%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : ALG203+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 : n017.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 12:51:54 PM UTC 2026
% Result : Theorem 41.20s 5.68s
% Output : Proof 41.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 4
% Syntax : Number of formulae : 63 ( 49 unt; 0 def)
% Number of atoms : 140 ( 78 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 119 ( 42 ~; 29 |; 30 &)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 2 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 36 !; 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(c12,plain,
( j(h(X7)) = X7
| ~ sorti1(X7) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi11,negated_conjecture,
ifeq(sorti1(X0),true,j(h(X0)),X0) = X0,
inference(equality_encoding,[status(esa)],[c12]) ).
fof(f2,axiom,
( ? [V] :
( op1(V,V) != V
& sorti1(V) )
& ? [U] :
( op1(U,U) = U
& sorti1(U) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
fof(f2_nnf,plain,
( ? [V] :
( op1(V,V) != V
& sorti1(V) )
& ? [U] :
( op1(U,U) = U
& sorti1(U) ) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
( op1(sk1,sk1) != sk1
& sorti1(sk1)
& op1(sk0,sk0) = sk0
& sorti1(sk0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f2_nnf]) ).
cnf(c4,plain,
sorti1(sk1),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi4,axiom,
sorti1(sk1) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t2,plain,
j(h(sk1)) = sk1,
inference(hyper_resolution,[status(thm)],[hi11,hi4]) ).
cnf(t361,plain,
j(h(sk1)) = sk1,
inference(orient,[status(thm)],[t2]) ).
fof(f3,axiom,
~ ( ? [V] :
( op2(V,V) != V
& sorti2(V) )
& ? [U] :
( op2(U,U) = U
& sorti2(U) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
fof(f3_nnf,plain,
( ! [V] :
( op2(V,V) = V
| ~ sorti2(V) )
| ! [U] :
( op2(U,U) != U
| ~ sorti2(U) ) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [U,V] :
( op2(V,V) = V
| ~ sorti2(V)
| op2(U,U) != U
| ~ sorti2(U) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c6,plain,
( op2(X1,X1) = X1
| ~ sorti2(X1)
| op2(X0,X0) != X0
| ~ sorti2(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t253,plain,
ifeq(sorti2(X1),true,ifeq(op2(X1,X1),X1,ifeq(sorti2(X2),true,op2(X2,X2),X2),X2),X2) = X2,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t258,plain,
ifeq(sorti2(X1),true,ifeq(op2(X1,X1),X1,ifeq(sorti2(X2),true,op2(X2,X2),X2),X2),X2) = X2,
inference(orient,[status(thm)],[t253]) ).
cnf(c9,plain,
( h(op1(X2,X3)) = op2(h(X2),h(X3))
| ~ sorti1(X3)
| ~ sorti1(X2) ),
inference(cnf_transformation,[status(esa)],[f4_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)],[c9]) ).
cnf(t828,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(c3,plain,
op1(sk0,sk0) = sk0,
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t3,plain,
op1(sk0,sk0) = sk0,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t588,plain,
op1(sk0,sk0) = sk0,
inference(orient,[status(thm)],[t3]) ).
cnf(t875,plain,
op2(h(sk0),h(sk0)) = ifeq(sorti1(sk0),true,ifeq(sorti1(sk0),true,h(sk0),op2(h(sk0),h(sk0))),op2(h(sk0),h(sk0))),
inference(cp,[status(thm)],[t828,t588]) ).
cnf(c2,plain,
sorti1(sk0),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t0,plain,
sorti1(sk0) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t611,plain,
sorti1(sk0) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(t975,plain,
op2(h(sk0),h(sk0)) = ifeq(true,true,ifeq(sorti1(sk0),true,h(sk0),op2(h(sk0),h(sk0))),op2(h(sk0),h(sk0))),
inference(step,[status(thm)],[t875,t611]) ).
cnf(t10,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t10]) ).
cnf(t976,plain,
op2(h(sk0),h(sk0)) = ifeq(sorti1(sk0),true,h(sk0),op2(h(sk0),h(sk0))),
inference(step,[status(thm)],[t975,t256]) ).
cnf(t977,plain,
op2(h(sk0),h(sk0)) = ifeq(true,true,h(sk0),op2(h(sk0),h(sk0))),
inference(step,[status(thm)],[t976,t611]) ).
cnf(t978,plain,
op2(h(sk0),h(sk0)) = h(sk0),
inference(step,[status(thm)],[t977,t256]) ).
cnf(t898,plain,
op2(h(sk0),h(sk0)) = h(sk0),
inference(orient,[status(thm)],[t978]) ).
cnf(t899,plain,
X1 = ifeq(sorti2(h(sk0)),true,ifeq(h(sk0),h(sk0),ifeq(sorti2(X1),true,op2(X1,X1),X1),X1),X1),
inference(cp,[status(thm)],[t258,t898]) ).
cnf(c7,plain,
( sorti2(h(X0))
| ~ sorti1(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t74,plain,
ifeq(sorti1(X1),true,sorti2(h(X1)),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t705,plain,
ifeq(sorti1(X1),true,sorti2(h(X1)),true) = true,
inference(orient,[status(thm)],[t74]) ).
cnf(t706,plain,
true = ifeq(true,true,sorti2(h(sk0)),true),
inference(cp,[status(thm)],[t705,t611]) ).
cnf(t974,plain,
true = sorti2(h(sk0)),
inference(step,[status(thm)],[t706,t256]) ).
cnf(t891,plain,
sorti2(h(sk0)) = true,
inference(orient,[status(thm)],[t974]) ).
cnf(t979,plain,
X1 = ifeq(true,true,ifeq(h(sk0),h(sk0),ifeq(sorti2(X1),true,op2(X1,X1),X1),X1),X1),
inference(step,[status(thm)],[t899,t891]) ).
cnf(t980,plain,
X1 = ifeq(h(sk0),h(sk0),ifeq(sorti2(X1),true,op2(X1,X1),X1),X1),
inference(step,[status(thm)],[t979,t256]) ).
cnf(t981,plain,
X1 = ifeq(sorti2(X1),true,op2(X1,X1),X1),
inference(step,[status(thm)],[t980,t256]) ).
cnf(t901,plain,
ifeq(sorti2(X1),true,op2(X1,X1),X1) = X1,
inference(orient,[status(thm)],[t981]) ).
cnf(hi6,negated_conjecture,
ifeq(sorti1(X0),true,sorti2(h(X0)),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t4,plain,
sorti2(h(sk1)) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi4]) ).
cnf(t613,plain,
sorti2(h(sk1)) = true,
inference(orient,[status(thm)],[t4]) ).
cnf(t914,plain,
h(sk1) = ifeq(true,true,op2(h(sk1),h(sk1)),h(sk1)),
inference(cp,[status(thm)],[t901,t613]) ).
cnf(t983,plain,
h(sk1) = op2(h(sk1),h(sk1)),
inference(step,[status(thm)],[t914,t256]) ).
cnf(hi8,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)],[c9]) ).
cnf(t79,plain,
op2(h(sk1),h(sk1)) = h(op1(sk1,sk1)),
inference(hyper_resolution,[status(thm)],[hi8,hi4,hi4]) ).
cnf(t266,plain,
op2(h(sk1),h(sk1)) = h(op1(sk1,sk1)),
inference(orient,[status(thm)],[t79]) ).
cnf(t984,plain,
h(sk1) = h(op1(sk1,sk1)),
inference(step,[status(thm)],[t983,t266]) ).
cnf(t920,plain,
h(op1(sk1,sk1)) = h(sk1),
inference(orient,[status(thm)],[t984]) ).
cnf(c5,plain,
op1(sk1,sk1) != sk1,
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(goal_0,negated_conjecture,
op1(sk1,sk1) != sk1,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(g0_0,plain,
j(h(op1(sk1,sk1))) != sk1,
inference(rw,[status(thm)],[goal_0]) ).
cnf(g0_1,plain,
j(h(op1(sk1,sk1))) != j(h(sk1)),
inference(rw,[status(thm)],[g0_0,t361]) ).
cnf(g0_2,plain,
j(h(op1(sk1,sk1))) != j(h(op1(sk1,sk1))),
inference(rw,[status(thm)],[g0_1,t920]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG203+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n017.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 04:58:32 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 41.20/5.68 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 41.20/5.68 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------