%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN083+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/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 03:33:46 PM UTC 2026
% Result : Theorem 5.98s 1.24s
% Output : Proof 5.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of formulae : 15 ( 15 unt; 0 def)
% Number of atoms : 15 ( 14 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 30 ( 0 sgn 17 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,axiom,
! [X,Y,Z] : f(X,f(Y,Z)) = f(f(X,Y),Z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p61_1) ).
fof(f0_nnf,plain,
! [X,Y,Z] : f(X,f(Y,Z)) = f(f(X,Y),Z),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y,Z] : f(X,f(Y,Z)) = f(f(X,Y),Z),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
f(X0,f(X1,X2)) = f(f(X0,X1),X2),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t0,plain,
f(f(X1,X2),X3) = f(X1,f(X2,X3)),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t1,plain,
f(f(X1,X2),X3) = f(X1,f(X2,X3)),
inference(orient,[status(thm)],[t0]) ).
fof(f1,conjecture,
! [X,Y,Z,W] : f(X,f(Y,f(Z,W))) = f(f(f(X,Y),Z),W),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel61) ).
fof(f1_neg,negated_conjecture,
~ ! [X,Y,Z,W] : f(X,f(Y,f(Z,W))) = f(f(f(X,Y),Z),W),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f1_nnf,plain,
? [X,Y,Z,W] : f(X,f(Y,f(Z,W))) != f(f(f(X,Y),Z),W),
inference(nnf_transformation,[status(thm)],[f1_neg]) ).
fof(f1_sk,plain,
f(sk0,f(sk1,f(sk2,sk3))) != f(f(f(sk0,sk1),sk2),sk3),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2,sk3])],[f1_nnf]) ).
cnf(c1,plain,
f(sk0,f(sk1,f(sk2,sk3))) != f(f(f(sk0,sk1),sk2),sk3),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(goal_0,negated_conjecture,
f(sk0,f(sk1,f(sk2,sk3))) != f(f(f(sk0,sk1),sk2),sk3),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(g0_0,plain,
f(sk0,f(sk1,f(sk2,sk3))) != f(f(sk0,sk1),f(sk2,sk3)),
inference(rw,[status(thm)],[goal_0,t1]) ).
cnf(g0_1,plain,
f(sk0,f(sk1,f(sk2,sk3))) != f(sk0,f(sk1,f(sk2,sk3))),
inference(rw,[status(thm)],[g0_0,t1]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN083+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.38 % Computer : n020.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Fri Sep 25 00:09:33 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.98/1.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.98/1.24 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------