%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : ALG071+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 : n016.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 215.18s 27.94s
% Output : Proof 215.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 6
% Syntax : Number of formulae : 125 ( 97 unt; 0 def)
% Number of atoms : 224 ( 131 equ)
% Maximal formula atoms : 14 ( 1 avg)
% Number of connectives : 157 ( 58 ~; 47 |; 28 &)
% ( 0 <=>; 24 =>; 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 : 109 ( 2 sgn 50 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [U] :
( sorti1(U)
=> ? [V] :
( op1(U,op1(V,U)) = V
& op1(V,op1(V,U)) != U
& sorti1(V) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
fof(f2_nnf,plain,
! [U] :
( ? [V] :
( op1(U,op1(V,U)) = V
& op1(V,op1(V,U)) != U
& sorti1(V) )
| ~ sorti1(U) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [U] :
( ( op1(U,op1(sk0(U),U)) = sk0(U)
& op1(sk0(U),op1(sk0(U),U)) != U
& sorti1(sk0(U)) )
| ~ sorti1(U) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f2_nnf]) ).
cnf(c3,plain,
( op1(sk0(X0),op1(sk0(X0),X0)) != X0
| ~ sorti1(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t199,plain,
ifeq(sorti1(X1),true,ifeq(op1(sk0(X1),op1(sk0(X1),X1)),X1,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t589,plain,
ifeq(sorti1(X1),true,ifeq(op1(sk0(X1),op1(sk0(X1),X1)),X1,false,true),true) = true,
inference(orient,[status(thm)],[t199]) ).
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(c12,plain,
( j(h(X7)) = X7
| ~ sorti1(X7) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t48,plain,
ifeq(sorti1(X1),true,j(h(X1)),X1) = X1,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t257,plain,
ifeq(sorti1(X1),true,j(h(X1)),X1) = X1,
inference(orient,[status(thm)],[t48]) ).
cnf(c9,plain,
( h(op1(X2,X3)) = op2(h(X2),h(X3))
| ~ sorti1(X3)
| ~ sorti1(X2) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t216,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)],[c9]) ).
cnf(t404,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)],[t216]) ).
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]) ).
fof(f3,axiom,
~ ! [U] :
( sorti2(U)
=> ? [V] :
( op2(U,op2(V,U)) = V
& op2(V,op2(V,U)) != U
& sorti2(V) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
fof(f3_nnf,plain,
? [U] :
( ! [V] :
( op2(U,op2(V,U)) != V
| op2(V,op2(V,U)) = U
| ~ sorti2(V) )
& sorti2(U) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [V] :
( ( op2(sk1,op2(V,sk1)) != V
| op2(V,op2(V,sk1)) = sk1
| ~ sorti2(V) )
& sorti2(sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f3_nnf]) ).
cnf(c5,plain,
sorti2(sk1),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi4,axiom,
sorti2(sk1) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(h2,plain,
sorti1(j(sk1)) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi4]) ).
cnf(c2,plain,
( sorti1(sk0(X0))
| ~ sorti1(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
ifeq(sorti1(X0),true,sorti1(sk0(X0)),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h8,plain,
sorti1(sk0(j(sk1))) = true,
inference(hyper_resolution,[status(thm)],[hi2,h2]) ).
cnf(c7,plain,
( sorti2(h(X0))
| ~ sorti1(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi6,negated_conjecture,
ifeq(sorti1(X0),true,sorti2(h(X0)),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(h34,plain,
sorti2(h(sk0(j(sk1)))) = true,
inference(hyper_resolution,[status(thm)],[hi6,h8]) ).
fof(f1,axiom,
! [U] :
( sorti2(U)
=> ! [V] :
( sorti2(V)
=> sorti2(op2(U,V)) ) ),
file('/export/starexec/sandbox/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(h181,plain,
sorti2(op2(h(sk0(j(sk1))),sk1)) = true,
inference(hyper_resolution,[status(thm)],[hi1,h34,hi4]) ).
cnf(c11,plain,
( h(j(X6)) = X6
| ~ sorti2(X6) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi10,negated_conjecture,
ifeq(sorti2(X0),true,h(j(X0)),X0) = X0,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t138,plain,
h(j(op2(h(sk0(j(sk1))),sk1))) = op2(h(sk0(j(sk1))),sk1),
inference(hyper_resolution,[status(thm)],[hi10,h181]) ).
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(t157,plain,
op1(j(h(sk0(j(sk1)))),j(sk1)) = j(op2(h(sk0(j(sk1))),sk1)),
inference(hyper_resolution,[status(thm)],[hi9,h34,hi4]) ).
cnf(hi11,negated_conjecture,
ifeq(sorti1(X0),true,j(h(X0)),X0) = X0,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t26,plain,
j(h(sk0(j(sk1)))) = sk0(j(sk1)),
inference(hyper_resolution,[status(thm)],[hi11,h8]) ).
cnf(t301,plain,
j(h(sk0(j(sk1)))) = sk0(j(sk1)),
inference(orient,[status(thm)],[t26]) ).
cnf(t30919,plain,
op1(sk0(j(sk1)),j(sk1)) = j(op2(h(sk0(j(sk1))),sk1)),
inference(step,[status(thm)],[t157,t301]) ).
cnf(t353,plain,
j(op2(h(sk0(j(sk1))),sk1)) = op1(sk0(j(sk1)),j(sk1)),
inference(orient,[status(thm)],[t30919]) ).
cnf(t30925,plain,
h(op1(sk0(j(sk1)),j(sk1))) = op2(h(sk0(j(sk1))),sk1),
inference(step,[status(thm)],[t138,t353]) ).
cnf(t371,plain,
h(op1(sk0(j(sk1)),j(sk1))) = op2(h(sk0(j(sk1))),sk1),
inference(orient,[status(thm)],[t30925]) ).
cnf(t433,plain,
op2(h(X1),h(op1(sk0(j(sk1)),j(sk1)))) = ifeq(sorti1(X1),true,ifeq(sorti1(op1(sk0(j(sk1)),j(sk1))),true,h(op1(X1,op1(sk0(j(sk1)),j(sk1)))),op2(h(X1),op2(h(sk0(j(sk1))),sk1))),op2(h(X1),h(op1(sk0(j(sk1)),j(sk1))))),
inference(cp,[status(thm)],[t404,t371]) ).
cnf(t32331,plain,
op2(h(X1),op2(h(sk0(j(sk1))),sk1)) = ifeq(sorti1(X1),true,ifeq(sorti1(op1(sk0(j(sk1)),j(sk1))),true,h(op1(X1,op1(sk0(j(sk1)),j(sk1)))),op2(h(X1),op2(h(sk0(j(sk1))),sk1))),op2(h(X1),h(op1(sk0(j(sk1)),j(sk1))))),
inference(step,[status(thm)],[t433,t371]) ).
cnf(t59,plain,
sorti1(j(op2(h(sk0(j(sk1))),sk1))) = true,
inference(hyper_resolution,[status(thm)],[hi7,h181]) ).
cnf(t30966,plain,
sorti1(op1(sk0(j(sk1)),j(sk1))) = true,
inference(step,[status(thm)],[t59,t353]) ).
cnf(t514,plain,
sorti1(op1(sk0(j(sk1)),j(sk1))) = true,
inference(orient,[status(thm)],[t30966]) ).
cnf(t32332,plain,
op2(h(X1),op2(h(sk0(j(sk1))),sk1)) = ifeq(sorti1(X1),true,ifeq(true,true,h(op1(X1,op1(sk0(j(sk1)),j(sk1)))),op2(h(X1),op2(h(sk0(j(sk1))),sk1))),op2(h(X1),h(op1(sk0(j(sk1)),j(sk1))))),
inference(step,[status(thm)],[t32331,t514]) ).
cnf(t6,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t6]) ).
cnf(t32333,plain,
op2(h(X1),op2(h(sk0(j(sk1))),sk1)) = ifeq(sorti1(X1),true,h(op1(X1,op1(sk0(j(sk1)),j(sk1)))),op2(h(X1),h(op1(sk0(j(sk1)),j(sk1))))),
inference(step,[status(thm)],[t32332,t256]) ).
cnf(t32334,plain,
op2(h(X1),op2(h(sk0(j(sk1))),sk1)) = ifeq(sorti1(X1),true,h(op1(X1,op1(sk0(j(sk1)),j(sk1)))),op2(h(X1),op2(h(sk0(j(sk1))),sk1))),
inference(step,[status(thm)],[t32333,t371]) ).
cnf(t30281,plain,
ifeq(sorti1(X1),true,h(op1(X1,op1(sk0(j(sk1)),j(sk1)))),op2(h(X1),op2(h(sk0(j(sk1))),sk1))) = op2(h(X1),op2(h(sk0(j(sk1))),sk1)),
inference(orient,[status(thm)],[t32334]) ).
cnf(h168,plain,
sorti1(j(h(sk0(j(sk1))))) = true,
inference(hyper_resolution,[status(thm)],[hi7,h34]) ).
cnf(h790,plain,
sorti2(h(j(h(sk0(j(sk1)))))) = true,
inference(hyper_resolution,[status(thm)],[hi6,h168]) ).
cnf(t54,plain,
sorti1(j(h(j(h(sk0(j(sk1))))))) = true,
inference(hyper_resolution,[status(thm)],[hi7,h790]) ).
cnf(t122,plain,
j(h(j(h(sk0(j(sk1)))))) = j(h(sk0(j(sk1)))),
inference(hyper_resolution,[status(thm)],[hi11,h168]) ).
cnf(t268,plain,
j(h(j(h(sk0(j(sk1)))))) = j(h(sk0(j(sk1)))),
inference(orient,[status(thm)],[t122]) ).
cnf(t30960,plain,
sorti1(j(h(sk0(j(sk1))))) = true,
inference(step,[status(thm)],[t54,t268]) ).
cnf(t30961,plain,
sorti1(sk0(j(sk1))) = true,
inference(step,[status(thm)],[t30960,t301]) ).
cnf(t496,plain,
sorti1(sk0(j(sk1))) = true,
inference(orient,[status(thm)],[t30961]) ).
cnf(t30833,plain,
op2(h(sk0(j(sk1))),op2(h(sk0(j(sk1))),sk1)) = ifeq(true,true,h(op1(sk0(j(sk1)),op1(sk0(j(sk1)),j(sk1)))),op2(h(sk0(j(sk1))),op2(h(sk0(j(sk1))),sk1))),
inference(cp,[status(thm)],[t30281,t496]) ).
cnf(c6,plain,
( op2(sk1,op2(X1,sk1)) != X1
| op2(X1,op2(X1,sk1)) = sk1
| ~ sorti2(X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t207,plain,
ifeq(sorti2(X1),true,ifeq(op2(sk1,op2(X1,sk1)),X1,op2(X1,op2(X1,sk1)),sk1),sk1) = sk1,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t359,plain,
ifeq(sorti2(X1),true,ifeq(op2(sk1,op2(X1,sk1)),X1,op2(X1,op2(X1,sk1)),sk1),sk1) = sk1,
inference(orient,[status(thm)],[t207]) ).
cnf(c4,plain,
( op1(X0,op1(sk0(X0),X0)) = sk0(X0)
| ~ sorti1(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi3,axiom,
ifeq(sorti1(X0),true,op1(X0,op1(sk0(X0),X0)),sk0(X0)) = sk0(X0),
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t127,plain,
op1(j(sk1),op1(sk0(j(sk1)),j(sk1))) = sk0(j(sk1)),
inference(hyper_resolution,[status(thm)],[hi3,h2]) ).
cnf(t374,plain,
op1(j(sk1),op1(sk0(j(sk1)),j(sk1))) = sk0(j(sk1)),
inference(orient,[status(thm)],[t127]) ).
cnf(t422,plain,
op2(h(j(sk1)),h(op1(sk0(j(sk1)),j(sk1)))) = ifeq(sorti1(j(sk1)),true,ifeq(sorti1(op1(sk0(j(sk1)),j(sk1))),true,h(sk0(j(sk1))),op2(h(j(sk1)),h(op1(sk0(j(sk1)),j(sk1))))),op2(h(j(sk1)),h(op1(sk0(j(sk1)),j(sk1))))),
inference(cp,[status(thm)],[t404,t374]) ).
cnf(t1,plain,
h(j(sk1)) = sk1,
inference(hyper_resolution,[status(thm)],[hi10,hi4]) ).
cnf(t356,plain,
h(j(sk1)) = sk1,
inference(orient,[status(thm)],[t1]) ).
cnf(t31826,plain,
op2(sk1,h(op1(sk0(j(sk1)),j(sk1)))) = ifeq(sorti1(j(sk1)),true,ifeq(sorti1(op1(sk0(j(sk1)),j(sk1))),true,h(sk0(j(sk1))),op2(h(j(sk1)),h(op1(sk0(j(sk1)),j(sk1))))),op2(h(j(sk1)),h(op1(sk0(j(sk1)),j(sk1))))),
inference(step,[status(thm)],[t422,t356]) ).
cnf(t31827,plain,
op2(sk1,op2(h(sk0(j(sk1))),sk1)) = ifeq(sorti1(j(sk1)),true,ifeq(sorti1(op1(sk0(j(sk1)),j(sk1))),true,h(sk0(j(sk1))),op2(h(j(sk1)),h(op1(sk0(j(sk1)),j(sk1))))),op2(h(j(sk1)),h(op1(sk0(j(sk1)),j(sk1))))),
inference(step,[status(thm)],[t31826,t371]) ).
cnf(t2,plain,
sorti1(j(sk1)) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi4]) ).
cnf(t490,plain,
sorti1(j(sk1)) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(t31828,plain,
op2(sk1,op2(h(sk0(j(sk1))),sk1)) = ifeq(true,true,ifeq(sorti1(op1(sk0(j(sk1)),j(sk1))),true,h(sk0(j(sk1))),op2(h(j(sk1)),h(op1(sk0(j(sk1)),j(sk1))))),op2(h(j(sk1)),h(op1(sk0(j(sk1)),j(sk1))))),
inference(step,[status(thm)],[t31827,t490]) ).
cnf(t31829,plain,
op2(sk1,op2(h(sk0(j(sk1))),sk1)) = ifeq(sorti1(op1(sk0(j(sk1)),j(sk1))),true,h(sk0(j(sk1))),op2(h(j(sk1)),h(op1(sk0(j(sk1)),j(sk1))))),
inference(step,[status(thm)],[t31828,t256]) ).
cnf(t31830,plain,
op2(sk1,op2(h(sk0(j(sk1))),sk1)) = ifeq(true,true,h(sk0(j(sk1))),op2(h(j(sk1)),h(op1(sk0(j(sk1)),j(sk1))))),
inference(step,[status(thm)],[t31829,t514]) ).
cnf(t31831,plain,
op2(sk1,op2(h(sk0(j(sk1))),sk1)) = h(sk0(j(sk1))),
inference(step,[status(thm)],[t31830,t256]) ).
cnf(t13377,plain,
op2(sk1,op2(h(sk0(j(sk1))),sk1)) = h(sk0(j(sk1))),
inference(orient,[status(thm)],[t31831]) ).
cnf(t13378,plain,
sk1 = ifeq(sorti2(h(sk0(j(sk1)))),true,ifeq(h(sk0(j(sk1))),h(sk0(j(sk1))),op2(h(sk0(j(sk1))),op2(h(sk0(j(sk1))),sk1)),sk1),sk1),
inference(cp,[status(thm)],[t359,t13377]) ).
cnf(h4752,plain,
sorti1(j(h(j(h(sk0(j(sk1))))))) = true,
inference(hyper_resolution,[status(thm)],[hi7,h790]) ).
cnf(t109,plain,
sorti2(h(j(h(j(h(sk0(j(sk1)))))))) = true,
inference(hyper_resolution,[status(thm)],[hi6,h4752]) ).
cnf(t30967,plain,
sorti2(h(j(h(sk0(j(sk1)))))) = true,
inference(step,[status(thm)],[t109,t268]) ).
cnf(t30968,plain,
sorti2(h(sk0(j(sk1)))) = true,
inference(step,[status(thm)],[t30967,t301]) ).
cnf(t530,plain,
sorti2(h(sk0(j(sk1)))) = true,
inference(orient,[status(thm)],[t30968]) ).
cnf(t31832,plain,
sk1 = ifeq(true,true,ifeq(h(sk0(j(sk1))),h(sk0(j(sk1))),op2(h(sk0(j(sk1))),op2(h(sk0(j(sk1))),sk1)),sk1),sk1),
inference(step,[status(thm)],[t13378,t530]) ).
cnf(t31833,plain,
sk1 = ifeq(h(sk0(j(sk1))),h(sk0(j(sk1))),op2(h(sk0(j(sk1))),op2(h(sk0(j(sk1))),sk1)),sk1),
inference(step,[status(thm)],[t31832,t256]) ).
cnf(t31834,plain,
sk1 = op2(h(sk0(j(sk1))),op2(h(sk0(j(sk1))),sk1)),
inference(step,[status(thm)],[t31833,t256]) ).
cnf(t13379,plain,
op2(h(sk0(j(sk1))),op2(h(sk0(j(sk1))),sk1)) = sk1,
inference(orient,[status(thm)],[t31834]) ).
cnf(t32335,plain,
sk1 = ifeq(true,true,h(op1(sk0(j(sk1)),op1(sk0(j(sk1)),j(sk1)))),op2(h(sk0(j(sk1))),op2(h(sk0(j(sk1))),sk1))),
inference(step,[status(thm)],[t30833,t13379]) ).
cnf(t32336,plain,
sk1 = h(op1(sk0(j(sk1)),op1(sk0(j(sk1)),j(sk1)))),
inference(step,[status(thm)],[t32335,t256]) ).
cnf(t30886,plain,
h(op1(sk0(j(sk1)),op1(sk0(j(sk1)),j(sk1)))) = sk1,
inference(orient,[status(thm)],[t32336]) ).
cnf(t30887,plain,
op1(sk0(j(sk1)),op1(sk0(j(sk1)),j(sk1))) = ifeq(sorti1(op1(sk0(j(sk1)),op1(sk0(j(sk1)),j(sk1)))),true,j(sk1),op1(sk0(j(sk1)),op1(sk0(j(sk1)),j(sk1)))),
inference(cp,[status(thm)],[t257,t30886]) ).
fof(f0,axiom,
! [U] :
( sorti1(U)
=> ! [V] :
( sorti1(V)
=> sorti1(op1(U,V)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
fof(f0_nnf,plain,
! [U] :
( ! [V] :
( sorti1(op1(U,V))
| ~ sorti1(V) )
| ~ sorti1(U) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [U,V] :
( sorti1(op1(U,V))
| ~ sorti1(V)
| ~ sorti1(U) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( sorti1(op1(X0,X1))
| ~ sorti1(X1)
| ~ sorti1(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t155,plain,
ifeq(sorti1(X1),true,ifeq(sorti1(X2),true,sorti1(op1(X1,X2)),true),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t602,plain,
ifeq(sorti1(X1),true,ifeq(sorti1(X2),true,sorti1(op1(X1,X2)),true),true) = true,
inference(orient,[status(thm)],[t155]) ).
cnf(t610,plain,
true = ifeq(true,true,ifeq(sorti1(X1),true,sorti1(op1(sk0(j(sk1)),X1)),true),true),
inference(cp,[status(thm)],[t602,t496]) ).
cnf(t31108,plain,
true = ifeq(sorti1(X1),true,sorti1(op1(sk0(j(sk1)),X1)),true),
inference(step,[status(thm)],[t610,t256]) ).
cnf(t2112,plain,
ifeq(sorti1(X1),true,sorti1(op1(sk0(j(sk1)),X1)),true) = true,
inference(orient,[status(thm)],[t31108]) ).
cnf(t2163,plain,
true = ifeq(true,true,sorti1(op1(sk0(j(sk1)),op1(sk0(j(sk1)),j(sk1)))),true),
inference(cp,[status(thm)],[t2112,t514]) ).
cnf(t31338,plain,
true = sorti1(op1(sk0(j(sk1)),op1(sk0(j(sk1)),j(sk1)))),
inference(step,[status(thm)],[t2163,t256]) ).
cnf(t5193,plain,
sorti1(op1(sk0(j(sk1)),op1(sk0(j(sk1)),j(sk1)))) = true,
inference(orient,[status(thm)],[t31338]) ).
cnf(t32337,plain,
op1(sk0(j(sk1)),op1(sk0(j(sk1)),j(sk1))) = ifeq(true,true,j(sk1),op1(sk0(j(sk1)),op1(sk0(j(sk1)),j(sk1)))),
inference(step,[status(thm)],[t30887,t5193]) ).
cnf(t32338,plain,
op1(sk0(j(sk1)),op1(sk0(j(sk1)),j(sk1))) = j(sk1),
inference(step,[status(thm)],[t32337,t256]) ).
cnf(t30902,plain,
op1(sk0(j(sk1)),op1(sk0(j(sk1)),j(sk1))) = j(sk1),
inference(orient,[status(thm)],[t32338]) ).
cnf(t30904,plain,
true = ifeq(sorti1(j(sk1)),true,ifeq(j(sk1),j(sk1),false,true),true),
inference(cp,[status(thm)],[t589,t30902]) ).
cnf(t32339,plain,
true = ifeq(true,true,ifeq(j(sk1),j(sk1),false,true),true),
inference(step,[status(thm)],[t30904,t490]) ).
cnf(t32340,plain,
true = ifeq(j(sk1),j(sk1),false,true),
inference(step,[status(thm)],[t32339,t256]) ).
cnf(t32341,plain,
true = false,
inference(step,[status(thm)],[t32340,t256]) ).
cnf(t30905,plain,
false = true,
inference(orient,[status(thm)],[t32341]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t30905]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG071+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.36 % Computer : n016.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % 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 04:46:43 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 215.18/27.94 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 215.18/27.94 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------