%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : ALG070+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n007.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 12:51:31 PM UTC 2026
% Result : Theorem 33.19s 4.90s
% Output : Proof 33.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 56 ( 38 unt; 0 def)
% Number of atoms : 141 ( 67 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 133 ( 48 ~; 37 |; 24 &)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-4 aty)
% Number of variables : 71 ( 2 sgn 46 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox2/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(c11,plain,
( h(j(X6)) = X6
| ~ sorti2(X6) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t52,plain,
ifeq(sorti2(X1),true,h(j(X1)),X1) = X1,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t257,plain,
ifeq(sorti2(X1),true,h(j(X1)),X1) = X1,
inference(orient,[status(thm)],[t52]) ).
fof(f3,axiom,
~ ! [U] :
( sorti2(U)
=> ! [V] :
( sorti2(V)
=> ( op2(U,V) = U
| op2(U,U) != V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
fof(f3_nnf,plain,
? [U] :
( ? [V] :
( op2(U,V) != U
& op2(U,U) = V
& sorti2(V) )
& sorti2(U) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
( op2(sk0,sk1) != sk0
& op2(sk0,sk0) = sk1
& sorti2(sk1)
& sorti2(sk0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f3_nnf]) ).
cnf(c3,plain,
sorti2(sk0),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t0,plain,
sorti2(sk0) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t686,plain,
sorti2(sk0) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(t687,plain,
sk0 = ifeq(true,true,h(j(sk0)),sk0),
inference(cp,[status(thm)],[t257,t686]) ).
cnf(t5,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t5]) ).
cnf(t1323,plain,
sk0 = h(j(sk0)),
inference(step,[status(thm)],[t687,t256]) ).
cnf(t1198,plain,
h(j(sk0)) = sk0,
inference(orient,[status(thm)],[t1323]) ).
cnf(c10,plain,
( j(op2(X4,X5)) = op1(j(X4),j(X5))
| ~ sorti2(X5)
| ~ sorti2(X4) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi9,negated_conjecture,
ifeq(sorti2(X0),true,ifeq(sorti2(X1),true,j(op2(X0,X1)),op1(j(X0),j(X1))),op1(j(X0),j(X1))) = op1(j(X0),j(X1)),
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(hi3,axiom,
sorti2(sk0) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(h1,plain,
j(op2(sk0,sk0)) = op1(j(sk0),j(sk0)),
inference(hyper_resolution,[status(thm)],[hi9,hi3,hi3]) ).
fof(f1,axiom,
! [U] :
( sorti2(U)
=> ! [V] :
( sorti2(V)
=> sorti2(op2(U,V)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
fof(f1_nnf,plain,
! [U] :
( ! [V] :
( sorti2(op2(U,V))
| ~ sorti2(V) )
| ~ sorti2(U) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [U,V] :
( sorti2(op2(U,V))
| ~ sorti2(V)
| ~ sorti2(U) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( sorti2(op2(X0,X1))
| ~ sorti2(X1)
| ~ sorti2(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
ifeq(sorti2(X0),true,ifeq(sorti2(X1),true,sorti2(op2(X0,X1)),true),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h3,plain,
sorti2(op2(sk0,sk0)) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi3,hi3]) ).
cnf(c8,plain,
( sorti1(j(X1))
| ~ sorti2(X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi7,negated_conjecture,
ifeq(sorti2(X0),true,sorti1(j(X0)),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(h22,plain,
sorti1(j(op2(sk0,sk0))) = true,
inference(hyper_resolution,[status(thm)],[hi7,h3]) ).
cnf(h2,plain,
sorti1(j(sk0)) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi3]) ).
fof(f2,axiom,
! [U] :
( sorti1(U)
=> ! [V] :
( sorti1(V)
=> ( op1(U,V) = U
| op1(U,U) != V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
fof(f2_nnf,plain,
! [U] :
( ! [V] :
( op1(U,V) = U
| op1(U,U) != V
| ~ sorti1(V) )
| ~ sorti1(U) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [U,V] :
( op1(U,V) = U
| op1(U,U) != V
| ~ sorti1(V)
| ~ sorti1(U) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( op1(X0,X1) = X0
| op1(X0,X0) != X1
| ~ sorti1(X1)
| ~ sorti1(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
ifeq(sorti1(X0),true,ifeq(sorti1(X1),true,ifeq(op1(X0,X0),X1,op1(X0,X1),X0),X0),X0) = X0,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t54,plain,
op1(j(sk0),j(op2(sk0,sk0))) = j(sk0),
inference(hyper_resolution,[status(thm)],[hi2,h2,h22,h1]) ).
cnf(t261,plain,
op1(j(sk0),j(op2(sk0,sk0))) = j(sk0),
inference(orient,[status(thm)],[t54]) ).
cnf(c5,plain,
op2(sk0,sk0) = sk1,
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t2,plain,
op2(sk0,sk0) = sk1,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t369,plain,
op2(sk0,sk0) = sk1,
inference(orient,[status(thm)],[t2]) ).
cnf(t1252,plain,
op1(j(sk0),j(sk1)) = j(sk0),
inference(step,[status(thm)],[t261,t369]) ).
cnf(c4,plain,
sorti2(sk1),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi4,axiom,
sorti2(sk1) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t55,plain,
op1(j(sk0),j(sk1)) = j(op2(sk0,sk1)),
inference(hyper_resolution,[status(thm)],[hi9,hi3,hi4]) ).
cnf(t283,plain,
op1(j(sk0),j(sk1)) = j(op2(sk0,sk1)),
inference(orient,[status(thm)],[t55]) ).
cnf(t1253,plain,
j(op2(sk0,sk1)) = j(sk0),
inference(step,[status(thm)],[t1252,t283]) ).
cnf(t372,plain,
j(op2(sk0,sk1)) = j(sk0),
inference(rw,[status(thm)],[t1253]) ).
cnf(t1235,plain,
j(op2(sk0,sk1)) = j(sk0),
inference(orient,[status(thm)],[t372]) ).
cnf(c6,plain,
op2(sk0,sk1) != sk0,
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(goal_0,negated_conjecture,
op2(sk0,sk1) != sk0,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(g0_0,plain,
op2(sk0,sk1) != h(j(sk0)),
inference(rw,[status(thm)],[goal_0,t1198]) ).
cnf(g0_1,plain,
h(j(op2(sk0,sk1))) != h(j(sk0)),
inference(rw,[status(thm)],[g0_0]) ).
cnf(g0_2,plain,
h(j(sk0)) != h(j(sk0)),
inference(rw,[status(thm)],[g0_1,t1235]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG070+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n007.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
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Fri Sep 25 04:39:24 UTC 2026
% 0.02/0.38 % CPUTime :
% 0.02/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 33.19/4.90 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 33.19/4.90 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------