%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN333+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 : n026.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 03:34:23 PM UTC 2026
% Result : Theorem 3.99s 0.98s
% Output : Proof 3.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 2
% Syntax : Number of formulae : 34 ( 28 unt; 0 def)
% Number of atoms : 63 ( 26 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 46 ( 17 ~; 11 |; 14 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 2 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-4 aty)
% Number of variables : 61 ( 16 sgn 6 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,conjecture,
? [X,Y] :
! [Z] :
( big_f(X,Y)
=> ( ( ( big_g(X,Y)
& big_f(X,Y) )
=> ( big_g(Z,Z)
& big_g(X,Z) ) )
& big_f(Z,Z)
& big_f(Y,Z) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',church_46_14_5) ).
fof(f0_neg,negated_conjecture,
~ ? [X,Y] :
! [Z] :
( big_f(X,Y)
=> ( ( ( big_g(X,Y)
& big_f(X,Y) )
=> ( big_g(Z,Z)
& big_g(X,Z) ) )
& big_f(Z,Z)
& big_f(Y,Z) ) ),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
! [X,Y] :
? [Z] :
( ( ( ( ~ big_g(Z,Z)
| ~ big_g(X,Z) )
& big_g(X,Y)
& big_f(X,Y) )
| ~ big_f(Z,Z)
| ~ big_f(Y,Z) )
& big_f(X,Y) ),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
! [X,Y] :
( ( ( ( ~ big_g(sk0(X,Y),sk0(X,Y))
| ~ big_g(X,sk0(X,Y)) )
& big_g(X,Y)
& big_f(X,Y) )
| ~ big_f(sk0(X,Y),sk0(X,Y))
| ~ big_f(Y,sk0(X,Y)) )
& big_f(X,Y) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f0_nnf]) ).
cnf(c3,plain,
( ~ big_g(sk0(X0,X1),sk0(X0,X1))
| ~ big_g(X0,sk0(X0,X1))
| ~ big_f(sk0(X0,X1),sk0(X0,X1))
| ~ big_f(X1,sk0(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t4,plain,
ifeq(big_f(X1,sk0(X2,X1)),true,ifeq(big_f(sk0(X2,X1),sk0(X2,X1)),true,ifeq(big_g(X2,sk0(X2,X1)),true,ifeq(big_g(sk0(X2,X1),sk0(X2,X1)),true,false,true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t6,plain,
ifeq(big_f(X1,sk0(X2,X1)),true,ifeq(big_f(sk0(X2,X1),sk0(X2,X1)),true,ifeq(big_g(X2,sk0(X2,X1)),true,ifeq(big_g(sk0(X2,X1),sk0(X2,X1)),true,false,true),true),true),true) = true,
inference(orient,[status(thm)],[t4]) ).
cnf(c0,plain,
big_f(X0,X1),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t0,plain,
big_f(X1,X2) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t9,plain,
big_f(X1,X2) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(t18,plain,
ifeq(true,true,ifeq(big_f(sk0(X2,X1),sk0(X2,X1)),true,ifeq(big_g(X2,sk0(X2,X1)),true,ifeq(big_g(sk0(X2,X1),sk0(X2,X1)),true,false,true),true),true),true) = true,
inference(step,[status(thm)],[t6,t9]) ).
cnf(t1,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t5,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t1]) ).
cnf(t19,plain,
ifeq(big_f(sk0(X2,X1),sk0(X2,X1)),true,ifeq(big_g(X2,sk0(X2,X1)),true,ifeq(big_g(sk0(X2,X1),sk0(X2,X1)),true,false,true),true),true) = true,
inference(step,[status(thm)],[t18,t5]) ).
cnf(t20,plain,
ifeq(true,true,ifeq(big_g(X2,sk0(X2,X1)),true,ifeq(big_g(sk0(X2,X1),sk0(X2,X1)),true,false,true),true),true) = true,
inference(step,[status(thm)],[t19,t9]) ).
cnf(t21,plain,
ifeq(big_g(X2,sk0(X2,X1)),true,ifeq(big_g(sk0(X2,X1),sk0(X2,X1)),true,false,true),true) = true,
inference(step,[status(thm)],[t20,t5]) ).
cnf(t11,plain,
ifeq(big_g(X2,sk0(X2,X1)),true,ifeq(big_g(sk0(X2,X1),sk0(X2,X1)),true,false,true),true) = true,
inference(rw,[status(thm)],[t21]) ).
cnf(c2,plain,
( big_g(X0,X1)
| ~ big_f(sk0(X0,X1),sk0(X0,X1))
| ~ big_f(X1,sk0(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t3,plain,
ifeq(big_f(X1,sk0(X2,X1)),true,ifeq(big_f(sk0(X2,X1),sk0(X2,X1)),true,big_g(X2,X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t8,plain,
ifeq(big_f(X1,sk0(X2,X1)),true,ifeq(big_f(sk0(X2,X1),sk0(X2,X1)),true,big_g(X2,X1),true),true) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(t14,plain,
ifeq(true,true,ifeq(big_f(sk0(X2,X1),sk0(X2,X1)),true,big_g(X2,X1),true),true) = true,
inference(step,[status(thm)],[t8,t9]) ).
cnf(t15,plain,
ifeq(big_f(sk0(X2,X1),sk0(X2,X1)),true,big_g(X2,X1),true) = true,
inference(step,[status(thm)],[t14,t5]) ).
cnf(t16,plain,
ifeq(true,true,big_g(X2,X1),true) = true,
inference(step,[status(thm)],[t15,t9]) ).
cnf(t17,plain,
big_g(X2,X1) = true,
inference(step,[status(thm)],[t16,t5]) ).
cnf(t10,plain,
big_g(X2,X1) = true,
inference(rw,[status(thm)],[t17]) ).
cnf(t12,plain,
big_g(X1,X2) = true,
inference(orient,[status(thm)],[t10]) ).
cnf(t22,plain,
ifeq(true,true,ifeq(big_g(sk0(X2,X1),sk0(X2,X1)),true,false,true),true) = true,
inference(step,[status(thm)],[t11,t12]) ).
cnf(t23,plain,
ifeq(big_g(sk0(X2,X1),sk0(X2,X1)),true,false,true) = true,
inference(step,[status(thm)],[t22,t5]) ).
cnf(t24,plain,
ifeq(true,true,false,true) = true,
inference(step,[status(thm)],[t23,t12]) ).
cnf(t25,plain,
false = true,
inference(step,[status(thm)],[t24,t5]) ).
cnf(t13,plain,
false = true,
inference(orient,[status(thm)],[t25]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t13]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN333+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.38 % Computer : n026.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Fri Sep 25 00:55:24 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.99/0.98 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.99/0.98 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------