%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN310-1 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n003.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 03:34:18 PM UTC 2026
% Result : Unsatisfiable 5.62s 1.29s
% Output : Proof 5.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 6
% Syntax : Number of formulae : 44 ( 28 unt; 0 def)
% Number of atoms : 60 ( 20 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 38 ( 22 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-4 aty)
% Number of variables : 60 ( 0 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f3,negated_conjecture,
( p(X,X1,X2)
| ~ p(f(X),X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause4) ).
fof(f3_nnf,plain,
! [X,X1,X2] :
( p(X,X1,X2)
| ~ p(f(X),X1,X2) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,X1,X2] :
( p(X,X1,X2)
| ~ p(f(X),X1,X2) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( p(X0,X1,X2)
| ~ p(f(X0),X1,X2) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi3,negated_conjecture,
ifeq(p(f(X0),X1,X2),true,p(X0,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(f5,negated_conjecture,
p(f(g(a)),f(g(b)),f(g(c))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause6) ).
fof(f5_nnf,plain,
p(f(g(a)),f(g(b)),f(g(c))),
inference(nnf_transformation,[status(thm)],[f5]) ).
cnf(c5,plain,
p(f(g(a)),f(g(b)),f(g(c))),
inference(cnf_transformation,[status(esa)],[f5_nnf]) ).
cnf(hi4,negated_conjecture,
p(f(g(a)),f(g(b)),f(g(c))) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(h0,plain,
p(g(a),f(g(b)),f(g(c))) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi4]) ).
cnf(f0,negated_conjecture,
( p(X,X1,X2)
| ~ p(X2,X1,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause1) ).
fof(f0_nnf,plain,
! [X2,X1,X] :
( p(X,X1,X2)
| ~ p(X2,X1,X) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X2,X1,X] :
( p(X,X1,X2)
| ~ p(X2,X1,X) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( p(X2,X1,X0)
| ~ p(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,negated_conjecture,
ifeq(p(X0,X1,X2),true,p(X2,X1,X0),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h4,plain,
p(f(g(c)),f(g(b)),g(a)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h0]) ).
cnf(h11,plain,
p(g(c),f(g(b)),g(a)) = true,
inference(hyper_resolution,[status(thm)],[hi3,h4]) ).
cnf(f2,negated_conjecture,
( p(X,X1,X2)
| ~ p(X,X1,g(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause3) ).
fof(f2_nnf,plain,
! [X,X1,X2] :
( p(X,X1,X2)
| ~ p(X,X1,g(X2)) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,X1,X2] :
( p(X,X1,X2)
| ~ p(X,X1,g(X2)) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( p(X0,X1,X2)
| ~ p(X0,X1,g(X2)) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,negated_conjecture,
ifeq(p(X0,X1,g(X2)),true,p(X0,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h25,plain,
p(g(c),f(g(b)),a) = true,
inference(hyper_resolution,[status(thm)],[hi2,h11]) ).
cnf(f1,negated_conjecture,
( p(X,X1,X2)
| ~ p(X1,X,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause2) ).
fof(f1_nnf,plain,
! [X1,X,X2] :
( p(X,X1,X2)
| ~ p(X1,X,X2) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X1,X,X2] :
( p(X,X1,X2)
| ~ p(X1,X,X2) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( p(X1,X0,X2)
| ~ p(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,negated_conjecture,
ifeq(p(X0,X1,X2),true,p(X1,X0,X2),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h32,plain,
p(f(g(b)),g(c),a) = true,
inference(hyper_resolution,[status(thm)],[hi1,h25]) ).
cnf(h39,plain,
p(g(b),g(c),a) = true,
inference(hyper_resolution,[status(thm)],[hi3,h32]) ).
cnf(h47,plain,
p(a,g(c),g(b)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h39]) ).
cnf(h54,plain,
p(a,g(c),b) = true,
inference(hyper_resolution,[status(thm)],[hi2,h47]) ).
cnf(h59,plain,
p(g(c),a,b) = true,
inference(hyper_resolution,[status(thm)],[hi1,h54]) ).
cnf(h67,plain,
p(b,a,g(c)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h59]) ).
cnf(h75,plain,
p(b,a,c) = true,
inference(hyper_resolution,[status(thm)],[hi2,h67]) ).
cnf(t0,plain,
p(a,b,c) = true,
inference(hyper_resolution,[status(thm)],[hi1,h75]) ).
cnf(t168,plain,
p(a,b,c) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(f4,negated_conjecture,
~ p(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause5) ).
fof(f4_nnf,plain,
~ p(a,b,c),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
~ p(a,b,c),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
~ p(a,b,c),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(goal_0,negated_conjecture,
p(a,b,c) != true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t168]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN310-1 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n003.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 00:49:22 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.62/1.29 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.62/1.29 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------