%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : KLE057+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 : Thu Sep 24 08:46:57 AM UTC 2026
% Result : Theorem 0.10s 0.40s
% Output : Proof 0.10s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('KLE001+0.ax',additive_commutativity) ).
fof(additive_associativity,axiom,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
file('KLE001+0.ax',additive_associativity) ).
fof(additive_identity,axiom,
! [A] : addition(A,zero) = A,
file('KLE001+0.ax',additive_identity) ).
fof(additive_idempotence,axiom,
! [A] : addition(A,A) = A,
file('KLE001+0.ax',additive_idempotence) ).
fof(multiplicative_associativity,axiom,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
file('KLE001+0.ax',multiplicative_associativity) ).
fof(multiplicative_right_identity,axiom,
! [A] : multiplication(A,one) = A,
file('KLE001+0.ax',multiplicative_right_identity) ).
fof(multiplicative_left_identity,axiom,
! [A] : multiplication(one,A) = A,
file('KLE001+0.ax',multiplicative_left_identity) ).
fof(right_distributivity,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('KLE001+0.ax',right_distributivity) ).
fof(left_distributivity,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('KLE001+0.ax',left_distributivity) ).
fof(right_annihilation,axiom,
! [A] : multiplication(A,zero) = zero,
file('KLE001+0.ax',right_annihilation) ).
fof(left_annihilation,axiom,
! [A] : multiplication(zero,A) = zero,
file('KLE001+0.ax',left_annihilation) ).
fof(order,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('KLE001+0.ax',order) ).
fof(domain1,axiom,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
file('KLE001+5.ax',domain1) ).
fof(domain2,axiom,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
file('KLE001+5.ax',domain2) ).
fof(domain3,axiom,
! [X0] : addition(domain(X0),one) = one,
file('KLE001+5.ax',domain3) ).
fof(domain4,axiom,
domain(zero) = zero,
file('KLE001+5.ax',domain4) ).
fof(domain5,axiom,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
file('KLE001+5.ax',domain5) ).
fof(goals,conjecture,
! [X0] :
( X0 = zero
=> domain(X0) = zero ),
file('theBenchmark.p',goals) ).
fof(f_1_1,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(fof_nnf,[status(thm)],[additive_commutativity]) ).
fof(f_1_2,plain,
! [U_1,U_0] : addition(U_1,U_0) = addition(U_0,U_1),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
addition(U_1,U_0) = addition(U_0,U_1),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(fof_nnf,[status(thm)],[additive_associativity]) ).
fof(f_2_2,plain,
! [U_4,U_3,U_2] : addition(U_2,addition(U_3,U_4)) = addition(addition(U_2,U_3),U_4),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
addition(U_2,addition(U_3,U_4)) = addition(addition(U_2,U_3),U_4),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [A] : addition(A,zero) = A,
inference(fof_nnf,[status(thm)],[additive_identity]) ).
fof(f_3_2,plain,
! [U_5] : addition(U_5,zero) = U_5,
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
addition(U_5,zero) = U_5,
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [A] : addition(A,A) = A,
inference(fof_nnf,[status(thm)],[additive_idempotence]) ).
fof(f_4_2,plain,
! [U_6] : addition(U_6,U_6) = U_6,
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
addition(U_6,U_6) = U_6,
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
inference(fof_nnf,[status(thm)],[multiplicative_associativity]) ).
fof(f_5_2,plain,
! [U_9,U_8,U_7] : multiplication(U_9,multiplication(U_8,U_7)) = multiplication(multiplication(U_9,U_8),U_7),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
multiplication(U_9,multiplication(U_8,U_7)) = multiplication(multiplication(U_9,U_8),U_7),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
! [A] : multiplication(A,one) = A,
inference(fof_nnf,[status(thm)],[multiplicative_right_identity]) ).
fof(f_6_2,plain,
! [U_10] : multiplication(U_10,one) = U_10,
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
multiplication(U_10,one) = U_10,
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
! [A] : multiplication(one,A) = A,
inference(fof_nnf,[status(thm)],[multiplicative_left_identity]) ).
fof(f_7_2,plain,
! [U_11] : multiplication(one,U_11) = U_11,
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
multiplication(one,U_11) = U_11,
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(fof_nnf,[status(thm)],[right_distributivity]) ).
fof(f_8_2,plain,
! [U_14,U_13,U_12] : multiplication(U_14,addition(U_13,U_12)) = addition(multiplication(U_14,U_13),multiplication(U_14,U_12)),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
multiplication(U_14,addition(U_13,U_12)) = addition(multiplication(U_14,U_13),multiplication(U_14,U_12)),
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_1,plain,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(fof_nnf,[status(thm)],[left_distributivity]) ).
fof(f_9_2,plain,
! [U_17,U_16,U_15] : multiplication(addition(U_17,U_16),U_15) = addition(multiplication(U_17,U_15),multiplication(U_16,U_15)),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
multiplication(addition(U_17,U_16),U_15) = addition(multiplication(U_17,U_15),multiplication(U_16,U_15)),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_1,plain,
! [A] : multiplication(A,zero) = zero,
inference(fof_nnf,[status(thm)],[right_annihilation]) ).
fof(f_10_2,plain,
! [U_18] : multiplication(U_18,zero) = zero,
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
multiplication(U_18,zero) = zero,
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_1,plain,
! [A] : multiplication(zero,A) = zero,
inference(fof_nnf,[status(thm)],[left_annihilation]) ).
fof(f_11_2,plain,
! [U_19] : multiplication(zero,U_19) = zero,
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
multiplication(zero,U_19) = zero,
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,plain,
! [A,B] :
( ( leq(A,B)
| addition(A,B) != B )
& ( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(fof_nnf,[status(thm)],[order]) ).
fof(f_12_2,plain,
! [U_21,U_20] :
( ( leq(U_21,U_20)
| addition(U_21,U_20) != U_20 )
& ( addition(U_21,U_20) = U_20
| ~ leq(U_21,U_20) ) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
( ! [U_25,U_23] :
( leq(U_25,U_23)
| addition(U_25,U_23) != U_23 )
& ! [U_24,U_22] :
( addition(U_24,U_22) = U_22
| ~ leq(U_24,U_22) ) ),
inference(miniscope,[status(thm)],[f_12_2]) ).
cnf(f_12_4,plain,
( addition(U_24,U_22) = U_22
| ~ leq(U_24,U_22) ),
inference(clausify,[status(thm)],[f_12_3]) ).
cnf(f_12_5,plain,
( leq(U_25,U_23)
| addition(U_25,U_23) != U_23 ),
inference(clausify,[status(thm)],[f_12_3]) ).
fof(f_13_1,plain,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(fof_nnf,[status(thm)],[domain1]) ).
fof(f_13_2,plain,
! [U_26] : addition(U_26,multiplication(domain(U_26),U_26)) = multiplication(domain(U_26),U_26),
inference(variable_rename,[status(thm)],[f_13_1]) ).
cnf(f_13_3,plain,
addition(U_26,multiplication(domain(U_26),U_26)) = multiplication(domain(U_26),U_26),
inference(clausify,[status(thm)],[f_13_2]) ).
fof(f_14_1,plain,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(fof_nnf,[status(thm)],[domain2]) ).
fof(f_14_2,plain,
! [U_28,U_27] : domain(multiplication(U_28,U_27)) = domain(multiplication(U_28,domain(U_27))),
inference(variable_rename,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
domain(multiplication(U_28,U_27)) = domain(multiplication(U_28,domain(U_27))),
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_1,plain,
! [X0] : addition(domain(X0),one) = one,
inference(fof_nnf,[status(thm)],[domain3]) ).
fof(f_15_2,plain,
! [U_29] : addition(domain(U_29),one) = one,
inference(variable_rename,[status(thm)],[f_15_1]) ).
cnf(f_15_3,plain,
addition(domain(U_29),one) = one,
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_1,plain,
domain(zero) = zero,
inference(fof_nnf,[status(thm)],[domain4]) ).
cnf(f_16_2,plain,
domain(zero) = zero,
inference(clausify,[status(thm)],[f_16_1]) ).
fof(f_17_1,plain,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(fof_nnf,[status(thm)],[domain5]) ).
fof(f_17_2,plain,
! [U_31,U_30] : domain(addition(U_31,U_30)) = addition(domain(U_31),domain(U_30)),
inference(variable_rename,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
domain(addition(U_31,U_30)) = addition(domain(U_31),domain(U_30)),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_1,negated_conjecture,
~ ! [X0] :
( X0 = zero
=> domain(X0) = zero ),
inference(negate,[status(cth)],[goals]) ).
fof(f_18_2,negated_conjecture,
? [X0] :
( domain(X0) != zero
& X0 = zero ),
inference(fof_nnf,[status(thm)],[f_18_1]) ).
fof(f_18_3,negated_conjecture,
? [U_32] :
( domain(U_32) != zero
& U_32 = zero ),
inference(variable_rename,[status(thm)],[f_18_2]) ).
fof(f_18_4,negated_conjecture,
( domain(sK1) != zero
& sK1 = zero ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_32,sK1)],[f_18_3]) ).
fof(f_18_5,negated_conjecture,
( domain(sK1) != zero
& sK1 = zero ),
inference(definitional_conversion,[status(esa)],[f_18_4]) ).
cnf(f_18_6,negated_conjecture,
sK1 = zero,
inference(clausify,[status(thm)],[f_18_5]) ).
cnf(f_18_7,negated_conjecture,
domain(sK1) != zero,
inference(clausify,[status(thm)],[f_18_5]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( addition(Eq_x_0,Eq_x_1) = addition(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( multiplication(Eq_x_0,Eq_x_1) = multiplication(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( domain(Eq_x_0) = domain(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( leq(Eq_y_0,Eq_y_1)
| ~ leq(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE057+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n006.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 19 11:49:57 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.40 % SZS status Theorem for theBenchmark
% 0.10/0.40 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------