%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN234-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n009.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 03:34:08 PM UTC 2026
% Result : Unsatisfiable 6.72s 1.36s
% Output : Proof 6.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 38 ( 26 unt; 0 def)
% Number of atoms : 58 ( 12 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 46 ( 26 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-4 aty)
% Number of variables : 30 ( 0 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f58,axiom,
( ~ k0(J)
| ~ l0(I)
| m1(I,J,I) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_021) ).
fof(f58_nnf,plain,
! [I,J] :
( ~ k0(J)
| ~ l0(I)
| m1(I,J,I) ),
inference(nnf_transformation,[status(thm)],[f58]) ).
fof(f58_sk,plain,
! [I,J] :
( ~ k0(J)
| ~ l0(I)
| m1(I,J,I) ),
inference(skolemisation,[status(esa)],[f58_nnf]) ).
cnf(c58,plain,
( ~ k0(X1)
| ~ l0(X0)
| m1(X0,X1,X0) ),
inference(cnf_transformation,[status(esa)],[f58_sk]) ).
cnf(hi58,axiom,
ifeq(l0(X0),true,ifeq(k0(X1),true,m1(X0,X1,X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c58]) ).
cnf(f19,axiom,
l0(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_20) ).
fof(f19_nnf,plain,
l0(a),
inference(nnf_transformation,[status(thm)],[f19]) ).
cnf(c19,plain,
l0(a),
inference(cnf_transformation,[status(esa)],[f19_nnf]) ).
cnf(hi19,axiom,
l0(a) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(f27,axiom,
k0(e),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_28) ).
fof(f27_nnf,plain,
k0(e),
inference(nnf_transformation,[status(thm)],[f27]) ).
cnf(c27,plain,
k0(e),
inference(cnf_transformation,[status(esa)],[f27_nnf]) ).
cnf(hi27,axiom,
k0(e) = true,
inference(equality_encoding,[status(esa)],[c27]) ).
cnf(h78,plain,
m1(a,e,a) = true,
inference(hyper_resolution,[status(thm)],[hi58,hi19,hi27]) ).
cnf(f213,axiom,
( ~ m1(E,D,E)
| p2(D,E,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_176) ).
fof(f213_nnf,plain,
! [D,E] :
( ~ m1(E,D,E)
| p2(D,E,D) ),
inference(nnf_transformation,[status(thm)],[f213]) ).
fof(f213_sk,plain,
! [D,E] :
( ~ m1(E,D,E)
| p2(D,E,D) ),
inference(skolemisation,[status(esa)],[f213_nnf]) ).
cnf(c213,plain,
( ~ m1(X1,X0,X1)
| p2(X0,X1,X0) ),
inference(cnf_transformation,[status(esa)],[f213_sk]) ).
cnf(hi210,axiom,
ifeq(m1(X0,X1,X0),true,p2(X1,X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c213]) ).
cnf(h243,plain,
p2(e,a,e) = true,
inference(hyper_resolution,[status(thm)],[hi210,h78]) ).
cnf(f252,axiom,
( ~ p2(G,H,G)
| ~ r0(G)
| l3(G,H) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_215) ).
fof(f252_nnf,plain,
! [G,H] :
( ~ p2(G,H,G)
| ~ r0(G)
| l3(G,H) ),
inference(nnf_transformation,[status(thm)],[f252]) ).
fof(f252_sk,plain,
! [G,H] :
( ~ p2(G,H,G)
| ~ r0(G)
| l3(G,H) ),
inference(skolemisation,[status(esa)],[f252_nnf]) ).
cnf(c252,plain,
( ~ p2(X0,X1,X0)
| ~ r0(X0)
| l3(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f252_sk]) ).
cnf(hi247,axiom,
ifeq(r0(X0),true,ifeq(p2(X0,X1,X0),true,l3(X0,X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c252]) ).
cnf(f12,axiom,
r0(e),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_13) ).
fof(f12_nnf,plain,
r0(e),
inference(nnf_transformation,[status(thm)],[f12]) ).
cnf(c12,plain,
r0(e),
inference(cnf_transformation,[status(esa)],[f12_nnf]) ).
cnf(hi12,axiom,
r0(e) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t16,plain,
l3(e,a) = true,
inference(hyper_resolution,[status(thm)],[hi247,hi12,h243]) ).
cnf(t61,plain,
l3(e,a) = true,
inference(orient,[status(thm)],[t16]) ).
cnf(f368,negated_conjecture,
~ l3(e,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(f368_nnf,plain,
~ l3(e,a),
inference(nnf_transformation,[status(thm)],[f368]) ).
fof(f368_sk,plain,
~ l3(e,a),
inference(skolemisation,[status(esa)],[f368_nnf]) ).
cnf(c368,plain,
~ l3(e,a),
inference(cnf_transformation,[status(esa)],[f368_sk]) ).
cnf(goal_0,negated_conjecture,
l3(e,a) != true,
inference(equality_encoding,[status(esa)],[c368]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t61]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN234-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n009.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 00:34:43 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.72/1.36 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.72/1.36 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------