%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : ALG030+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 : n020.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 12:51:13 PM UTC 2026
% Result : Theorem 79.51s 10.60s
% Output : Proof 79.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 61 ( 43 unt; 0 def)
% Number of atoms : 139 ( 65 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 123 ( 45 ~; 32 |; 22 &)
% ( 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 : 73 ( 2 sgn 46 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
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] :
( sorti1(U)
=> ! [V] :
( sorti1(V)
=> op1(U,V) = op1(V,U) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
fof(f2_nnf,plain,
? [U] :
( ? [V] :
( op1(U,V) != op1(V,U)
& sorti1(V) )
& sorti1(U) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
( op1(sk0,sk1) != op1(sk1,sk0)
& sorti1(sk1)
& sorti1(sk0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f2_nnf]) ).
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(c2,plain,
sorti1(sk0),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
sorti1(sk0) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h11,plain,
sorti1(op1(sk1,sk0)) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi3,hi2]) ).
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(c11,plain,
( j(h(X7)) = X7
| ~ sorti1(X7) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi10,negated_conjecture,
ifeq(sorti1(X0),true,j(h(X0)),X0) = X0,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t26,plain,
j(h(op1(sk1,sk0))) = op1(sk1,sk0),
inference(hyper_resolution,[status(thm)],[hi10,h11]) ).
cnf(t382,plain,
j(h(op1(sk1,sk0))) = op1(sk1,sk0),
inference(orient,[status(thm)],[t26]) ).
fof(f3,axiom,
~ ~ ! [U] :
( sorti2(U)
=> ! [V] :
( sorti2(V)
=> op2(U,V) = op2(V,U) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
fof(f3_nnf,plain,
! [U] :
( ! [V] :
( op2(U,V) = op2(V,U)
| ~ sorti2(V) )
| ~ sorti2(U) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [U,V] :
( op2(U,V) = op2(V,U)
| ~ sorti2(V)
| ~ sorti2(U) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c5,plain,
( op2(X0,X1) = op2(X1,X0)
| ~ sorti2(X1)
| ~ sorti2(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t253,plain,
ifeq(sorti2(X1),true,ifeq(sorti2(X2),true,op2(X1,X2),op2(X2,X1)),op2(X2,X1)) = op2(X2,X1),
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t629,plain,
ifeq(sorti2(X1),true,ifeq(sorti2(X2),true,op2(X1,X2),op2(X2,X1)),op2(X2,X1)) = op2(X2,X1),
inference(orient,[status(thm)],[t253]) ).
cnf(c8,plain,
( h(op1(X2,X3)) = op2(h(X2),h(X3))
| ~ sorti1(X3)
| ~ sorti1(X2) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi7,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)],[c8]) ).
cnf(t49,plain,
op2(h(sk0),h(sk1)) = h(op1(sk0,sk1)),
inference(hyper_resolution,[status(thm)],[hi7,hi2,hi3]) ).
cnf(t319,plain,
op2(h(sk0),h(sk1)) = h(op1(sk0,sk1)),
inference(orient,[status(thm)],[t49]) ).
cnf(t638,plain,
op2(h(sk1),h(sk0)) = ifeq(sorti2(h(sk0)),true,ifeq(sorti2(h(sk1)),true,h(op1(sk0,sk1)),op2(h(sk1),h(sk0))),op2(h(sk1),h(sk0))),
inference(cp,[status(thm)],[t629,t319]) ).
cnf(t50,plain,
op2(h(sk1),h(sk0)) = h(op1(sk1,sk0)),
inference(hyper_resolution,[status(thm)],[hi7,hi3,hi2]) ).
cnf(t298,plain,
op2(h(sk1),h(sk0)) = h(op1(sk1,sk0)),
inference(orient,[status(thm)],[t50]) ).
cnf(t21939,plain,
h(op1(sk1,sk0)) = ifeq(sorti2(h(sk0)),true,ifeq(sorti2(h(sk1)),true,h(op1(sk0,sk1)),op2(h(sk1),h(sk0))),op2(h(sk1),h(sk0))),
inference(step,[status(thm)],[t638,t298]) ).
cnf(c6,plain,
( sorti2(h(X0))
| ~ sorti1(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t46,plain,
ifeq(sorti1(X1),true,sorti2(h(X1)),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t1327,plain,
ifeq(sorti1(X1),true,sorti2(h(X1)),true) = true,
inference(orient,[status(thm)],[t46]) ).
cnf(t0,plain,
sorti1(sk0) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t1218,plain,
sorti1(sk0) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(t1328,plain,
true = ifeq(true,true,sorti2(h(sk0)),true),
inference(cp,[status(thm)],[t1327,t1218]) ).
cnf(t4,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t4]) ).
cnf(t21024,plain,
true = sorti2(h(sk0)),
inference(step,[status(thm)],[t1328,t256]) ).
cnf(t1592,plain,
sorti2(h(sk0)) = true,
inference(orient,[status(thm)],[t21024]) ).
cnf(t21940,plain,
h(op1(sk1,sk0)) = ifeq(true,true,ifeq(sorti2(h(sk1)),true,h(op1(sk0,sk1)),op2(h(sk1),h(sk0))),op2(h(sk1),h(sk0))),
inference(step,[status(thm)],[t21939,t1592]) ).
cnf(t21941,plain,
h(op1(sk1,sk0)) = ifeq(sorti2(h(sk1)),true,h(op1(sk0,sk1)),op2(h(sk1),h(sk0))),
inference(step,[status(thm)],[t21940,t256]) ).
cnf(t1,plain,
sorti1(sk1) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t1214,plain,
sorti1(sk1) = true,
inference(orient,[status(thm)],[t1]) ).
cnf(t1329,plain,
true = ifeq(true,true,sorti2(h(sk1)),true),
inference(cp,[status(thm)],[t1327,t1214]) ).
cnf(t21025,plain,
true = sorti2(h(sk1)),
inference(step,[status(thm)],[t1329,t256]) ).
cnf(t1599,plain,
sorti2(h(sk1)) = true,
inference(orient,[status(thm)],[t21025]) ).
cnf(t21942,plain,
h(op1(sk1,sk0)) = ifeq(true,true,h(op1(sk0,sk1)),op2(h(sk1),h(sk0))),
inference(step,[status(thm)],[t21941,t1599]) ).
cnf(t21943,plain,
h(op1(sk1,sk0)) = h(op1(sk0,sk1)),
inference(step,[status(thm)],[t21942,t256]) ).
cnf(t20905,plain,
h(op1(sk0,sk1)) = h(op1(sk1,sk0)),
inference(orient,[status(thm)],[t21943]) ).
cnf(c4,plain,
op1(sk0,sk1) != op1(sk1,sk0),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(goal_0,negated_conjecture,
op1(sk1,sk0) != op1(sk0,sk1),
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(g0_0,plain,
j(h(op1(sk0,sk1))) != op1(sk0,sk1),
inference(rw,[status(thm)],[goal_0]) ).
cnf(g0_1,plain,
j(h(op1(sk0,sk1))) != j(h(op1(sk1,sk0))),
inference(rw,[status(thm)],[g0_0,t382]) ).
cnf(g0_2,plain,
j(h(op1(sk0,sk1))) != j(h(op1(sk0,sk1))),
inference(rw,[status(thm)],[g0_1,t20905]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG030+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n020.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
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 04:34:04 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 79.51/10.60 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 79.51/10.60 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------