%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : ALG072+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 : n006.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 37.58s 5.82s
% Output : Proof 37.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 8
% Syntax : Number of formulae : 181 ( 150 unt; 0 def)
% Number of atoms : 309 ( 207 equ)
% Maximal formula atoms : 14 ( 1 avg)
% Number of connectives : 193 ( 65 ~; 54 |; 50 &)
% ( 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 : 14 ( 14 usr; 7 con; 0-4 aty)
% Number of variables : 112 ( 2 sgn 48 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
? [U] :
( ! [V] :
( sorti1(V)
=> ! [W] :
( sorti1(W)
=> ( ( U != unit1
& op1(V,U) = W )
| op1(V,W) != U ) ) )
& sorti1(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax7) ).
fof(f6_nnf,plain,
? [U] :
( ! [V] :
( ! [W] :
( ( U != unit1
& op1(V,U) = W )
| op1(V,W) != U
| ~ sorti1(W) )
| ~ sorti1(V) )
& sorti1(U) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [V,W] :
( ( ( sk2 != unit1
& op1(V,sk2) = W )
| op1(V,W) != sk2
| ~ sorti1(W)
| ~ sorti1(V) )
& sorti1(sk2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2])],[f6_nnf]) ).
cnf(c14,plain,
( sk2 != unit1
| op1(X1,X2) != sk2
| ~ sorti1(X2)
| ~ sorti1(X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t253,plain,
ifeq(sorti1(X1),true,ifeq(sorti1(X2),true,ifeq(op1(X1,X2),sk2,ifeq(sk2,unit1,false,true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t858,plain,
ifeq(sorti1(X1),true,ifeq(sorti1(X2),true,ifeq(op1(X1,X2),sk2,ifeq(sk2,unit1,false,true),true),true),true) = true,
inference(orient,[status(thm)],[t253]) ).
fof(f1,axiom,
( ? [V] :
( unit1 = V
& sorti1(V) )
& ! [U] :
( sorti1(U)
=> ( op1(U,unit1) = U
& op1(unit1,U) = U ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
fof(f1_nnf,plain,
( ? [V] :
( unit1 = V
& sorti1(V) )
& ! [U] :
( ( op1(U,unit1) = U
& op1(unit1,U) = U )
| ~ sorti1(U) ) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [U] :
( unit1 = sk0
& sorti1(sk0)
& ( ( op1(U,unit1) = U
& op1(unit1,U) = U )
| ~ sorti1(U) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f1_nnf]) ).
cnf(c2,plain,
( op1(X0,unit1) = X0
| ~ sorti1(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi2,axiom,
ifeq(sorti1(X0),true,op1(X0,unit1),X0) = X0,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(c12,plain,
sorti1(sk2),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi12,axiom,
sorti1(sk2) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t14,plain,
op1(sk2,unit1) = sk2,
inference(hyper_resolution,[status(thm)],[hi2,hi12]) ).
cnf(t1063,plain,
op1(sk2,unit1) = sk2,
inference(orient,[status(thm)],[t14]) ).
cnf(t1064,plain,
true = ifeq(sorti1(sk2),true,ifeq(sorti1(unit1),true,ifeq(sk2,sk2,ifeq(sk2,unit1,false,true),true),true),true),
inference(cp,[status(thm)],[t858,t1063]) ).
fof(f8,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(f8_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)],[f8]) ).
fof(f8_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)],[f8_neg]) ).
fof(f8_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)],[f8_nnf]) ).
cnf(c19,plain,
( sorti2(h(X0))
| ~ sorti1(X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi18,negated_conjecture,
ifeq(sorti1(X0),true,sorti2(h(X0)),true) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(h42,plain,
sorti2(h(sk2)) = true,
inference(hyper_resolution,[status(thm)],[hi18,hi12]) ).
cnf(c20,plain,
( sorti1(j(X1))
| ~ sorti2(X1) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi19,negated_conjecture,
ifeq(sorti2(X0),true,sorti1(j(X0)),true) = true,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(h594,plain,
sorti1(j(h(sk2))) = true,
inference(hyper_resolution,[status(thm)],[hi19,h42]) ).
cnf(h5101,plain,
sorti2(h(j(h(sk2)))) = true,
inference(hyper_resolution,[status(thm)],[hi18,h594]) ).
cnf(t128,plain,
sorti1(j(h(j(h(sk2))))) = true,
inference(hyper_resolution,[status(thm)],[hi19,h5101]) ).
cnf(c23,plain,
( h(j(X6)) = X6
| ~ sorti2(X6) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi22,negated_conjecture,
ifeq(sorti2(X0),true,h(j(X0)),X0) = X0,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(t66,plain,
h(j(h(sk2))) = h(sk2),
inference(hyper_resolution,[status(thm)],[hi22,h42]) ).
cnf(t293,plain,
h(j(h(sk2))) = h(sk2),
inference(orient,[status(thm)],[t66]) ).
cnf(t7526,plain,
sorti1(j(h(sk2))) = true,
inference(step,[status(thm)],[t128,t293]) ).
cnf(c24,plain,
( j(h(X7)) = X7
| ~ sorti1(X7) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi23,negated_conjecture,
ifeq(sorti1(X0),true,j(h(X0)),X0) = X0,
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(t10,plain,
j(h(sk2)) = sk2,
inference(hyper_resolution,[status(thm)],[hi23,hi12]) ).
cnf(t444,plain,
j(h(sk2)) = sk2,
inference(orient,[status(thm)],[t10]) ).
cnf(t7527,plain,
sorti1(sk2) = true,
inference(step,[status(thm)],[t7526,t444]) ).
cnf(t574,plain,
sorti1(sk2) = true,
inference(orient,[status(thm)],[t7527]) ).
cnf(t7608,plain,
true = ifeq(true,true,ifeq(sorti1(unit1),true,ifeq(sk2,sk2,ifeq(sk2,unit1,false,true),true),true),true),
inference(step,[status(thm)],[t1064,t574]) ).
cnf(t72,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t72]) ).
cnf(t7609,plain,
true = ifeq(sorti1(unit1),true,ifeq(sk2,sk2,ifeq(sk2,unit1,false,true),true),true),
inference(step,[status(thm)],[t7608,t256]) ).
fof(f0,axiom,
sorti1(unit1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
fof(f0_nnf,plain,
sorti1(unit1),
inference(nnf_transformation,[status(thm)],[f0]) ).
cnf(c0,plain,
sorti1(unit1),
inference(cnf_transformation,[status(esa)],[f0_nnf]) ).
cnf(hi0,axiom,
sorti1(unit1) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h2,plain,
sorti2(h(unit1)) = true,
inference(hyper_resolution,[status(thm)],[hi18,hi0]) ).
cnf(t32,plain,
sorti1(j(h(unit1))) = true,
inference(hyper_resolution,[status(thm)],[hi19,h2]) ).
cnf(t11,plain,
j(h(unit1)) = unit1,
inference(hyper_resolution,[status(thm)],[hi23,hi0]) ).
cnf(t455,plain,
j(h(unit1)) = unit1,
inference(orient,[status(thm)],[t11]) ).
cnf(t7530,plain,
sorti1(unit1) = true,
inference(step,[status(thm)],[t32,t455]) ).
cnf(t582,plain,
sorti1(unit1) = true,
inference(orient,[status(thm)],[t7530]) ).
cnf(t7610,plain,
true = ifeq(true,true,ifeq(sk2,sk2,ifeq(sk2,unit1,false,true),true),true),
inference(step,[status(thm)],[t7609,t582]) ).
cnf(t7611,plain,
true = ifeq(sk2,sk2,ifeq(sk2,unit1,false,true),true),
inference(step,[status(thm)],[t7610,t256]) ).
cnf(t7612,plain,
true = ifeq(sk2,unit1,false,true),
inference(step,[status(thm)],[t7611,t256]) ).
cnf(t1376,plain,
ifeq(sk2,unit1,false,true) = true,
inference(orient,[status(thm)],[t7612]) ).
cnf(t203,plain,
ifeq(sorti1(X1),true,j(h(X1)),X1) = X1,
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(t262,plain,
ifeq(sorti1(X1),true,j(h(X1)),X1) = X1,
inference(orient,[status(thm)],[t203]) ).
fof(f7,axiom,
~ ? [U] :
( ! [V] :
( sorti2(V)
=> ! [W] :
( sorti2(W)
=> ( ( U != unit2
& op2(V,U) = W )
| op2(V,W) != U ) ) )
& sorti2(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax8) ).
fof(f7_nnf,plain,
! [U] :
( ? [V] :
( ? [W] :
( ( U = unit2
| op2(V,U) != W )
& op2(V,W) = U
& sorti2(W) )
& sorti2(V) )
| ~ sorti2(U) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [U] :
( ( ( U = unit2
| op2(sk3(U),U) != sk4(U) )
& op2(sk3(U),sk4(U)) = U
& sorti2(sk4(U))
& sorti2(sk3(U)) )
| ~ sorti2(U) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3,sk4])],[f7_nnf]) ).
cnf(c18,plain,
( X0 = unit2
| op2(sk3(X0),X0) != sk4(X0)
| ~ sorti2(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(t250,plain,
ifeq(sorti2(X1),true,ifeq(op2(sk3(X1),X1),sk4(X1),X1,unit2),unit2) = unit2,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t1077,plain,
ifeq(sorti2(X1),true,ifeq(op2(sk3(X1),X1),sk4(X1),X1,unit2),unit2) = unit2,
inference(orient,[status(thm)],[t250]) ).
cnf(c21,plain,
( h(op1(X2,X3)) = op2(h(X2),h(X3))
| ~ sorti1(X3)
| ~ sorti1(X2) ),
inference(cnf_transformation,[status(esa)],[f8_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)],[c21]) ).
cnf(t1125,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(c13,plain,
( op1(X1,sk2) = X2
| op1(X1,X2) != sk2
| ~ sorti1(X2)
| ~ sorti1(X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t252,plain,
ifeq(sorti1(X1),true,ifeq(sorti1(X2),true,ifeq(op1(X1,X2),sk2,op1(X1,sk2),X2),X2),X2) = X2,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t261,plain,
ifeq(sorti1(X1),true,ifeq(sorti1(X2),true,ifeq(op1(X1,X2),sk2,op1(X1,sk2),X2),X2),X2) = X2,
inference(orient,[status(thm)],[t252]) ).
cnf(c22,plain,
( j(op2(X4,X5)) = op1(j(X4),j(X5))
| ~ sorti2(X5)
| ~ sorti2(X4) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t255,plain,
ifeq(sorti2(X1),true,ifeq(sorti2(X2),true,j(op2(X1,X2)),op1(j(X1),j(X2))),op1(j(X1),j(X2))) = op1(j(X1),j(X2)),
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(t923,plain,
ifeq(sorti2(X1),true,ifeq(sorti2(X2),true,j(op2(X1,X2)),op1(j(X1),j(X2))),op1(j(X1),j(X2))) = op1(j(X1),j(X2)),
inference(orient,[status(thm)],[t255]) ).
cnf(c17,plain,
( op2(sk3(X0),sk4(X0)) = X0
| ~ sorti2(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi16,axiom,
ifeq(sorti2(X0),true,op2(sk3(X0),sk4(X0)),X0) = X0,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t221,plain,
op2(sk3(h(sk2)),sk4(h(sk2))) = h(sk2),
inference(hyper_resolution,[status(thm)],[hi16,h42]) ).
cnf(t376,plain,
op2(sk3(h(sk2)),sk4(h(sk2))) = h(sk2),
inference(orient,[status(thm)],[t221]) ).
cnf(t963,plain,
op1(j(sk3(h(sk2))),j(sk4(h(sk2)))) = ifeq(sorti2(sk3(h(sk2))),true,ifeq(sorti2(sk4(h(sk2))),true,j(h(sk2)),op1(j(sk3(h(sk2))),j(sk4(h(sk2))))),op1(j(sk3(h(sk2))),j(sk4(h(sk2))))),
inference(cp,[status(thm)],[t923,t376]) ).
cnf(c15,plain,
( sorti2(sk3(X0))
| ~ sorti2(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi14,axiom,
ifeq(sorti2(X0),true,sorti2(sk3(X0)),true) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t52,plain,
sorti2(sk3(h(sk2))) = true,
inference(hyper_resolution,[status(thm)],[hi14,h42]) ).
cnf(t552,plain,
sorti2(sk3(h(sk2))) = true,
inference(orient,[status(thm)],[t52]) ).
cnf(t8194,plain,
op1(j(sk3(h(sk2))),j(sk4(h(sk2)))) = ifeq(true,true,ifeq(sorti2(sk4(h(sk2))),true,j(h(sk2)),op1(j(sk3(h(sk2))),j(sk4(h(sk2))))),op1(j(sk3(h(sk2))),j(sk4(h(sk2))))),
inference(step,[status(thm)],[t963,t552]) ).
cnf(t8195,plain,
op1(j(sk3(h(sk2))),j(sk4(h(sk2)))) = ifeq(sorti2(sk4(h(sk2))),true,j(h(sk2)),op1(j(sk3(h(sk2))),j(sk4(h(sk2))))),
inference(step,[status(thm)],[t8194,t256]) ).
cnf(c16,plain,
( sorti2(sk4(X0))
| ~ sorti2(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi15,axiom,
ifeq(sorti2(X0),true,sorti2(sk4(X0)),true) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t59,plain,
sorti2(sk4(h(sk2))) = true,
inference(hyper_resolution,[status(thm)],[hi15,h42]) ).
cnf(t532,plain,
sorti2(sk4(h(sk2))) = true,
inference(orient,[status(thm)],[t59]) ).
cnf(t8196,plain,
op1(j(sk3(h(sk2))),j(sk4(h(sk2)))) = ifeq(true,true,j(h(sk2)),op1(j(sk3(h(sk2))),j(sk4(h(sk2))))),
inference(step,[status(thm)],[t8195,t532]) ).
cnf(t8197,plain,
op1(j(sk3(h(sk2))),j(sk4(h(sk2)))) = j(h(sk2)),
inference(step,[status(thm)],[t8196,t256]) ).
cnf(t8198,plain,
op1(j(sk3(h(sk2))),j(sk4(h(sk2)))) = sk2,
inference(step,[status(thm)],[t8197,t444]) ).
cnf(t7428,plain,
op1(j(sk3(h(sk2))),j(sk4(h(sk2)))) = sk2,
inference(orient,[status(thm)],[t8198]) ).
cnf(t7429,plain,
j(sk4(h(sk2))) = ifeq(sorti1(j(sk3(h(sk2)))),true,ifeq(sorti1(j(sk4(h(sk2)))),true,ifeq(sk2,sk2,op1(j(sk3(h(sk2))),sk2),j(sk4(h(sk2)))),j(sk4(h(sk2)))),j(sk4(h(sk2)))),
inference(cp,[status(thm)],[t261,t7428]) ).
cnf(h597,plain,
sorti2(sk3(h(sk2))) = true,
inference(hyper_resolution,[status(thm)],[hi14,h42]) ).
cnf(t99,plain,
sorti1(j(sk3(h(sk2)))) = true,
inference(hyper_resolution,[status(thm)],[hi19,h597]) ).
cnf(t620,plain,
sorti1(j(sk3(h(sk2)))) = true,
inference(orient,[status(thm)],[t99]) ).
cnf(t8199,plain,
j(sk4(h(sk2))) = ifeq(true,true,ifeq(sorti1(j(sk4(h(sk2)))),true,ifeq(sk2,sk2,op1(j(sk3(h(sk2))),sk2),j(sk4(h(sk2)))),j(sk4(h(sk2)))),j(sk4(h(sk2)))),
inference(step,[status(thm)],[t7429,t620]) ).
cnf(t8200,plain,
j(sk4(h(sk2))) = ifeq(sorti1(j(sk4(h(sk2)))),true,ifeq(sk2,sk2,op1(j(sk3(h(sk2))),sk2),j(sk4(h(sk2)))),j(sk4(h(sk2)))),
inference(step,[status(thm)],[t8199,t256]) ).
cnf(h596,plain,
sorti2(sk4(h(sk2))) = true,
inference(hyper_resolution,[status(thm)],[hi15,h42]) ).
cnf(t104,plain,
sorti1(j(sk4(h(sk2)))) = true,
inference(hyper_resolution,[status(thm)],[hi19,h596]) ).
cnf(t592,plain,
sorti1(j(sk4(h(sk2)))) = true,
inference(orient,[status(thm)],[t104]) ).
cnf(t8201,plain,
j(sk4(h(sk2))) = ifeq(true,true,ifeq(sk2,sk2,op1(j(sk3(h(sk2))),sk2),j(sk4(h(sk2)))),j(sk4(h(sk2)))),
inference(step,[status(thm)],[t8200,t592]) ).
cnf(t8202,plain,
j(sk4(h(sk2))) = ifeq(sk2,sk2,op1(j(sk3(h(sk2))),sk2),j(sk4(h(sk2)))),
inference(step,[status(thm)],[t8201,t256]) ).
cnf(t8203,plain,
j(sk4(h(sk2))) = op1(j(sk3(h(sk2))),sk2),
inference(step,[status(thm)],[t8202,t256]) ).
cnf(t7430,plain,
op1(j(sk3(h(sk2))),sk2) = j(sk4(h(sk2))),
inference(orient,[status(thm)],[t8203]) ).
cnf(t7433,plain,
op2(h(j(sk3(h(sk2)))),h(sk2)) = ifeq(sorti1(j(sk3(h(sk2)))),true,ifeq(sorti1(sk2),true,h(j(sk4(h(sk2)))),op2(h(j(sk3(h(sk2)))),h(sk2))),op2(h(j(sk3(h(sk2)))),h(sk2))),
inference(cp,[status(thm)],[t1125,t7430]) ).
cnf(t135,plain,
h(j(sk3(h(sk2)))) = sk3(h(sk2)),
inference(hyper_resolution,[status(thm)],[hi22,h597]) ).
cnf(t347,plain,
h(j(sk3(h(sk2)))) = sk3(h(sk2)),
inference(orient,[status(thm)],[t135]) ).
cnf(t8204,plain,
op2(sk3(h(sk2)),h(sk2)) = ifeq(sorti1(j(sk3(h(sk2)))),true,ifeq(sorti1(sk2),true,h(j(sk4(h(sk2)))),op2(h(j(sk3(h(sk2)))),h(sk2))),op2(h(j(sk3(h(sk2)))),h(sk2))),
inference(step,[status(thm)],[t7433,t347]) ).
cnf(t8205,plain,
op2(sk3(h(sk2)),h(sk2)) = ifeq(true,true,ifeq(sorti1(sk2),true,h(j(sk4(h(sk2)))),op2(h(j(sk3(h(sk2)))),h(sk2))),op2(h(j(sk3(h(sk2)))),h(sk2))),
inference(step,[status(thm)],[t8204,t620]) ).
cnf(t8206,plain,
op2(sk3(h(sk2)),h(sk2)) = ifeq(sorti1(sk2),true,h(j(sk4(h(sk2)))),op2(h(j(sk3(h(sk2)))),h(sk2))),
inference(step,[status(thm)],[t8205,t256]) ).
cnf(t8207,plain,
op2(sk3(h(sk2)),h(sk2)) = ifeq(true,true,h(j(sk4(h(sk2)))),op2(h(j(sk3(h(sk2)))),h(sk2))),
inference(step,[status(thm)],[t8206,t574]) ).
cnf(t8208,plain,
op2(sk3(h(sk2)),h(sk2)) = h(j(sk4(h(sk2)))),
inference(step,[status(thm)],[t8207,t256]) ).
cnf(t141,plain,
h(j(sk4(h(sk2)))) = sk4(h(sk2)),
inference(hyper_resolution,[status(thm)],[hi22,h596]) ).
cnf(t320,plain,
h(j(sk4(h(sk2)))) = sk4(h(sk2)),
inference(orient,[status(thm)],[t141]) ).
cnf(t8209,plain,
op2(sk3(h(sk2)),h(sk2)) = sk4(h(sk2)),
inference(step,[status(thm)],[t8208,t320]) ).
cnf(t7434,plain,
op2(sk3(h(sk2)),h(sk2)) = sk4(h(sk2)),
inference(orient,[status(thm)],[t8209]) ).
cnf(t7435,plain,
unit2 = ifeq(sorti2(h(sk2)),true,ifeq(sk4(h(sk2)),sk4(h(sk2)),h(sk2),unit2),unit2),
inference(cp,[status(thm)],[t1077,t7434]) ).
cnf(t115,plain,
sorti2(h(j(h(sk2)))) = true,
inference(hyper_resolution,[status(thm)],[hi18,h594]) ).
cnf(t7512,plain,
sorti2(h(sk2)) = true,
inference(step,[status(thm)],[t115,t293]) ).
cnf(t508,plain,
sorti2(h(sk2)) = true,
inference(orient,[status(thm)],[t7512]) ).
cnf(t8210,plain,
unit2 = ifeq(true,true,ifeq(sk4(h(sk2)),sk4(h(sk2)),h(sk2),unit2),unit2),
inference(step,[status(thm)],[t7435,t508]) ).
cnf(t8211,plain,
unit2 = ifeq(sk4(h(sk2)),sk4(h(sk2)),h(sk2),unit2),
inference(step,[status(thm)],[t8210,t256]) ).
cnf(t8212,plain,
unit2 = h(sk2),
inference(step,[status(thm)],[t8211,t256]) ).
cnf(t7436,plain,
h(sk2) = unit2,
inference(orient,[status(thm)],[t8212]) ).
cnf(t7437,plain,
sk2 = ifeq(sorti1(sk2),true,j(unit2),sk2),
inference(cp,[status(thm)],[t262,t7436]) ).
cnf(t8224,plain,
sk2 = ifeq(true,true,j(unit2),sk2),
inference(step,[status(thm)],[t7437,t574]) ).
cnf(t8225,plain,
sk2 = j(unit2),
inference(step,[status(thm)],[t8224,t256]) ).
fof(f3,axiom,
( ? [V] :
( unit2 = V
& sorti2(V) )
& ! [U] :
( sorti2(U)
=> ( op2(U,unit2) = U
& op2(unit2,U) = U ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
fof(f3_nnf,plain,
( ? [V] :
( unit2 = V
& sorti2(V) )
& ! [U] :
( ( op2(U,unit2) = U
& op2(unit2,U) = U )
| ~ sorti2(U) ) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [U] :
( unit2 = sk1
& sorti2(sk1)
& ( ( op2(U,unit2) = U
& op2(unit2,U) = U )
| ~ sorti2(U) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f3_nnf]) ).
cnf(c7,plain,
( op2(X0,unit2) = X0
| ~ sorti2(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi7,axiom,
ifeq(sorti2(X0),true,op2(X0,unit2),X0) = X0,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t81,plain,
op2(h(unit1),unit2) = h(unit1),
inference(hyper_resolution,[status(thm)],[hi7,h2]) ).
cnf(t378,plain,
op2(h(unit1),unit2) = h(unit1),
inference(orient,[status(thm)],[t81]) ).
cnf(t961,plain,
op1(j(h(unit1)),j(unit2)) = ifeq(sorti2(h(unit1)),true,ifeq(sorti2(unit2),true,j(h(unit1)),op1(j(h(unit1)),j(unit2))),op1(j(h(unit1)),j(unit2))),
inference(cp,[status(thm)],[t923,t378]) ).
cnf(t7579,plain,
op1(unit1,j(unit2)) = ifeq(sorti2(h(unit1)),true,ifeq(sorti2(unit2),true,j(h(unit1)),op1(j(h(unit1)),j(unit2))),op1(j(h(unit1)),j(unit2))),
inference(step,[status(thm)],[t961,t455]) ).
fof(f2,axiom,
sorti2(unit2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
fof(f2_nnf,plain,
sorti2(unit2),
inference(nnf_transformation,[status(thm)],[f2]) ).
cnf(c5,plain,
sorti2(unit2),
inference(cnf_transformation,[status(esa)],[f2_nnf]) ).
cnf(hi5,axiom,
sorti2(unit2) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(h17,plain,
sorti1(j(unit2)) = true,
inference(hyper_resolution,[status(thm)],[hi19,hi5]) ).
cnf(c1,plain,
( op1(unit1,X0) = X0
| ~ sorti1(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
ifeq(sorti1(X0),true,op1(unit1,X0),X0) = X0,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t78,plain,
op1(unit1,j(unit2)) = j(unit2),
inference(hyper_resolution,[status(thm)],[hi1,h17]) ).
cnf(t463,plain,
op1(unit1,j(unit2)) = j(unit2),
inference(orient,[status(thm)],[t78]) ).
cnf(t7580,plain,
j(unit2) = ifeq(sorti2(h(unit1)),true,ifeq(sorti2(unit2),true,j(h(unit1)),op1(j(h(unit1)),j(unit2))),op1(j(h(unit1)),j(unit2))),
inference(step,[status(thm)],[t7579,t463]) ).
cnf(h56,plain,
sorti1(j(h(unit1))) = true,
inference(hyper_resolution,[status(thm)],[hi19,h2]) ).
cnf(t116,plain,
sorti2(h(j(h(unit1)))) = true,
inference(hyper_resolution,[status(thm)],[hi18,h56]) ).
cnf(t67,plain,
h(j(h(unit1))) = h(unit1),
inference(hyper_resolution,[status(thm)],[hi22,h2]) ).
cnf(t298,plain,
h(j(h(unit1))) = h(unit1),
inference(orient,[status(thm)],[t67]) ).
cnf(t7513,plain,
sorti2(h(unit1)) = true,
inference(step,[status(thm)],[t116,t298]) ).
cnf(t509,plain,
sorti2(h(unit1)) = true,
inference(orient,[status(thm)],[t7513]) ).
cnf(t7581,plain,
j(unit2) = ifeq(true,true,ifeq(sorti2(unit2),true,j(h(unit1)),op1(j(h(unit1)),j(unit2))),op1(j(h(unit1)),j(unit2))),
inference(step,[status(thm)],[t7580,t509]) ).
cnf(t7582,plain,
j(unit2) = ifeq(sorti2(unit2),true,j(h(unit1)),op1(j(h(unit1)),j(unit2))),
inference(step,[status(thm)],[t7581,t256]) ).
cnf(c8,plain,
sorti2(sk1),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi8,axiom,
sorti2(sk1) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(h27,plain,
sorti1(j(sk1)) = true,
inference(hyper_resolution,[status(thm)],[hi19,hi8]) ).
cnf(t46,plain,
sorti2(h(j(sk1))) = true,
inference(hyper_resolution,[status(thm)],[hi18,h27]) ).
cnf(t7,plain,
h(j(sk1)) = sk1,
inference(hyper_resolution,[status(thm)],[hi22,hi8]) ).
cnf(t301,plain,
h(j(sk1)) = sk1,
inference(orient,[status(thm)],[t7]) ).
cnf(t7514,plain,
sorti2(sk1) = true,
inference(step,[status(thm)],[t46,t301]) ).
cnf(c9,plain,
unit2 = sk1,
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t1,plain,
unit2 = sk1,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t496,plain,
sk1 = unit2,
inference(orient,[status(thm)],[t1]) ).
cnf(t7515,plain,
sorti2(unit2) = true,
inference(step,[status(thm)],[t7514,t496]) ).
cnf(t511,plain,
sorti2(unit2) = true,
inference(orient,[status(thm)],[t7515]) ).
cnf(t7583,plain,
j(unit2) = ifeq(true,true,j(h(unit1)),op1(j(h(unit1)),j(unit2))),
inference(step,[status(thm)],[t7582,t511]) ).
cnf(t7584,plain,
j(unit2) = j(h(unit1)),
inference(step,[status(thm)],[t7583,t256]) ).
cnf(t7585,plain,
j(unit2) = unit1,
inference(step,[status(thm)],[t7584,t455]) ).
cnf(t1205,plain,
j(unit2) = unit1,
inference(orient,[status(thm)],[t7585]) ).
cnf(t8226,plain,
sk2 = unit1,
inference(step,[status(thm)],[t8225,t1205]) ).
cnf(t7446,plain,
sk2 = unit1,
inference(orient,[status(thm)],[t8226]) ).
cnf(t8227,plain,
ifeq(unit1,unit1,false,true) = true,
inference(step,[status(thm)],[t1376,t7446]) ).
cnf(t8228,plain,
false = true,
inference(step,[status(thm)],[t8227,t256]) ).
cnf(t7447,plain,
false = true,
inference(rw,[status(thm)],[t8228]) ).
cnf(t7454,plain,
false = true,
inference(orient,[status(thm)],[t7447]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t7454]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG072+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.34 % Computer : n006.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Fri Sep 25 04:41:41 UTC 2026
% 0.09/0.34 % CPUTime :
% 0.09/0.34 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 37.58/5.82 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 37.58/5.82 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------