%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : LCL132-1 : TPTP v9.3.1. Released v1.0.0.
% 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 : n002.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 08:48:43 AM UTC 2026
% Result : Unsatisfiable 261.45s 261.70s
% Output : Proof 261.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 7
% Syntax : Number of clauses : 39 ( 28 unt; 0 nHn; 36 RR)
% Number of literals : 58 ( 43 equ; 21 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 14 ( 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(prove_wajsberg_lemma,negated_conjecture,
implies(x,x) != truth,
file('theBenchmark.p',prove_wajsberg_lemma) ).
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,
( 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(t1,plain,
implies(x,x) != truth,
inference(start,[status(thm),parent(0:0)],[prove_wajsberg_lemma]) ).
cnf(t2,plain,
( truth != implies(x,x)
| implies(x,x) = truth ),
inference(extension,[status(thm),parent(t1:1)],[equality_2]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( implies(truth,implies(implies(truth,x),implies(truth,x))) != implies(x,x)
| truth != implies(truth,implies(implies(truth,x),implies(truth,x)))
| truth = implies(x,x) ),
inference(extension,[status(thm),parent(t2:2)],[equality_3]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( implies(implies(truth,truth),implies(implies(truth,x),implies(truth,x))) != implies(truth,implies(implies(truth,x),implies(truth,x)))
| truth != implies(implies(truth,truth),implies(implies(truth,x),implies(truth,x)))
| truth = implies(truth,implies(implies(truth,x),implies(truth,x))) ),
inference(extension,[status(thm),parent(t4:2)],[equality_3]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( implies(implies(truth,truth),implies(implies(truth,x),implies(truth,x))) != truth
| truth = implies(implies(truth,truth),implies(implies(truth,x),implies(truth,x))) ),
inference(extension,[status(thm),parent(t6:2)],[equality_2]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
implies(implies(truth,truth),implies(implies(truth,x),implies(truth,x))) = 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(implies(truth,x),implies(truth,x)) != implies(implies(truth,x),implies(truth,x))
| implies(truth,truth) != truth
| implies(implies(truth,truth),implies(implies(truth,x),implies(truth,x))) = implies(truth,implies(implies(truth,x),implies(truth,x))) ),
inference(extension,[status(thm),parent(t6:3)],[equality_4]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t6:3]) ).
cnf(t14,plain,
implies(truth,truth) = truth,
inference(extension,[status(thm),parent(t12:2)],[wajsberg_1]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
implies(implies(truth,x),implies(truth,x)) = implies(implies(truth,x),implies(truth,x)),
inference(extension,[status(thm),parent(t12:3)],[equality_1]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t12:3]) ).
cnf(t18,plain,
( implies(implies(truth,x),implies(truth,x)) != implies(x,x)
| implies(truth,implies(implies(truth,x),implies(truth,x))) != implies(implies(truth,x),implies(truth,x))
| implies(truth,implies(implies(truth,x),implies(truth,x))) = implies(x,x) ),
inference(extension,[status(thm),parent(t4:3)],[equality_3]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t4:3]) ).
cnf(t20,plain,
( implies(implies(truth,x),implies(truth,x)) != implies(implies(truth,x),implies(truth,x))
| implies(truth,implies(implies(truth,x),implies(truth,x))) != implies(implies(truth,x),implies(truth,x))
| implies(truth,implies(implies(truth,x),implies(truth,x))) = implies(implies(truth,x),implies(truth,x)) ),
inference(extension,[status(thm),parent(t18:2)],[equality_3]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
implies(truth,implies(implies(truth,x),implies(truth,x))) = implies(implies(truth,x),implies(truth,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,
implies(implies(truth,x),implies(truth,x)) = implies(implies(truth,x),implies(truth,x)),
inference(extension,[status(thm),parent(t20:3)],[equality_1]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t20:3]) ).
cnf(t26,plain,
( implies(truth,x) != x
| implies(truth,x) != x
| implies(implies(truth,x),implies(truth,x)) = implies(x,x) ),
inference(extension,[status(thm),parent(t18:3)],[equality_4]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t18:3]) ).
cnf(t28,plain,
implies(truth,x) = x,
inference(extension,[status(thm),parent(t26:2)],[wajsberg_1]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t26:2]) ).
cnf(l14,lemma,
implies(truth,x) = x,
inference(lemma,[status(cth),parent(t26:2),below(t18:3)],[t26:2]) ).
cnf(t30,plain,
implies(truth,x) = x,
inference(lemma_extension,[status(thm),parent(t26:3)],[l14:1]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t26:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL132-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 This is a CNF_UNS_RFO_PEQ_UEQ 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
% 0.07/0.36 % Computer : n002.cluster.edu
% 0.07/0.36 % Model : x86_64 x86_64
% 0.07/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.36 % Memory : 8046.5625MB
% 0.07/0.36 % OS : Linux 6.8.0-71-generic
% 0.07/0.36 % CPULimit : 300
% 0.07/0.36 % WCLimit : 300
% 0.07/0.36 % DateTime : Sat Sep 19 14:13:35 UTC 2026
% 0.07/0.36 % CPUTime :
% 261.45/261.70 % SZS status Unsatisfiable for theBenchmark
% 261.45/261.70 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------