%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : ITP001+4 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n004.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 01:43:59 PM UTC 2026
% Result : Theorem 4.27s 1.01s
% Output : Proof 4.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 48 ( 25 unt; 0 def)
% Number of atoms : 96 ( 7 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 103 ( 55 ~; 27 |; 15 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-2 aty)
% Number of variables : 22 ( 1 sgn 15 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Etruth) ).
fof(f2_nnf,plain,
p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)),
inference(nnf_transformation,[status(thm)],[f2]) ).
cnf(c5,plain,
p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)),
inference(cnf_transformation,[status(esa)],[f2_nnf]) ).
cnf(t11,plain,
p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
fof(f86,conjecture,
p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ETRUTH) ).
fof(f86_neg,negated_conjecture,
~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)),
inference(negated_conjecture,[status(cth)],[f86]) ).
fof(f86_nnf,plain,
~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)),
inference(nnf_transformation,[status(thm)],[f86_neg]) ).
fof(f86_sk,plain,
~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)),
inference(skolemisation,[status(esa)],[f86_nnf]) ).
cnf(c213,plain,
~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)),
inference(cnf_transformation,[status(esa)],[f86_sk]) ).
cnf(t10,plain,
p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) = false,
inference(equality_encoding,[status(esa)],[c213]) ).
cnf(t1731,plain,
p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) = false,
inference(orient,[status(thm)],[t10]) ).
cnf(t1817,plain,
false = true,
inference(step,[status(thm)],[t11,t1731]) ).
cnf(t1734,plain,
false = true,
inference(orient,[status(thm)],[t1817]) ).
fof(f3,axiom,
~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Enotfalse) ).
fof(f3_nnf,plain,
~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c6,plain,
~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
fof(f10,axiom,
! [V0_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0))))
<=> ~ p(s(tyop_2Emin_2Ebool,V0_2E0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Elogic_2E_7E) ).
fof(f10_nnf,plain,
! [V0_2E0] :
( ( p(s(tyop_2Emin_2Ebool,V0_2E0))
| p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))) )
& ( ~ p(s(tyop_2Emin_2Ebool,V0_2E0))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))) ) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [V0_2E0] :
( ( p(s(tyop_2Emin_2Ebool,V0_2E0))
| p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))) )
& ( ~ p(s(tyop_2Emin_2Ebool,V0_2E0))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))) ) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c17,plain,
( ~ p(s(tyop_2Emin_2Ebool,X0))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,X0)))) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
fof(f17,axiom,
! [X0_2E0] :
( ~ p(s(tyop_2Emin_2Ebool,X0_2E0))
<=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_7E_2E1) ).
fof(f17_nnf,plain,
! [X0_2E0] :
( ( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))))
| ~ p(s(tyop_2Emin_2Ebool,X0_2E0)) )
& ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))))
| p(s(tyop_2Emin_2Ebool,X0_2E0)) ) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [X0_2E0] :
( ( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))))
| ~ p(s(tyop_2Emin_2Ebool,X0_2E0)) )
& ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))))
| p(s(tyop_2Emin_2Ebool,X0_2E0)) ) ),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c35,plain,
( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0))))
| ~ p(s(tyop_2Emin_2Ebool,X0)) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
fof(f25,axiom,
~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Enotfalse) ).
fof(f25_nnf,plain,
~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)),
inference(skolemisation,[status(esa)],[f25_nnf]) ).
cnf(c49,plain,
~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
fof(f32,axiom,
! [V0_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0))))
<=> ~ p(s(tyop_2Emin_2Ebool,V0_2E0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Elogic_2E_7E) ).
fof(f32_nnf,plain,
! [V0_2E0] :
( ( p(s(tyop_2Emin_2Ebool,V0_2E0))
| p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))) )
& ( ~ p(s(tyop_2Emin_2Ebool,V0_2E0))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))) ) ),
inference(nnf_transformation,[status(thm)],[f32]) ).
fof(f32_sk,plain,
! [V0_2E0] :
( ( p(s(tyop_2Emin_2Ebool,V0_2E0))
| p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))) )
& ( ~ p(s(tyop_2Emin_2Ebool,V0_2E0))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))) ) ),
inference(skolemisation,[status(esa)],[f32_nnf]) ).
cnf(c60,plain,
( ~ p(s(tyop_2Emin_2Ebool,X0))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,X0)))) ),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
fof(f39,axiom,
! [X0_2E0] :
( ~ p(s(tyop_2Emin_2Ebool,X0_2E0))
<=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_7E_2E1) ).
fof(f39_nnf,plain,
! [X0_2E0] :
( ( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))))
| ~ p(s(tyop_2Emin_2Ebool,X0_2E0)) )
& ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))))
| p(s(tyop_2Emin_2Ebool,X0_2E0)) ) ),
inference(nnf_transformation,[status(thm)],[f39]) ).
fof(f39_sk,plain,
! [X0_2E0] :
( ( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))))
| ~ p(s(tyop_2Emin_2Ebool,X0_2E0)) )
& ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))))
| p(s(tyop_2Emin_2Ebool,X0_2E0)) ) ),
inference(skolemisation,[status(esa)],[f39_nnf]) ).
cnf(c78,plain,
( ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0))))
| ~ p(s(tyop_2Emin_2Ebool,X0)) ),
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
fof(f64,axiom,
? [V0f_2E0] :
( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EONTO_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Eind),V0f_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebool_2EONE__ONE_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Eind),V0f_2E0)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EINFINITY__AX) ).
fof(f64_nnf,plain,
? [V0f_2E0] :
( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EONTO_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Eind),V0f_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ebool_2EONE__ONE_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Eind),V0f_2E0)))) ),
inference(nnf_transformation,[status(thm)],[f64]) ).
fof(f64_sk,plain,
( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EONTO_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Eind),sk6))))
& p(s(tyop_2Emin_2Ebool,c_2Ebool_2EONE__ONE_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Eind),sk6)))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk6])],[f64_nnf]) ).
cnf(c107,plain,
~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EONTO_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Eind,tyop_2Emin_2Eind),sk6)))),
inference(cnf_transformation,[status(esa)],[f64_sk]) ).
fof(f71,axiom,
! [V0x_2E0] :
( ~ p(s(tyop_2Emin_2Ebool,V0x_2E0))
<=> ( p(s(tyop_2Emin_2Ebool,V0x_2E0))
=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ENOT__DEF) ).
fof(f71_nnf,plain,
! [V0x_2E0] :
( ( ( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))
& p(s(tyop_2Emin_2Ebool,V0x_2E0)) )
| ~ p(s(tyop_2Emin_2Ebool,V0x_2E0)) )
& ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))
| ~ p(s(tyop_2Emin_2Ebool,V0x_2E0))
| p(s(tyop_2Emin_2Ebool,V0x_2E0)) ) ),
inference(nnf_transformation,[status(thm)],[f71]) ).
fof(f71_sk,plain,
! [V0x_2E0] :
( ( ( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))
& p(s(tyop_2Emin_2Ebool,V0x_2E0)) )
| ~ p(s(tyop_2Emin_2Ebool,V0x_2E0)) )
& ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))
| ~ p(s(tyop_2Emin_2Ebool,V0x_2E0))
| p(s(tyop_2Emin_2Ebool,V0x_2E0)) ) ),
inference(skolemisation,[status(esa)],[f71_nnf]) ).
cnf(c135,plain,
( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))
| ~ p(s(tyop_2Emin_2Ebool,X0)) ),
inference(cnf_transformation,[status(esa)],[f71_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c6,c17,c35,c49,c60,c78,c107,c135,c213]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t1734]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP001+4 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.07/0.35 % Computer : n004.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Wed Sep 23 17:26:06 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.27/1.01 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.27/1.01 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------