%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : ALG040+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/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 12:51:17 PM UTC 2026
% Result : Theorem 16.79s 2.55s
% Output : Proof 16.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 4
% Syntax : Number of formulae : 64 ( 47 unt; 0 def)
% Number of atoms : 136 ( 71 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 109 ( 37 ~; 28 |; 24 &)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-4 aty)
% Number of variables : 67 ( 2 sgn 38 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
~ ? [U] :
( ! [V] :
( sorti2(V)
=> op2(V,V) = U )
& sorti2(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
fof(f3_nnf,plain,
! [U] :
( ? [V] :
( op2(V,V) != U
& sorti2(V) )
| ~ sorti2(U) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [U] :
( ( op2(sk1(U),sk1(U)) != U
& sorti2(sk1(U)) )
| ~ sorti2(U) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f3_nnf]) ).
cnf(c5,plain,
( op2(sk1(X0),sk1(X0)) != X0
| ~ sorti2(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t173,plain,
ifeq(sorti2(X1),true,ifeq(op2(sk1(X1),sk1(X1)),X1,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t405,plain,
ifeq(sorti2(X1),true,ifeq(op2(sk1(X1),sk1(X1)),X1,false,true),true) = true,
inference(orient,[status(thm)],[t173]) ).
fof(f4,conjecture,
( ( ! [V] :
( sorti2(V)
=> sorti1(j(V)) )
& ! [U] :
( sorti1(U)
=> sorti2(h(U)) ) )
=> ~ ( ! [X2] :
( sorti1(X2)
=> j(h(X2)) = X2 )
& ! [X1] :
( sorti2(X1)
=> h(j(X1)) = X1 )
& ! [Y] :
( sorti2(Y)
=> ! [Z] :
( sorti2(Z)
=> j(op2(Y,Z)) = op1(j(Y),j(Z)) ) )
& ! [W] :
( sorti1(W)
=> ! [X] :
( sorti1(X)
=> h(op1(W,X)) = op2(h(W),h(X)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f4_neg,negated_conjecture,
~ ( ( ! [V] :
( sorti2(V)
=> sorti1(j(V)) )
& ! [U] :
( sorti1(U)
=> sorti2(h(U)) ) )
=> ~ ( ! [X2] :
( sorti1(X2)
=> j(h(X2)) = X2 )
& ! [X1] :
( sorti2(X1)
=> h(j(X1)) = X1 )
& ! [Y] :
( sorti2(Y)
=> ! [Z] :
( sorti2(Z)
=> j(op2(Y,Z)) = op1(j(Y),j(Z)) ) )
& ! [W] :
( sorti1(W)
=> ! [X] :
( sorti1(X)
=> h(op1(W,X)) = op2(h(W),h(X)) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
fof(f4_nnf,plain,
( ! [X2] :
( j(h(X2)) = X2
| ~ sorti1(X2) )
& ! [X1] :
( h(j(X1)) = X1
| ~ sorti2(X1) )
& ! [Y] :
( ! [Z] :
( j(op2(Y,Z)) = op1(j(Y),j(Z))
| ~ sorti2(Z) )
| ~ sorti2(Y) )
& ! [W] :
( ! [X] :
( h(op1(W,X)) = op2(h(W),h(X))
| ~ sorti1(X) )
| ~ sorti1(W) )
& ! [V] :
( sorti1(j(V))
| ~ sorti2(V) )
& ! [U] :
( sorti2(h(U))
| ~ sorti1(U) ) ),
inference(nnf_transformation,[status(thm)],[f4_neg]) ).
fof(f4_sk,plain,
! [U,V,W,X,Y,Z,X1,X2] :
( ( j(h(X2)) = X2
| ~ sorti1(X2) )
& ( h(j(X1)) = X1
| ~ sorti2(X1) )
& ( j(op2(Y,Z)) = op1(j(Y),j(Z))
| ~ sorti2(Z)
| ~ sorti2(Y) )
& ( h(op1(W,X)) = op2(h(W),h(X))
| ~ sorti1(X)
| ~ sorti1(W) )
& ( sorti1(j(V))
| ~ sorti2(V) )
& ( sorti2(h(U))
| ~ sorti1(U) ) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c8,plain,
( h(op1(X2,X3)) = op2(h(X2),h(X3))
| ~ sorti1(X3)
| ~ sorti1(X2) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t254,plain,
ifeq(sorti1(X1),true,ifeq(sorti1(X2),true,h(op1(X1,X2)),op2(h(X1),h(X2))),op2(h(X1),h(X2))) = op2(h(X1),h(X2)),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t449,plain,
ifeq(sorti1(X1),true,ifeq(sorti1(X2),true,h(op1(X1,X2)),op2(h(X1),h(X2))),op2(h(X1),h(X2))) = op2(h(X1),h(X2)),
inference(orient,[status(thm)],[t254]) ).
cnf(c6,plain,
( sorti2(h(X0))
| ~ sorti1(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi5,negated_conjecture,
ifeq(sorti1(X0),true,sorti2(h(X0)),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
fof(f2,axiom,
? [U] :
( ! [V] :
( sorti1(V)
=> op1(V,V) = U )
& sorti1(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
fof(f2_nnf,plain,
? [U] :
( ! [V] :
( op1(V,V) = U
| ~ sorti1(V) )
& sorti1(U) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [V] :
( ( op1(V,V) = sk0
| ~ sorti1(V) )
& sorti1(sk0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f2_nnf]) ).
cnf(c2,plain,
sorti1(sk0),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
sorti1(sk0) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h2,plain,
sorti2(h(sk0)) = true,
inference(hyper_resolution,[status(thm)],[hi5,hi2]) ).
cnf(c4,plain,
( sorti2(sk1(X0))
| ~ sorti2(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi4,axiom,
ifeq(sorti2(X0),true,sorti2(sk1(X0)),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(h8,plain,
sorti2(sk1(h(sk0))) = true,
inference(hyper_resolution,[status(thm)],[hi4,h2]) ).
cnf(c7,plain,
( sorti1(j(X1))
| ~ sorti2(X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi6,negated_conjecture,
ifeq(sorti2(X0),true,sorti1(j(X0)),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(h36,plain,
sorti1(j(sk1(h(sk0)))) = true,
inference(hyper_resolution,[status(thm)],[hi6,h8]) ).
cnf(c3,plain,
( op1(X1,X1) = sk0
| ~ sorti1(X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi3,axiom,
ifeq(sorti1(X0),true,op1(X0,X0),sk0) = sk0,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t106,plain,
op1(j(sk1(h(sk0))),j(sk1(h(sk0)))) = sk0,
inference(hyper_resolution,[status(thm)],[hi3,h36]) ).
cnf(t266,plain,
op1(j(sk1(h(sk0))),j(sk1(h(sk0)))) = sk0,
inference(orient,[status(thm)],[t106]) ).
cnf(t472,plain,
op2(h(j(sk1(h(sk0)))),h(j(sk1(h(sk0))))) = ifeq(sorti1(j(sk1(h(sk0)))),true,ifeq(sorti1(j(sk1(h(sk0)))),true,h(sk0),op2(h(j(sk1(h(sk0)))),h(j(sk1(h(sk0)))))),op2(h(j(sk1(h(sk0)))),h(j(sk1(h(sk0)))))),
inference(cp,[status(thm)],[t449,t266]) ).
cnf(c10,plain,
( h(j(X6)) = X6
| ~ sorti2(X6) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi9,negated_conjecture,
ifeq(sorti2(X0),true,h(j(X0)),X0) = X0,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t25,plain,
h(j(sk1(h(sk0)))) = sk1(h(sk0)),
inference(hyper_resolution,[status(thm)],[hi9,h8]) ).
cnf(t313,plain,
h(j(sk1(h(sk0)))) = sk1(h(sk0)),
inference(orient,[status(thm)],[t25]) ).
cnf(t519,plain,
op2(sk1(h(sk0)),h(j(sk1(h(sk0))))) = ifeq(sorti1(j(sk1(h(sk0)))),true,ifeq(sorti1(j(sk1(h(sk0)))),true,h(sk0),op2(h(j(sk1(h(sk0)))),h(j(sk1(h(sk0)))))),op2(h(j(sk1(h(sk0)))),h(j(sk1(h(sk0)))))),
inference(step,[status(thm)],[t472,t313]) ).
cnf(t520,plain,
op2(sk1(h(sk0)),sk1(h(sk0))) = ifeq(sorti1(j(sk1(h(sk0)))),true,ifeq(sorti1(j(sk1(h(sk0)))),true,h(sk0),op2(h(j(sk1(h(sk0)))),h(j(sk1(h(sk0)))))),op2(h(j(sk1(h(sk0)))),h(j(sk1(h(sk0)))))),
inference(step,[status(thm)],[t519,t313]) ).
cnf(h142,plain,
sorti2(h(j(sk1(h(sk0))))) = true,
inference(hyper_resolution,[status(thm)],[hi5,h36]) ).
cnf(h733,plain,
sorti1(j(h(j(sk1(h(sk0)))))) = true,
inference(hyper_resolution,[status(thm)],[hi6,h142]) ).
cnf(h4729,plain,
sorti2(h(j(h(j(sk1(h(sk0))))))) = true,
inference(hyper_resolution,[status(thm)],[hi5,h733]) ).
cnf(t107,plain,
sorti1(j(h(j(h(j(sk1(h(sk0)))))))) = true,
inference(hyper_resolution,[status(thm)],[hi6,h4729]) ).
cnf(t120,plain,
h(j(h(j(sk1(h(sk0)))))) = h(j(sk1(h(sk0)))),
inference(hyper_resolution,[status(thm)],[hi9,h142]) ).
cnf(t298,plain,
h(j(h(j(sk1(h(sk0)))))) = h(j(sk1(h(sk0)))),
inference(orient,[status(thm)],[t120]) ).
cnf(t514,plain,
sorti1(j(h(j(sk1(h(sk0)))))) = true,
inference(step,[status(thm)],[t107,t298]) ).
cnf(t515,plain,
sorti1(j(sk1(h(sk0)))) = true,
inference(step,[status(thm)],[t514,t313]) ).
cnf(t390,plain,
sorti1(j(sk1(h(sk0)))) = true,
inference(orient,[status(thm)],[t515]) ).
cnf(t521,plain,
op2(sk1(h(sk0)),sk1(h(sk0))) = ifeq(true,true,ifeq(sorti1(j(sk1(h(sk0)))),true,h(sk0),op2(h(j(sk1(h(sk0)))),h(j(sk1(h(sk0)))))),op2(h(j(sk1(h(sk0)))),h(j(sk1(h(sk0)))))),
inference(step,[status(thm)],[t520,t390]) ).
cnf(t8,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t8]) ).
cnf(t522,plain,
op2(sk1(h(sk0)),sk1(h(sk0))) = ifeq(sorti1(j(sk1(h(sk0)))),true,h(sk0),op2(h(j(sk1(h(sk0)))),h(j(sk1(h(sk0)))))),
inference(step,[status(thm)],[t521,t256]) ).
cnf(t523,plain,
op2(sk1(h(sk0)),sk1(h(sk0))) = ifeq(true,true,h(sk0),op2(h(j(sk1(h(sk0)))),h(j(sk1(h(sk0)))))),
inference(step,[status(thm)],[t522,t390]) ).
cnf(t524,plain,
op2(sk1(h(sk0)),sk1(h(sk0))) = h(sk0),
inference(step,[status(thm)],[t523,t256]) ).
cnf(t497,plain,
op2(sk1(h(sk0)),sk1(h(sk0))) = h(sk0),
inference(orient,[status(thm)],[t524]) ).
cnf(t498,plain,
true = ifeq(sorti2(h(sk0)),true,ifeq(h(sk0),h(sk0),false,true),true),
inference(cp,[status(thm)],[t405,t497]) ).
cnf(t3,plain,
sorti2(h(sk0)) = true,
inference(hyper_resolution,[status(thm)],[hi5,hi2]) ).
cnf(t368,plain,
sorti2(h(sk0)) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(t525,plain,
true = ifeq(true,true,ifeq(h(sk0),h(sk0),false,true),true),
inference(step,[status(thm)],[t498,t368]) ).
cnf(t526,plain,
true = ifeq(h(sk0),h(sk0),false,true),
inference(step,[status(thm)],[t525,t256]) ).
cnf(t527,plain,
true = false,
inference(step,[status(thm)],[t526,t256]) ).
cnf(t499,plain,
false = true,
inference(orient,[status(thm)],[t527]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t499]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG040+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.35 % Computer : n009.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Fri Sep 25 04:36:43 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 16.79/2.55 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.79/2.55 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------