%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL109-5 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n009.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 02:00:58 PM UTC 2026
% Result : Unsatisfiable 1.65s 1.16s
% Output : Proof 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 10
% Syntax : Number of formulae : 88 ( 76 unt; 0 def)
% Number of atoms : 100 ( 83 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 32 ( 20 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-4 aty)
% Number of variables : 143 ( 21 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f0,axiom,
implies(truth,X) = X,
file('/export/starexec/sandbox2/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(t19,plain,
implies(truth,X1) = X1,
inference(orient,[status(thm)],[t0]) ).
cnf(f6,axiom,
( implies(X,Y) = truth
| ~ ordered(X,Y) ),
file('/export/starexec/sandbox2/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(t3,plain,
ifeq(ordered(X1,X2),true,implies(X1,X2),truth) = truth,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t34,plain,
ifeq(ordered(X1,X2),true,implies(X1,X2),truth) = truth,
inference(orient,[status(thm)],[t3]) ).
cnf(f8,axiom,
( ordered(implies(X,Z),implies(Y,Z))
| ~ ordered(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_1) ).
fof(f8_nnf,plain,
! [X,Y,Z] :
( ordered(implies(X,Z),implies(Y,Z))
| ~ ordered(X,Y) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X,Y,Z] :
( ordered(implies(X,Z),implies(Y,Z))
| ~ ordered(X,Y) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( ordered(implies(X0,X2),implies(X1,X2))
| ~ ordered(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t7,plain,
ifeq(ordered(X1,X2),true,ordered(implies(X1,X3),implies(X2,X3)),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t234,plain,
ifeq(ordered(X1,X2),true,ordered(implies(X1,X3),implies(X2,X3)),true) = true,
inference(orient,[status(thm)],[t7]) ).
cnf(f7,axiom,
( ordered(X,Y)
| implies(X,Y) != truth ),
file('/export/starexec/sandbox2/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(t2,plain,
ifeq(implies(X1,X2),truth,ordered(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t24,plain,
ifeq(implies(X1,X2),truth,ordered(X1,X2),true) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(f1,axiom,
implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth,
file('/export/starexec/sandbox2/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(t6,plain,
implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))) = truth,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t114,plain,
implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3))) = truth,
inference(orient,[status(thm)],[t6]) ).
cnf(t115,plain,
truth = implies(X1,implies(implies(X1,X2),implies(truth,X2))),
inference(cp,[status(thm)],[t114,t19]) ).
cnf(t458,plain,
truth = implies(X1,implies(implies(X1,X2),X2)),
inference(step,[status(thm)],[t115,t19]) ).
cnf(t165,plain,
implies(X1,implies(implies(X1,X2),X2)) = truth,
inference(orient,[status(thm)],[t458]) ).
cnf(f2,axiom,
implies(implies(X,Y),Y) = implies(implies(Y,X),X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wajsberg_3) ).
fof(f2_nnf,plain,
! [X,Y] : implies(implies(X,Y),Y) = implies(implies(Y,X),X),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Y] : implies(implies(X,Y),Y) = implies(implies(Y,X),X),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
implies(implies(X0,X1),X1) = implies(implies(X1,X0),X0),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t4,plain,
implies(implies(X1,X2),X2) = implies(implies(X2,X1),X1),
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t68,plain,
implies(implies(X1,X2),X2) = implies(implies(X2,X1),X1),
inference(orient,[status(thm)],[t4]) ).
cnf(t69,plain,
implies(implies(X1,truth),truth) = implies(X1,X1),
inference(cp,[status(thm)],[t68,t19]) ).
cnf(t91,plain,
implies(implies(X1,truth),truth) = implies(X1,X1),
inference(orient,[status(thm)],[t69]) ).
cnf(t174,plain,
truth = implies(X1,implies(X1,X1)),
inference(cp,[status(thm)],[t165,t91]) ).
cnf(t166,plain,
truth = implies(implies(truth,X1),X1),
inference(cp,[status(thm)],[t165,t19]) ).
cnf(t459,plain,
truth = implies(X1,X1),
inference(step,[status(thm)],[t166,t19]) ).
cnf(t185,plain,
implies(X1,X1) = truth,
inference(orient,[status(thm)],[t459]) ).
cnf(t465,plain,
truth = implies(X1,truth),
inference(step,[status(thm)],[t174,t185]) ).
cnf(t228,plain,
implies(X1,truth) = truth,
inference(orient,[status(thm)],[t465]) ).
cnf(t231,plain,
true = ifeq(truth,truth,ordered(X1,truth),true),
inference(cp,[status(thm)],[t24,t228]) ).
cnf(t1,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t22,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t1]) ).
cnf(t468,plain,
true = ordered(X1,truth),
inference(step,[status(thm)],[t231,t22]) ).
cnf(t277,plain,
ordered(X1,truth) = true,
inference(orient,[status(thm)],[t468]) ).
cnf(t278,plain,
true = ifeq(true,true,ordered(implies(X1,X2),implies(truth,X2)),true),
inference(cp,[status(thm)],[t234,t277]) ).
cnf(t478,plain,
true = ordered(implies(X1,X2),implies(truth,X2)),
inference(step,[status(thm)],[t278,t22]) ).
cnf(t479,plain,
true = ordered(implies(X1,X2),X2),
inference(step,[status(thm)],[t478,t19]) ).
cnf(t361,plain,
ordered(implies(X1,X2),X2) = true,
inference(orient,[status(thm)],[t479]) ).
cnf(f3,axiom,
implies(implies(not(X),not(Y)),implies(Y,X)) = truth,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wajsberg_4) ).
fof(f3_nnf,plain,
! [X,Y] : implies(implies(not(X),not(Y)),implies(Y,X)) = truth,
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,Y] : implies(implies(not(X),not(Y)),implies(Y,X)) = truth,
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
implies(implies(not(X0),not(X1)),implies(X1,X0)) = truth,
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t5,plain,
implies(implies(not(X1),not(X2)),implies(X2,X1)) = truth,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t44,plain,
implies(implies(not(X1),not(X2)),implies(X2,X1)) = truth,
inference(orient,[status(thm)],[t5]) ).
cnf(t45,plain,
truth = implies(implies(not(X1),not(truth)),X1),
inference(cp,[status(thm)],[t44,t19]) ).
cnf(t52,plain,
implies(implies(not(X1),not(truth)),X1) = truth,
inference(orient,[status(thm)],[t45]) ).
cnf(t366,plain,
true = ordered(truth,X1),
inference(cp,[status(thm)],[t361,t52]) ).
cnf(t386,plain,
ordered(truth,X1) = true,
inference(orient,[status(thm)],[t366]) ).
cnf(t389,plain,
truth = ifeq(true,true,implies(truth,X1),truth),
inference(cp,[status(thm)],[t34,t386]) ).
cnf(t481,plain,
truth = implies(truth,X1),
inference(step,[status(thm)],[t389,t22]) ).
cnf(t482,plain,
truth = X1,
inference(step,[status(thm)],[t481,t19]) ).
cnf(t390,plain,
truth = X1,
inference(orient,[status(thm)],[t482]) ).
cnf(t483,plain,
truth = X1,
inference(step,[status(thm)],[t19,t390]) ).
cnf(t391,plain,
truth = X1,
inference(rw,[status(thm)],[t483]) ).
cnf(t492,plain,
f1 = X1,
inference(step,[status(thm)],[t391,t390]) ).
cnf(t444,plain,
f1 = X1,
inference(orient,[status(thm)],[t492]) ).
cnf(f16,negated_conjecture,
big_V(implies(x,y),implies(y,x)) != truth,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_mv_4) ).
fof(f16_nnf,plain,
big_V(implies(x,y),implies(y,x)) != truth,
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
big_V(implies(x,y),implies(y,x)) != truth,
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
big_V(implies(x,y),implies(y,x)) != truth,
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(u4,negated_conjecture,
big_V(implies(x,y),implies(y,x)) != truth,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(f4,axiom,
big_V(X,Y) = implies(implies(X,Y),Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',big_V_definition) ).
fof(f4_nnf,plain,
! [X,Y] : big_V(X,Y) = implies(implies(X,Y),Y),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X,Y] : big_V(X,Y) = implies(implies(X,Y),Y),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
big_V(X0,X1) = implies(implies(X0,X1),X1),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(d0,axiom,
big_V(X0,X1) = implies(implies(X0,X1),X1),
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(goal_0,negated_conjecture,
implies(implies(implies(x,y),implies(y,x)),implies(y,x)) != truth,
inference(definition_unfolding,[status(thm)],[u4,d0]) ).
cnf(g0_0,plain,
f1 != truth,
inference(rw,[status(thm)],[goal_0,t444]) ).
cnf(g0_1,plain,
f1 != f1,
inference(rw,[status(thm)],[g0_0,t444]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL109-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n009.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 : Wed Sep 23 21:57:45 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 1.65/1.16 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.65/1.16 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------