%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : ALG073+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 : n010.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 12:51:32 PM UTC 2026
% Result : Theorem 42.56s 5.93s
% Output : Proof 42.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 6
% Syntax : Number of formulae : 122 ( 98 unt; 0 def)
% Number of atoms : 225 ( 136 equ)
% Maximal formula atoms : 14 ( 1 avg)
% Number of connectives : 161 ( 58 ~; 47 |; 34 &)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 2 avg)
% Maximal term depth : 7 ( 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 : 93 ( 2 sgn 48 !; 6 ?)
% 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/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(c13,plain,
( j(h(X7)) = X7
| ~ sorti1(X7) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t51,plain,
ifeq(sorti1(X1),true,j(h(X1)),X1) = X1,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t257,plain,
ifeq(sorti1(X1),true,j(h(X1)),X1) = X1,
inference(orient,[status(thm)],[t51]) ).
fof(f3,axiom,
~ ? [U] :
( ? [V] :
( op2(U,V) != U
& op2(V,V) = U
& op2(U,U) = V
& sorti2(V) )
& sorti2(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
fof(f3_nnf,plain,
! [U] :
( ! [V] :
( op2(U,V) = U
| op2(V,V) != U
| op2(U,U) != V
| ~ sorti2(V) )
| ~ sorti2(U) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [U,V] :
( op2(U,V) = U
| op2(V,V) != U
| op2(U,U) != V
| ~ sorti2(V)
| ~ sorti2(U) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c7,plain,
( op2(X0,X1) = X0
| op2(X1,X1) != X0
| op2(X0,X0) != X1
| ~ sorti2(X1)
| ~ sorti2(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t253,plain,
ifeq(sorti2(X1),true,ifeq(sorti2(X2),true,ifeq(op2(X1,X1),X2,ifeq(op2(X2,X2),X1,op2(X1,X2),X1),X1),X1),X1) = X1,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t259,plain,
ifeq(sorti2(X1),true,ifeq(sorti2(X2),true,ifeq(op2(X1,X1),X2,ifeq(op2(X2,X2),X1,op2(X1,X2),X1),X1),X1),X1) = X1,
inference(orient,[status(thm)],[t253]) ).
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(t260,plain,
X1 = ifeq(sorti2(X1),true,ifeq(sorti2(op2(X1,X1)),true,ifeq(op2(op2(X1,X1),op2(X1,X1)),X1,op2(X1,op2(X1,X1)),X1),X1),X1),
inference(cp,[status(thm)],[t259,t256]) ).
cnf(t711,plain,
ifeq(sorti2(X1),true,ifeq(sorti2(op2(X1,X1)),true,ifeq(op2(op2(X1,X1),op2(X1,X1)),X1,op2(X1,op2(X1,X1)),X1),X1),X1) = X1,
inference(orient,[status(thm)],[t260]) ).
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(hi0,axiom,
ifeq(sorti1(X0),true,ifeq(sorti1(X1),true,sorti1(op1(X0,X1)),true),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
fof(f2,axiom,
? [U] :
( ? [V] :
( op1(U,V) != U
& op1(V,V) = U
& op1(U,U) = V
& sorti1(V) )
& sorti1(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
fof(f2_nnf,plain,
? [U] :
( ? [V] :
( op1(U,V) != U
& op1(V,V) = U
& op1(U,U) = V
& sorti1(V) )
& sorti1(U) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
( op1(sk0,sk1) != sk0
& op1(sk1,sk1) = sk0
& op1(sk0,sk0) = sk1
& sorti1(sk1)
& sorti1(sk0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[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(h3,plain,
sorti1(op1(sk0,sk0)) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi2,hi2]) ).
cnf(c3,plain,
sorti1(sk1),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi3,axiom,
sorti1(sk1) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(h24,plain,
sorti1(op1(sk1,op1(sk0,sk0))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi3,h3]) ).
cnf(c8,plain,
( sorti2(h(X0))
| ~ sorti1(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi7,negated_conjecture,
ifeq(sorti1(X0),true,sorti2(h(X0)),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t48,plain,
sorti2(h(op1(sk1,op1(sk0,sk0)))) = true,
inference(hyper_resolution,[status(thm)],[hi7,h24]) ).
cnf(c4,plain,
op1(sk0,sk0) = sk1,
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t2,plain,
op1(sk0,sk0) = sk1,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t364,plain,
op1(sk0,sk0) = sk1,
inference(orient,[status(thm)],[t2]) ).
cnf(t800,plain,
sorti2(h(op1(sk1,sk1))) = true,
inference(step,[status(thm)],[t48,t364]) ).
cnf(c5,plain,
op1(sk1,sk1) = sk0,
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t3,plain,
op1(sk1,sk1) = sk0,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t369,plain,
op1(sk1,sk1) = sk0,
inference(orient,[status(thm)],[t3]) ).
cnf(t801,plain,
sorti2(h(sk0)) = true,
inference(step,[status(thm)],[t800,t369]) ).
cnf(t517,plain,
sorti2(h(sk0)) = true,
inference(orient,[status(thm)],[t801]) ).
cnf(t720,plain,
h(sk0) = ifeq(true,true,ifeq(sorti2(op2(h(sk0),h(sk0))),true,ifeq(op2(op2(h(sk0),h(sk0)),op2(h(sk0),h(sk0))),h(sk0),op2(h(sk0),op2(h(sk0),h(sk0))),h(sk0)),h(sk0)),h(sk0)),
inference(cp,[status(thm)],[t711,t517]) ).
cnf(t833,plain,
h(sk0) = ifeq(sorti2(op2(h(sk0),h(sk0))),true,ifeq(op2(op2(h(sk0),h(sk0)),op2(h(sk0),h(sk0))),h(sk0),op2(h(sk0),op2(h(sk0),h(sk0))),h(sk0)),h(sk0)),
inference(step,[status(thm)],[t720,t256]) ).
cnf(h9,plain,
sorti1(op1(sk1,sk1)) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi3,hi3]) ).
cnf(h44,plain,
sorti2(h(op1(sk1,sk1))) = true,
inference(hyper_resolution,[status(thm)],[hi7,h9]) ).
cnf(h2,plain,
sorti2(h(sk0)) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi2]) ).
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(t109,plain,
sorti2(op2(h(sk0),h(op1(sk1,sk1)))) = true,
inference(hyper_resolution,[status(thm)],[hi1,h2,h44]) ).
cnf(t805,plain,
sorti2(op2(h(sk0),h(sk0))) = true,
inference(step,[status(thm)],[t109,t369]) ).
cnf(t574,plain,
sorti2(op2(h(sk0),h(sk0))) = true,
inference(orient,[status(thm)],[t805]) ).
cnf(t834,plain,
h(sk0) = ifeq(true,true,ifeq(op2(op2(h(sk0),h(sk0)),op2(h(sk0),h(sk0))),h(sk0),op2(h(sk0),op2(h(sk0),h(sk0))),h(sk0)),h(sk0)),
inference(step,[status(thm)],[t833,t574]) ).
cnf(t835,plain,
h(sk0) = ifeq(op2(op2(h(sk0),h(sk0)),op2(h(sk0),h(sk0))),h(sk0),op2(h(sk0),op2(h(sk0),h(sk0))),h(sk0)),
inference(step,[status(thm)],[t834,t256]) ).
cnf(c10,plain,
( h(op1(X2,X3)) = op2(h(X2),h(X3))
| ~ sorti1(X3)
| ~ sorti1(X2) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi9,negated_conjecture,
ifeq(sorti1(X0),true,ifeq(sorti1(X1),true,h(op1(X0,X1)),op2(h(X0),h(X1))),op2(h(X0),h(X1))) = op2(h(X0),h(X1)),
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t166,plain,
op2(h(op1(sk1,sk1)),h(sk0)) = h(op1(op1(sk1,sk1),sk0)),
inference(hyper_resolution,[status(thm)],[hi9,h9,hi2]) ).
cnf(t319,plain,
op2(h(op1(sk1,sk1)),h(sk0)) = h(op1(op1(sk1,sk1),sk0)),
inference(orient,[status(thm)],[t166]) ).
cnf(t768,plain,
op2(h(sk0),h(sk0)) = h(op1(op1(sk1,sk1),sk0)),
inference(step,[status(thm)],[t319,t369]) ).
cnf(t769,plain,
op2(h(sk0),h(sk0)) = h(op1(sk0,sk0)),
inference(step,[status(thm)],[t768,t369]) ).
cnf(t770,plain,
op2(h(sk0),h(sk0)) = h(sk1),
inference(step,[status(thm)],[t769,t364]) ).
cnf(t370,plain,
op2(h(sk0),h(sk0)) = h(sk1),
inference(rw,[status(thm)],[t770]) ).
cnf(t694,plain,
op2(h(sk0),h(sk0)) = h(sk1),
inference(orient,[status(thm)],[t370]) ).
cnf(t836,plain,
h(sk0) = ifeq(op2(h(sk1),op2(h(sk0),h(sk0))),h(sk0),op2(h(sk0),op2(h(sk0),h(sk0))),h(sk0)),
inference(step,[status(thm)],[t835,t694]) ).
cnf(t837,plain,
h(sk0) = ifeq(op2(h(sk1),h(sk1)),h(sk0),op2(h(sk0),op2(h(sk0),h(sk0))),h(sk0)),
inference(step,[status(thm)],[t836,t694]) ).
cnf(c12,plain,
( h(j(X6)) = X6
| ~ sorti2(X6) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t53,plain,
ifeq(sorti2(X1),true,h(j(X1)),X1) = X1,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t258,plain,
ifeq(sorti2(X1),true,h(j(X1)),X1) = X1,
inference(orient,[status(thm)],[t53]) ).
cnf(h22,plain,
sorti2(h(op1(sk0,sk0))) = true,
inference(hyper_resolution,[status(thm)],[hi7,h3]) ).
cnf(h8,plain,
sorti2(h(sk1)) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi3]) ).
cnf(t111,plain,
sorti2(op2(h(sk1),h(op1(sk0,sk0)))) = true,
inference(hyper_resolution,[status(thm)],[hi1,h8,h22]) ).
cnf(t804,plain,
sorti2(op2(h(sk1),h(sk1))) = true,
inference(step,[status(thm)],[t111,t364]) ).
cnf(t562,plain,
sorti2(op2(h(sk1),h(sk1))) = true,
inference(orient,[status(thm)],[t804]) ).
cnf(t563,plain,
op2(h(sk1),h(sk1)) = ifeq(true,true,h(j(op2(h(sk1),h(sk1)))),op2(h(sk1),h(sk1))),
inference(cp,[status(thm)],[t258,t562]) ).
cnf(t806,plain,
op2(h(sk1),h(sk1)) = h(j(op2(h(sk1),h(sk1)))),
inference(step,[status(thm)],[t563,t256]) ).
cnf(c11,plain,
( j(op2(X4,X5)) = op1(j(X4),j(X5))
| ~ sorti2(X5)
| ~ sorti2(X4) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi10,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)],[c11]) ).
cnf(t244,plain,
op1(j(h(sk1)),j(h(op1(sk0,sk0)))) = j(op2(h(sk1),h(op1(sk0,sk0)))),
inference(hyper_resolution,[status(thm)],[hi10,h8,h22]) ).
cnf(h48,plain,
sorti1(op1(sk0,op1(sk1,sk1))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi2,h9]) ).
cnf(hi12,negated_conjecture,
ifeq(sorti1(X0),true,j(h(X0)),X0) = X0,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t152,plain,
j(h(op1(sk0,op1(sk1,sk1)))) = op1(sk0,op1(sk1,sk1)),
inference(hyper_resolution,[status(thm)],[hi12,h48]) ).
cnf(t786,plain,
j(h(op1(sk0,sk0))) = op1(sk0,op1(sk1,sk1)),
inference(step,[status(thm)],[t152,t369]) ).
cnf(t787,plain,
j(h(sk1)) = op1(sk0,op1(sk1,sk1)),
inference(step,[status(thm)],[t786,t364]) ).
cnf(t788,plain,
j(h(sk1)) = op1(sk0,sk0),
inference(step,[status(thm)],[t787,t369]) ).
cnf(t789,plain,
j(h(sk1)) = sk1,
inference(step,[status(thm)],[t788,t364]) ).
cnf(t389,plain,
j(h(sk1)) = sk1,
inference(orient,[status(thm)],[t789]) ).
cnf(t790,plain,
op1(sk1,j(h(op1(sk0,sk0)))) = j(op2(h(sk1),h(op1(sk0,sk0)))),
inference(step,[status(thm)],[t244,t389]) ).
cnf(t791,plain,
op1(sk1,j(h(sk1))) = j(op2(h(sk1),h(op1(sk0,sk0)))),
inference(step,[status(thm)],[t790,t364]) ).
cnf(t792,plain,
op1(sk1,sk1) = j(op2(h(sk1),h(op1(sk0,sk0)))),
inference(step,[status(thm)],[t791,t389]) ).
cnf(t793,plain,
sk0 = j(op2(h(sk1),h(op1(sk0,sk0)))),
inference(step,[status(thm)],[t792,t369]) ).
cnf(t794,plain,
sk0 = j(op2(h(sk1),h(sk1))),
inference(step,[status(thm)],[t793,t364]) ).
cnf(t476,plain,
j(op2(h(sk1),h(sk1))) = sk0,
inference(orient,[status(thm)],[t794]) ).
cnf(t807,plain,
op2(h(sk1),h(sk1)) = h(sk0),
inference(step,[status(thm)],[t806,t476]) ).
cnf(t698,plain,
op2(h(sk1),h(sk1)) = h(sk0),
inference(orient,[status(thm)],[t807]) ).
cnf(t838,plain,
h(sk0) = ifeq(h(sk0),h(sk0),op2(h(sk0),op2(h(sk0),h(sk0))),h(sk0)),
inference(step,[status(thm)],[t837,t698]) ).
cnf(t839,plain,
h(sk0) = op2(h(sk0),op2(h(sk0),h(sk0))),
inference(step,[status(thm)],[t838,t256]) ).
cnf(t840,plain,
h(sk0) = op2(h(sk0),h(sk1)),
inference(step,[status(thm)],[t839,t694]) ).
cnf(t55,plain,
op2(h(sk0),h(sk1)) = h(op1(sk0,sk1)),
inference(hyper_resolution,[status(thm)],[hi9,hi2,hi3]) ).
cnf(t292,plain,
op2(h(sk0),h(sk1)) = h(op1(sk0,sk1)),
inference(orient,[status(thm)],[t55]) ).
cnf(t841,plain,
h(sk0) = h(op1(sk0,sk1)),
inference(step,[status(thm)],[t840,t292]) ).
cnf(t746,plain,
h(op1(sk0,sk1)) = h(sk0),
inference(orient,[status(thm)],[t841]) ).
cnf(t749,plain,
op1(sk0,sk1) = ifeq(sorti1(op1(sk0,sk1)),true,j(h(sk0)),op1(sk0,sk1)),
inference(cp,[status(thm)],[t257,t746]) ).
cnf(t4,plain,
sorti1(op1(sk0,sk1)) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi2,hi3]) ).
cnf(t495,plain,
sorti1(op1(sk0,sk1)) = true,
inference(orient,[status(thm)],[t4]) ).
cnf(t854,plain,
op1(sk0,sk1) = ifeq(true,true,j(h(sk0)),op1(sk0,sk1)),
inference(step,[status(thm)],[t749,t495]) ).
cnf(t855,plain,
op1(sk0,sk1) = j(h(sk0)),
inference(step,[status(thm)],[t854,t256]) ).
cnf(t154,plain,
j(h(op1(sk1,op1(sk0,sk0)))) = op1(sk1,op1(sk0,sk0)),
inference(hyper_resolution,[status(thm)],[hi12,h24]) ).
cnf(t782,plain,
j(h(op1(sk1,sk1))) = op1(sk1,op1(sk0,sk0)),
inference(step,[status(thm)],[t154,t364]) ).
cnf(t783,plain,
j(h(sk0)) = op1(sk1,op1(sk0,sk0)),
inference(step,[status(thm)],[t782,t369]) ).
cnf(t784,plain,
j(h(sk0)) = op1(sk1,sk1),
inference(step,[status(thm)],[t783,t364]) ).
cnf(t785,plain,
j(h(sk0)) = sk0,
inference(step,[status(thm)],[t784,t369]) ).
cnf(t383,plain,
j(h(sk0)) = sk0,
inference(orient,[status(thm)],[t785]) ).
cnf(t856,plain,
op1(sk0,sk1) = sk0,
inference(step,[status(thm)],[t855,t383]) ).
cnf(t759,plain,
op1(sk0,sk1) = sk0,
inference(orient,[status(thm)],[t856]) ).
cnf(c6,plain,
op1(sk0,sk1) != sk0,
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(goal_0,negated_conjecture,
op1(sk0,sk1) != sk0,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(g0_0,plain,
sk0 != sk0,
inference(rw,[status(thm)],[goal_0,t759]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG073+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.34 % Computer : n010.cluster.edu
% 0.10/0.34 % Model : x86_64 x86_64
% 0.10/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34 % Memory : 8046.5625MB
% 0.10/0.34 % OS : Linux 6.8.0-71-generic
% 0.10/0.34 % CPULimit : 300
% 0.10/0.34 % WCLimit : 300
% 0.10/0.34 % DateTime : Fri Sep 25 04:41:58 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 42.56/5.93 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 42.56/5.93 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------