%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL143-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n019.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 : Fri Sep 25 02:01:04 PM UTC 2026
% Result : Unsatisfiable 6.81s 6.34s
% Output : Proof 6.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 39 ( 31 unt; 0 def)
% Number of atoms : 47 ( 31 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 22 ( 14 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-4 aty)
% Number of variables : 50 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f7,axiom,
( ordered(X,Y)
| implies(X,Y) != truth ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',partial_order_definition2) ).
fof(f7_nnf,plain,
! [X,Y] :
( ordered(X,Y)
| implies(X,Y) != truth ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X,Y] :
( ordered(X,Y)
| implies(X,Y) != truth ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( ordered(X0,X1)
| implies(X0,X1) != truth ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi5,axiom,
ifeq(implies(X0,X1),truth,ordered(X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(f1,axiom,
implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_2) ).
fof(f1_nnf,plain,
! [X,Y,Z] : implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth,
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y,Z] : implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth,
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))) = truth,
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))) = truth,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t14,plain,
ordered(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))) = true,
inference(hyper_resolution,[status(thm)],[hi5,hi1]) ).
cnf(t57,plain,
ordered(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))) = true,
inference(orient,[status(thm)],[t14]) ).
cnf(f6,axiom,
( implies(X,Y) = truth
| ~ ordered(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',partial_order_definition1) ).
fof(f6_nnf,plain,
! [X,Y] :
( implies(X,Y) = truth
| ~ ordered(X,Y) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X,Y] :
( implies(X,Y) = truth
| ~ ordered(X,Y) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( implies(X0,X1) = truth
| ~ ordered(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi4,axiom,
ifeq(ordered(X0,X1),true,implies(X0,X1),truth) = truth,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(f8,negated_conjecture,
ordered(x,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antecedent) ).
fof(f8_nnf,plain,
ordered(x,y),
inference(nnf_transformation,[status(thm)],[f8]) ).
cnf(c8,plain,
ordered(x,y),
inference(cnf_transformation,[status(esa)],[f8_nnf]) ).
cnf(hi6,negated_conjecture,
ordered(x,y) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t2,plain,
implies(x,y) = truth,
inference(hyper_resolution,[status(thm)],[hi4,hi6]) ).
cnf(t45,plain,
implies(x,y) = truth,
inference(orient,[status(thm)],[t2]) ).
cnf(t65,plain,
true = ordered(implies(X1,x),implies(truth,implies(X1,y))),
inference(cp,[status(thm)],[t57,t45]) ).
cnf(f0,axiom,
implies(truth,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_1) ).
fof(f0_nnf,plain,
! [X] : implies(truth,X) = X,
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X] : implies(truth,X) = X,
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
implies(truth,X0) = X0,
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t0,plain,
implies(truth,X1) = X1,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t15,plain,
implies(truth,X1) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(t377,plain,
true = ordered(implies(X1,x),implies(X1,y)),
inference(step,[status(thm)],[t65,t15]) ).
cnf(t334,plain,
ordered(implies(X1,x),implies(X1,y)) = true,
inference(orient,[status(thm)],[t377]) ).
cnf(f9,negated_conjecture,
~ ordered(implies(z,x),implies(z,y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_wajsberg_theorem) ).
fof(f9_nnf,plain,
~ ordered(implies(z,x),implies(z,y)),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
~ ordered(implies(z,x),implies(z,y)),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
~ ordered(implies(z,x),implies(z,y)),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(goal_0,negated_conjecture,
ordered(implies(z,x),implies(z,y)) != true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t334]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL143-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/5.38 % Computer : n019.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.09/5.38 % CPULimit : 300
% 0.09/5.38 % WCLimit : 300
% 0.09/5.38 % DateTime : Wed Sep 23 22:04:41 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.81/6.34 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.81/6.34 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------