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(61,plain,
! [SV11: $i,SV16: $i] :
( ( ! [SY23: $i] :
( ( mult @ SY23 @ ( plus @ SV16 @ SV11 ) )
= ( plus @ ( mult @ SY23 @ SV16 ) @ ( mult @ SY23 @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(62,plain,
! [SV12: $i,SV17: $i] :
( ( ! [SY24: $i] :
( ( mult @ ( mult @ ( mult @ SY24 @ SV17 ) @ SV12 ) @ SV17 )
= ( mult @ SY24 @ ( mult @ ( mult @ SV17 @ SV12 ) @ SV17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(63,plain,
! [SV13: $i,SV18: $i] :
( ( ( mult @ SV18 @ ( mult @ SV13 @ SV13 ) )
= ( mult @ ( mult @ SV18 @ SV13 ) @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(64,plain,
! [SV11: $i,SV16: $i,SV19: $i] :
( ( ( mult @ SV19 @ ( plus @ SV16 @ SV11 ) )
= ( plus @ ( mult @ SV19 @ SV16 ) @ ( mult @ SV19 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(65,plain,
! [SV12: $i,SV17: $i,SV20: $i] :
( ( ( mult @ ( mult @ ( mult @ SV20 @ SV17 ) @ SV12 ) @ SV17 )
= ( mult @ SV20 @ ( mult @ ( mult @ SV17 @ SV12 ) @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(66,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[52,65,64,63,60,59,58,53]) ).
thf(67,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[66,46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP715+1 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Oct 6 10:52:01 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.30/2.40
% 12.30/2.40 No.of.Axioms: 7
% 12.30/2.40
% 12.30/2.40 Length.of.Defs: 0
% 12.30/2.40
% 12.30/2.40 Contains.Choice.Funs: false
% 12.30/2.40 .
% 12.30/2.40
% 12.30/2.40 ********************************
% 12.30/2.40 * All subproblems solved! *
% 12.30/2.40 ********************************
% 12.30/2.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:7,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:66,loop_count:0,foatp_calls:1,translation:fof_full)
% 12.30/2.40
% 12.30/2.40 %**** Beginning of derivation protocol ****
% 12.30/2.40 % SZS output start CNFRefutation
% See solution above
% 12.30/2.40
% 12.30/2.40 %**** End of derivation protocol ****
% 12.30/2.40 %**** no. of clauses in derivation: 63 ****
% 12.30/2.40 %**** clause counter: 66 ****
% 12.30/2.40
% 12.30/2.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:7,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:66,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------