%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : LCL162-1 : TPTP v9.3.1. Released v1.0.0.
% 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 10:28:06 AM UTC 2026
% Result : Unsatisfiable 44.43s 7.65s
% Output : CNFRefutation 44.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 15
% Syntax : Number of formulae : 71 ( 71 unt; 0 typ; 0 def)
% Number of atoms : 181 ( 118 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 367 ( 6 ~; 0 |; 0 &; 361 @)
% ( 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 : 12 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 92 ( 0 ^; 92 !; 0 ?; 92 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_and_star,type,
and_star: $i > $i > $i ).
thf(tp_falsehood,type,
falsehood: $i ).
thf(tp_implies,type,
implies: $i > $i > $i ).
thf(tp_not,type,
not: $i > $i ).
thf(tp_truth,type,
truth: $i ).
thf(tp_x,type,
x: $i ).
thf(tp_xor,type,
xor: $i > $i > $i ).
thf(tp_y,type,
y: $i ).
thf(tp_z,type,
z: $i ).
thf(1,axiom,
! [X: $i,Y: $i] :
( ( implies @ X @ Y )
= ( xor @ truth @ ( and_star @ X @ ( xor @ truth @ Y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_definition) ).
thf(2,axiom,
( ( not @ truth )
= falsehood ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',false_definition) ).
thf(3,axiom,
! [X: $i,Y: $i] :
( ( and_star @ X @ Y )
= ( and_star @ Y @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_star_commutativity) ).
thf(4,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( and_star @ ( and_star @ X @ Y ) @ Z )
= ( and_star @ X @ ( and_star @ Y @ Z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_star_associativity) ).
thf(5,axiom,
! [X: $i,Y: $i] :
( ( xor @ X @ Y )
= ( xor @ Y @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xor_commutativity) ).
thf(6,axiom,
! [X: $i,Y: $i] :
( ( and_star @ ( xor @ ( and_star @ ( xor @ truth @ X ) @ Y ) @ truth ) @ Y )
= ( and_star @ ( xor @ ( and_star @ ( xor @ truth @ Y ) @ X ) @ truth ) @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_8) ).
thf(7,axiom,
! [X: $i,Y: $i] :
( ( xor @ X @ ( xor @ truth @ Y ) )
= ( xor @ ( xor @ X @ truth ) @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7) ).
thf(8,axiom,
! [X: $i] :
( ( and_star @ ( xor @ truth @ X ) @ X )
= falsehood ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6) ).
thf(9,axiom,
! [X: $i] :
( ( and_star @ X @ falsehood )
= falsehood ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).
thf(10,axiom,
! [X: $i] :
( ( and_star @ X @ truth )
= X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).
thf(11,axiom,
! [X: $i] :
( ( xor @ X @ X )
= falsehood ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
thf(12,axiom,
! [X: $i] :
( ( xor @ X @ falsehood )
= X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
thf(13,axiom,
! [X: $i] :
( ( not @ X )
= ( xor @ X @ truth ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).
thf(14,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(15,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[14]) ).
thf(16,negated_conjecture,
( ( implies @ ( implies @ x @ y ) @ ( implies @ ( implies @ y @ z ) @ ( implies @ x @ z ) ) )
!= truth ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_wajsberg_axiom) ).
thf(17,plain,
$false = $false,
inference(unfold_def,[status(thm)],[15]) ).
thf(18,plain,
( ( ! [X: $i,Y: $i] :
( ( implies @ X @ Y )
= ( xor @ truth @ ( and_star @ X @ ( xor @ truth @ Y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(19,plain,
( ( ( not @ truth )
= falsehood )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(20,plain,
( ( ! [X: $i,Y: $i] :
( ( and_star @ X @ Y )
= ( and_star @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(21,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( and_star @ ( and_star @ X @ Y ) @ Z )
= ( and_star @ X @ ( and_star @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(22,plain,
( ( ! [X: $i,Y: $i] :
( ( xor @ X @ Y )
= ( xor @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(23,plain,
( ( ! [X: $i,Y: $i] :
( ( and_star @ ( xor @ ( and_star @ ( xor @ truth @ X ) @ Y ) @ truth ) @ Y )
= ( and_star @ ( xor @ ( and_star @ ( xor @ truth @ Y ) @ X ) @ truth ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(24,plain,
( ( ! [X: $i,Y: $i] :
( ( xor @ X @ ( xor @ truth @ Y ) )
= ( xor @ ( xor @ X @ truth ) @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(25,plain,
( ( ! [X: $i] :
( ( and_star @ ( xor @ truth @ X ) @ X )
= falsehood ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(26,plain,
( ( ! [X: $i] :
( ( and_star @ X @ falsehood )
= falsehood ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(27,plain,
( ( ! [X: $i] :
( ( and_star @ X @ truth )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(28,plain,
( ( ! [X: $i] :
( ( xor @ X @ X )
= falsehood ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(29,plain,
( ( ! [X: $i] :
( ( xor @ X @ falsehood )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(30,plain,
( ( ! [X: $i] :
( ( not @ X )
= ( xor @ X @ truth ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(31,plain,
( ( ( implies @ ( implies @ x @ y ) @ ( implies @ ( implies @ y @ z ) @ ( implies @ x @ z ) ) )
!= truth )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(32,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[17]) ).
thf(33,plain,
( ( ( implies @ ( implies @ x @ y ) @ ( implies @ ( implies @ y @ z ) @ ( implies @ x @ z ) ) )
!= truth )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(34,plain,
( ( ! [X: $i] :
( ( not @ X )
= ( xor @ X @ truth ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(35,plain,
( ( ! [X: $i] :
( ( xor @ X @ falsehood )
= X ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(36,plain,
( ( ! [X: $i] :
( ( xor @ X @ X )
= falsehood ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(37,plain,
( ( ! [X: $i] :
( ( and_star @ X @ truth )
= X ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(38,plain,
( ( ! [X: $i] :
( ( and_star @ X @ falsehood )
= falsehood ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(39,plain,
( ( ! [X: $i] :
( ( and_star @ ( xor @ truth @ X ) @ X )
= falsehood ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(40,plain,
( ( ! [X: $i,Y: $i] :
( ( xor @ X @ ( xor @ truth @ Y ) )
= ( xor @ ( xor @ X @ truth ) @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(41,plain,
( ( ! [X: $i,Y: $i] :
( ( and_star @ ( xor @ ( and_star @ ( xor @ truth @ X ) @ Y ) @ truth ) @ Y )
= ( and_star @ ( xor @ ( and_star @ ( xor @ truth @ Y ) @ X ) @ truth ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(42,plain,
( ( ! [X: $i,Y: $i] :
( ( xor @ X @ Y )
= ( xor @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(43,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( and_star @ ( and_star @ X @ Y ) @ Z )
= ( and_star @ X @ ( and_star @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(44,plain,
( ( ! [X: $i,Y: $i] :
( ( and_star @ X @ Y )
= ( and_star @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(45,plain,
( ( ( not @ truth )
= falsehood )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(46,plain,
( ( ! [X: $i,Y: $i] :
( ( implies @ X @ Y )
= ( xor @ truth @ ( and_star @ X @ ( xor @ truth @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(47,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[32]) ).
thf(48,plain,
( ( ( implies @ ( implies @ x @ y ) @ ( implies @ ( implies @ y @ z ) @ ( implies @ x @ z ) ) )
!= truth )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(49,plain,
! [SV1: $i] :
( ( ( not @ SV1 )
= ( xor @ SV1 @ truth ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(50,plain,
! [SV2: $i] :
( ( ( xor @ SV2 @ falsehood )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(51,plain,
! [SV3: $i] :
( ( ( xor @ SV3 @ SV3 )
= falsehood )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(52,plain,
! [SV4: $i] :
( ( ( and_star @ SV4 @ truth )
= SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(53,plain,
! [SV5: $i] :
( ( ( and_star @ SV5 @ falsehood )
= falsehood )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(54,plain,
! [SV6: $i] :
( ( ( and_star @ ( xor @ truth @ SV6 ) @ SV6 )
= falsehood )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(55,plain,
! [SV7: $i] :
( ( ! [SY19: $i] :
( ( xor @ SV7 @ ( xor @ truth @ SY19 ) )
= ( xor @ ( xor @ SV7 @ truth ) @ SY19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(56,plain,
! [SV8: $i] :
( ( ! [SY20: $i] :
( ( and_star @ ( xor @ ( and_star @ ( xor @ truth @ SV8 ) @ SY20 ) @ truth ) @ SY20 )
= ( and_star @ ( xor @ ( and_star @ ( xor @ truth @ SY20 ) @ SV8 ) @ truth ) @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(57,plain,
! [SV9: $i] :
( ( ! [SY21: $i] :
( ( xor @ SV9 @ SY21 )
= ( xor @ SY21 @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(58,plain,
! [SV10: $i] :
( ( ! [SY22: $i,SY23: $i] :
( ( and_star @ ( and_star @ SV10 @ SY22 ) @ SY23 )
= ( and_star @ SV10 @ ( and_star @ SY22 @ SY23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(59,plain,
! [SV11: $i] :
( ( ! [SY24: $i] :
( ( and_star @ SV11 @ SY24 )
= ( and_star @ SY24 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(60,plain,
! [SV12: $i] :
( ( ! [SY25: $i] :
( ( implies @ SV12 @ SY25 )
= ( xor @ truth @ ( and_star @ SV12 @ ( xor @ truth @ SY25 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(61,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(62,plain,
( ( ( implies @ ( implies @ x @ y ) @ ( implies @ ( implies @ y @ z ) @ ( implies @ x @ z ) ) )
= truth )
= $false ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(63,plain,
! [SV13: $i,SV7: $i] :
( ( ( xor @ SV7 @ ( xor @ truth @ SV13 ) )
= ( xor @ ( xor @ SV7 @ truth ) @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(64,plain,
! [SV14: $i,SV8: $i] :
( ( ( and_star @ ( xor @ ( and_star @ ( xor @ truth @ SV8 ) @ SV14 ) @ truth ) @ SV14 )
= ( and_star @ ( xor @ ( and_star @ ( xor @ truth @ SV14 ) @ SV8 ) @ truth ) @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(65,plain,
! [SV15: $i,SV9: $i] :
( ( ( xor @ SV9 @ SV15 )
= ( xor @ SV15 @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(66,plain,
! [SV16: $i,SV10: $i] :
( ( ! [SY26: $i] :
( ( and_star @ ( and_star @ SV10 @ SV16 ) @ SY26 )
= ( and_star @ SV10 @ ( and_star @ SV16 @ SY26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(67,plain,
! [SV17: $i,SV11: $i] :
( ( ( and_star @ SV11 @ SV17 )
= ( and_star @ SV17 @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(68,plain,
! [SV18: $i,SV12: $i] :
( ( ( implies @ SV12 @ SV18 )
= ( xor @ truth @ ( and_star @ SV12 @ ( xor @ truth @ SV18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(69,plain,
! [SV19: $i,SV16: $i,SV10: $i] :
( ( ( and_star @ ( and_star @ SV10 @ SV16 ) @ SV19 )
= ( and_star @ SV10 @ ( and_star @ SV16 @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(70,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[45,69,68,67,65,64,63,62,61,54,53,52,51,50,49]) ).
thf(71,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL162-1 : TPTP v9.3.1. Released v1.0.0.
% 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 12:13:37 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
% 44.43/7.65
% 44.43/7.65 No.of.Axioms: 14
% 44.43/7.65
% 44.43/7.65 Length.of.Defs: 0
% 44.43/7.65
% 44.43/7.65 Contains.Choice.Funs: false
% 44.43/7.65 .
% 44.43/7.65
% 44.43/7.65 ********************************
% 44.43/7.65 * All subproblems solved! *
% 44.43/7.65 ********************************
% 44.43/7.65 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:14,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:70,loop_count:0,foatp_calls:1,translation:fof_full)
% 44.43/7.65
% 44.43/7.65 %**** Beginning of derivation protocol ****
% 44.43/7.65 % SZS output start CNFRefutation
% See solution above
% 44.43/7.65
% 44.43/7.65 %**** End of derivation protocol ****
% 44.43/7.65 %**** no. of clauses in derivation: 71 ****
% 44.43/7.65 %**** clause counter: 70 ****
% 44.43/7.65
% 44.43/7.65 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:14,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:70,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------