%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO499+1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n005.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 01:18:03 PM UTC 2026
% Result : Theorem 63.06s 8.76s
% Output : Proof 63.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 15
% Syntax : Number of formulae : 82 ( 52 unt; 0 def)
% Number of atoms : 188 ( 90 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 220 ( 114 ~; 71 |; 35 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 10 con; 0-4 aty)
% Number of variables : 142 ( 7 sgn 71 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f104,axiom,
! [Xp,Xq,Xr,Xa] :
( s_t(s(Xa,Xp),s(Xa,Xq),s(Xa,Xr))
| ~ s_t(Xp,Xq,Xr) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_15a) ).
fof(f104_nnf,plain,
! [Xp,Xq,Xr,Xa] :
( s_t(s(Xa,Xp),s(Xa,Xq),s(Xa,Xr))
| ~ s_t(Xp,Xq,Xr) ),
inference(nnf_transformation,[status(thm)],[f104]) ).
fof(f104_sk,plain,
! [Xp,Xq,Xr,Xa] :
( s_t(s(Xa,Xp),s(Xa,Xq),s(Xa,Xr))
| ~ s_t(Xp,Xq,Xr) ),
inference(skolemisation,[status(esa)],[f104_nnf]) ).
cnf(c118,plain,
( s_t(s(X3,X0),s(X3,X1),s(X3,X2))
| ~ s_t(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f104_sk]) ).
cnf(t190,plain,
ifeq(s_t(X1,X2,X3),true,s_t(s(X4,X1),s(X4,X2),s(X4,X3)),true) = true,
inference(equality_encoding,[status(esa)],[c118]) ).
cnf(t346,plain,
ifeq(s_t(X1,X2,X3),true,s_t(s(X4,X1),s(X4,X2),s(X4,X3)),true) = true,
inference(orient,[status(thm)],[t190]) ).
fof(f99,axiom,
! [Xa,Xp,Xr,Xq] :
( Xp = Xq
| s(Xa,Xq) != Xr
| s(Xa,Xp) != Xr ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_8) ).
fof(f99_nnf,plain,
! [Xa,Xp,Xr,Xq] :
( Xp = Xq
| s(Xa,Xq) != Xr
| s(Xa,Xp) != Xr ),
inference(nnf_transformation,[status(thm)],[f99]) ).
fof(f99_sk,plain,
! [Xa,Xp,Xr,Xq] :
( Xp = Xq
| s(Xa,Xq) != Xr
| s(Xa,Xp) != Xr ),
inference(skolemisation,[status(esa)],[f99_nnf]) ).
cnf(c113,plain,
( X1 = X3
| s(X0,X3) != X2
| s(X0,X1) != X2 ),
inference(cnf_transformation,[status(esa)],[f99_sk]) ).
cnf(hi103,axiom,
ifeq(s(X0,X1),X2,ifeq(s(X0,X3),X2,X1,X3),X3) = X3,
inference(equality_encoding,[status(esa)],[c113]) ).
cnf(hi183,axiom,
or(false,X0) = X0,
introduced(definition) ).
fof(f98,axiom,
! [Xa,Xp] : s(Xa,s(Xa,Xp)) = Xp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_7) ).
fof(f98_nnf,plain,
! [Xa,Xp] : s(Xa,s(Xa,Xp)) = Xp,
inference(nnf_transformation,[status(thm)],[f98]) ).
fof(f98_sk,plain,
! [Xa,Xp] : s(Xa,s(Xa,Xp)) = Xp,
inference(skolemisation,[status(esa)],[f98_nnf]) ).
cnf(c112,plain,
s(X0,s(X0,X1)) = X1,
inference(cnf_transformation,[status(esa)],[f98_sk]) ).
cnf(hi102,axiom,
s(X0,s(X0,X1)) = X1,
inference(equality_encoding,[status(esa)],[c112]) ).
cnf(t60,plain,
s(X1,or(false,s(X1,X2))) = X2,
inference(hyper_resolution,[status(thm)],[hi103,hi183,hi102]) ).
cnf(t8,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t277,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t8]) ).
cnf(t11497,plain,
s(X1,s(X1,X2)) = X2,
inference(step,[status(thm)],[t60,t277]) ).
cnf(t280,plain,
s(X1,s(X1,X2)) = X2,
inference(orient,[status(thm)],[t11497]) ).
cnf(t348,plain,
true = ifeq(s_t(s(X1,X2),X3,X4),true,s_t(X2,s(X1,X3),s(X1,X4)),true),
inference(cp,[status(thm)],[t346,t280]) ).
cnf(t11351,plain,
ifeq(s_t(s(X1,X2),X3,X4),true,s_t(X2,s(X1,X3),s(X1,X4)),true) = true,
inference(orient,[status(thm)],[t348]) ).
fof(f105,conjecture,
! [Xp,Xq,Xr,Xa] :
( ~ s_t(s(Xa,Xp),s(Xa,Xq),s(Xa,Xr))
| s_t(Xp,Xq,Xr) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_15b) ).
fof(f105_neg,negated_conjecture,
~ ! [Xp,Xq,Xr,Xa] :
( ~ s_t(s(Xa,Xp),s(Xa,Xq),s(Xa,Xr))
| s_t(Xp,Xq,Xr) ),
inference(negated_conjecture,[status(cth)],[f105]) ).
fof(f105_nnf,plain,
? [Xp,Xq,Xr,Xa] :
( s_t(s(Xa,Xp),s(Xa,Xq),s(Xa,Xr))
& ~ s_t(Xp,Xq,Xr) ),
inference(nnf_transformation,[status(thm)],[f105_neg]) ).
fof(f105_sk,plain,
( s_t(s(sk3,sk0),s(sk3,sk1),s(sk3,sk2))
& ~ s_t(sk0,sk1,sk2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2,sk3])],[f105_nnf]) ).
cnf(c120,plain,
s_t(s(sk3,sk0),s(sk3,sk1),s(sk3,sk2)),
inference(cnf_transformation,[status(esa)],[f105_sk]) ).
cnf(t109,plain,
s_t(s(sk3,sk0),s(sk3,sk1),s(sk3,sk2)) = true,
inference(equality_encoding,[status(esa)],[c120]) ).
cnf(t1274,plain,
s_t(s(sk3,sk0),s(sk3,sk1),s(sk3,sk2)) = true,
inference(orient,[status(thm)],[t109]) ).
cnf(t11352,plain,
true = ifeq(true,true,s_t(sk0,s(sk3,s(sk3,sk1)),s(sk3,s(sk3,sk2))),true),
inference(cp,[status(thm)],[t11351,t1274]) ).
cnf(t26,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t26]) ).
cnf(t11971,plain,
true = s_t(sk0,s(sk3,s(sk3,sk1)),s(sk3,s(sk3,sk2))),
inference(step,[status(thm)],[t11352,t256]) ).
cnf(t11972,plain,
true = s_t(sk0,sk1,s(sk3,s(sk3,sk2))),
inference(step,[status(thm)],[t11971,t280]) ).
cnf(t11973,plain,
true = s_t(sk0,sk1,sk2),
inference(step,[status(thm)],[t11972,t280]) ).
cnf(c119,plain,
~ s_t(sk0,sk1,sk2),
inference(cnf_transformation,[status(esa)],[f105_sk]) ).
cnf(t24,plain,
s_t(sk0,sk1,sk2) = false,
inference(equality_encoding,[status(esa)],[c119]) ).
cnf(t2386,plain,
s_t(sk0,sk1,sk2) = false,
inference(orient,[status(thm)],[t24]) ).
cnf(t11974,plain,
true = false,
inference(step,[status(thm)],[t11973,t2386]) ).
cnf(t11367,plain,
false = true,
inference(orient,[status(thm)],[t11974]) ).
fof(f7,axiom,
( ~ s_t(gamma,alpha,beta)
& ~ s_t(beta,gamma,alpha)
& ~ s_t(alpha,beta,gamma) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aA8) ).
fof(f7_nnf,plain,
( ~ s_t(gamma,alpha,beta)
& ~ s_t(beta,gamma,alpha)
& ~ s_t(alpha,beta,gamma) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
( ~ s_t(gamma,alpha,beta)
& ~ s_t(beta,gamma,alpha)
& ~ s_t(alpha,beta,gamma) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c9,plain,
~ s_t(alpha,beta,gamma),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(c10,plain,
~ s_t(beta,gamma,alpha),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(c11,plain,
~ s_t(gamma,alpha,beta),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
fof(f29,axiom,
alpha != beta,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_13a) ).
fof(f29_nnf,plain,
alpha != beta,
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
alpha != beta,
inference(skolemisation,[status(esa)],[f29_nnf]) ).
cnf(c33,plain,
alpha != beta,
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
fof(f30,axiom,
beta != gamma,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_13b) ).
fof(f30_nnf,plain,
beta != gamma,
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
beta != gamma,
inference(skolemisation,[status(esa)],[f30_nnf]) ).
cnf(c34,plain,
beta != gamma,
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
fof(f31,axiom,
alpha != gamma,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_13c) ).
fof(f31_nnf,plain,
alpha != gamma,
inference(nnf_transformation,[status(thm)],[f31]) ).
fof(f31_sk,plain,
alpha != gamma,
inference(skolemisation,[status(esa)],[f31_nnf]) ).
cnf(c35,plain,
alpha != gamma,
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
fof(f33,axiom,
! [Xb,Xa] : Xb != ext(Xa,Xb,alpha,gamma),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz3_14b) ).
fof(f33_nnf,plain,
! [Xb,Xa] : Xb != ext(Xa,Xb,alpha,gamma),
inference(nnf_transformation,[status(thm)],[f33]) ).
fof(f33_sk,plain,
! [Xb,Xa] : Xb != ext(Xa,Xb,alpha,gamma),
inference(skolemisation,[status(esa)],[f33_nnf]) ).
cnf(c37,plain,
X0 != ext(X1,X0,alpha,gamma),
inference(cnf_transformation,[status(esa)],[f33_sk]) ).
fof(f69,axiom,
! [Xa,Xp,Xb] :
( ( s_t(Xb,Xp,c63(Xa,Xp,Xb))
| ~ sameside(Xa,Xp,Xb) )
& ( s_t(Xa,Xp,c63(Xa,Xp,Xb))
| ~ sameside(Xa,Xp,Xb) )
& ( c63(Xa,Xp,Xb) != Xp
| ~ sameside(Xa,Xp,Xb) )
& ( Xb != Xp
| ~ sameside(Xa,Xp,Xb) )
& ( Xa != Xp
| ~ sameside(Xa,Xp,Xb) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_3a) ).
fof(f69_nnf,plain,
! [Xa,Xp,Xb] :
( ( s_t(Xb,Xp,c63(Xa,Xp,Xb))
| ~ sameside(Xa,Xp,Xb) )
& ( s_t(Xa,Xp,c63(Xa,Xp,Xb))
| ~ sameside(Xa,Xp,Xb) )
& ( c63(Xa,Xp,Xb) != Xp
| ~ sameside(Xa,Xp,Xb) )
& ( Xb != Xp
| ~ sameside(Xa,Xp,Xb) )
& ( Xa != Xp
| ~ sameside(Xa,Xp,Xb) ) ),
inference(nnf_transformation,[status(thm)],[f69]) ).
fof(f69_sk,plain,
! [Xa,Xp,Xb] :
( ( s_t(Xb,Xp,c63(Xa,Xp,Xb))
| ~ sameside(Xa,Xp,Xb) )
& ( s_t(Xa,Xp,c63(Xa,Xp,Xb))
| ~ sameside(Xa,Xp,Xb) )
& ( c63(Xa,Xp,Xb) != Xp
| ~ sameside(Xa,Xp,Xb) )
& ( Xb != Xp
| ~ sameside(Xa,Xp,Xb) )
& ( Xa != Xp
| ~ sameside(Xa,Xp,Xb) ) ),
inference(skolemisation,[status(esa)],[f69_nnf]) ).
cnf(c77,plain,
( X0 != X1
| ~ sameside(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f69_sk]) ).
cnf(c78,plain,
( X2 != X1
| ~ sameside(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f69_sk]) ).
cnf(c79,plain,
( c63(X0,X1,X2) != X1
| ~ sameside(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f69_sk]) ).
fof(f71,axiom,
! [Xa,Xp,Xb] :
( ( ~ s_t(Xa,Xp,Xb)
| ~ sameside(Xa,Xp,Xb) )
& ( s_col(Xa,Xp,Xb)
| ~ sameside(Xa,Xp,Xb) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz6_4a) ).
fof(f71_nnf,plain,
! [Xa,Xp,Xb] :
( ( ~ s_t(Xa,Xp,Xb)
| ~ sameside(Xa,Xp,Xb) )
& ( s_col(Xa,Xp,Xb)
| ~ sameside(Xa,Xp,Xb) ) ),
inference(nnf_transformation,[status(thm)],[f71]) ).
fof(f71_sk,plain,
! [Xa,Xp,Xb] :
( ( ~ s_t(Xa,Xp,Xb)
| ~ sameside(Xa,Xp,Xb) )
& ( s_col(Xa,Xp,Xb)
| ~ sameside(Xa,Xp,Xb) ) ),
inference(skolemisation,[status(esa)],[f71_nnf]) ).
cnf(c84,plain,
( ~ s_t(X0,X1,X2)
| ~ sameside(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f71_sk]) ).
fof(f113,axiom,
! [Xa,Xp,Xb] :
( ( sameside(Xa,Xp,Xb)
| Xb = Xp
| Xa = Xp
| ~ s_t(Xp,Xb,Xa) )
& ( sameside(Xa,Xp,Xb)
| xb = Xp
| Xa = Xp
| ~ s_t(Xp,Xa,Xb) )
& ( s_t(Xp,Xb,Xa)
| s_t(Xp,Xa,Xb)
| ~ sameside(Xa,Xp,Xb) )
& ( Xb != Xp
| ~ sameside(Xa,Xp,Xb) )
& ( Xa != Xp
| ~ sameside(Xa,Xp,Xb) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_Defn6_1) ).
fof(f113_nnf,plain,
! [Xa,Xp,Xb] :
( ( sameside(Xa,Xp,Xb)
| Xb = Xp
| Xa = Xp
| ~ s_t(Xp,Xb,Xa) )
& ( sameside(Xa,Xp,Xb)
| xb = Xp
| Xa = Xp
| ~ s_t(Xp,Xa,Xb) )
& ( s_t(Xp,Xb,Xa)
| s_t(Xp,Xa,Xb)
| ~ sameside(Xa,Xp,Xb) )
& ( Xb != Xp
| ~ sameside(Xa,Xp,Xb) )
& ( Xa != Xp
| ~ sameside(Xa,Xp,Xb) ) ),
inference(nnf_transformation,[status(thm)],[f113]) ).
fof(f113_sk,plain,
! [Xa,Xp,Xb] :
( ( sameside(Xa,Xp,Xb)
| Xb = Xp
| Xa = Xp
| ~ s_t(Xp,Xb,Xa) )
& ( sameside(Xa,Xp,Xb)
| xb = Xp
| Xa = Xp
| ~ s_t(Xp,Xa,Xb) )
& ( s_t(Xp,Xb,Xa)
| s_t(Xp,Xa,Xb)
| ~ sameside(Xa,Xp,Xb) )
& ( Xb != Xp
| ~ sameside(Xa,Xp,Xb) )
& ( Xa != Xp
| ~ sameside(Xa,Xp,Xb) ) ),
inference(skolemisation,[status(esa)],[f113_nnf]) ).
cnf(c152,plain,
( X0 != X1
| ~ sameside(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f113_sk]) ).
cnf(c153,plain,
( X2 != X1
| ~ sameside(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f113_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c9,c10,c11,c33,c34,c35,c37,c77,c78,c79,c84,c119,c152,c153]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t11367]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO499+1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n005.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 : Wed Sep 23 12:13:18 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 63.06/8.76 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 63.06/8.76 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------