%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : LCL143-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /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 : Thu Sep 24 08:48:44 AM UTC 2026
% Result : Unsatisfiable 261.03s 261.37s
% Output : Proof 261.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 10
% Syntax : Number of clauses : 39 ( 27 unt; 0 nHn; 36 RR)
% Number of literals : 60 ( 32 equ; 23 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 19 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(wajsberg_1,axiom,
implies(truth,X) = X,
file('LCL001-0.ax',wajsberg_1) ).
cnf(wajsberg_2,axiom,
implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth,
file('LCL001-0.ax',wajsberg_2) ).
cnf(partial_order_definition1,axiom,
( implies(X,Y) = truth
| ~ ordered(X,Y) ),
file('LCL001-1.ax',partial_order_definition1) ).
cnf(partial_order_definition2,axiom,
( ordered(X,Y)
| implies(X,Y) != truth ),
file('LCL001-1.ax',partial_order_definition2) ).
cnf(antecedent,negated_conjecture,
ordered(x,y),
file('theBenchmark.p',antecedent) ).
cnf(prove_wajsberg_theorem,negated_conjecture,
~ ordered(implies(z,x),implies(z,y)),
file('theBenchmark.p',prove_wajsberg_theorem) ).
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_4,axiom,
( implies(Eq_x_0,Eq_x_1) = implies(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( ordered(Eq_y_0,Eq_y_1)
| ~ ordered(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(t1,plain,
ordered(x,y),
inference(start,[status(thm),parent(0:0)],[antecedent]) ).
cnf(t2,plain,
( implies(x,y) = truth
| ~ ordered(x,y) ),
inference(extension,[status(thm),parent(t1:1)],[partial_order_definition1]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( implies(z,y) != implies(z,y)
| implies(implies(x,y),implies(z,y)) = implies(truth,implies(z,y))
| implies(x,y) != truth ),
inference(extension,[status(thm),parent(t2:2)],[equality_4]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( implies(z,x) != implies(truth,implies(z,x))
| ordered(implies(truth,implies(z,x)),implies(truth,implies(z,y)))
| ~ ordered(implies(z,x),implies(implies(x,y),implies(z,y)))
| implies(implies(x,y),implies(z,y)) != implies(truth,implies(z,y)) ),
inference(extension,[status(thm),parent(t4:2)],[equality_8]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( implies(implies(z,x),implies(implies(x,y),implies(z,y))) != truth
| ordered(implies(z,x),implies(implies(x,y),implies(z,y))) ),
inference(extension,[status(thm),parent(t6:2)],[partial_order_definition2]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
implies(implies(z,x),implies(implies(x,y),implies(z,y))) = truth,
inference(extension,[status(thm),parent(t8:2)],[wajsberg_2]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
( implies(truth,implies(z,x)) != implies(z,x)
| implies(truth,implies(z,y)) != implies(z,y)
| ordered(implies(z,x),implies(z,y))
| ~ ordered(implies(truth,implies(z,x)),implies(truth,implies(z,y))) ),
inference(extension,[status(thm),parent(t6:3)],[equality_8]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t6:3]) ).
cnf(t14,plain,
~ ordered(implies(z,x),implies(z,y)),
inference(extension,[status(thm),parent(t12:2)],[prove_wajsberg_theorem]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
implies(truth,implies(z,y)) = implies(z,y),
inference(extension,[status(thm),parent(t12:3)],[wajsberg_1]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t12:3]) ).
cnf(t18,plain,
implies(truth,implies(z,x)) = implies(z,x),
inference(extension,[status(thm),parent(t12:4)],[wajsberg_1]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t12:4]) ).
cnf(t20,plain,
( implies(truth,implies(z,x)) != implies(z,x)
| implies(z,x) = implies(truth,implies(z,x)) ),
inference(extension,[status(thm),parent(t6:4)],[equality_2]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t6:4]) ).
cnf(t22,plain,
implies(truth,implies(z,x)) = implies(z,x),
inference(extension,[status(thm),parent(t20:2)],[wajsberg_1]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
cnf(t24,plain,
( y != y
| z != z
| implies(z,y) = implies(z,y) ),
inference(extension,[status(thm),parent(t4:3)],[equality_4]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t4:3]) ).
cnf(t26,plain,
z = z,
inference(extension,[status(thm),parent(t24:2)],[equality_1]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t24:2]) ).
cnf(t28,plain,
y = y,
inference(extension,[status(thm),parent(t24:3)],[equality_1]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t24:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL143-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 This is a CNF_UNS_RFO_SEQ_HRN problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n018.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 19 14:15:10 UTC 2026
% 0.08/0.35 % CPUTime :
% 261.03/261.37 % SZS status Unsatisfiable for theBenchmark
% 261.03/261.37 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------