%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO118-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n016.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 01:17:05 PM UTC 2026
% Result : Unsatisfiable 14.47s 2.28s
% Output : Proof 14.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 13
% Syntax : Number of formulae : 71 ( 47 unt; 0 def)
% Number of atoms : 99 ( 48 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 74 ( 46 ~; 28 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-4 aty)
% Number of variables : 138 ( 30 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f77,axiom,
( between_c(ax2_sk4(A,D,C,B),B,C,D)
| ~ between_o(A,B,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',o3_24) ).
fof(f77_nnf,plain,
! [A,B,C,D] :
( between_c(ax2_sk4(A,D,C,B),B,C,D)
| ~ between_o(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f77]) ).
fof(f77_sk,plain,
! [A,B,C,D] :
( between_c(ax2_sk4(A,D,C,B),B,C,D)
| ~ between_o(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f77_nnf]) ).
cnf(c77,plain,
( between_c(ax2_sk4(X0,X3,X2,X1),X1,X2,X3)
| ~ between_o(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f77_sk]) ).
cnf(t62,plain,
ifeq(between_o(X1,X2,X3,X4),true,between_c(ax2_sk4(X1,X4,X3,X2),X2,X3,X4),true) = true,
inference(equality_encoding,[status(esa)],[c77]) ).
cnf(t163,plain,
ifeq(between_o(X1,X2,X3,X4),true,between_c(ax2_sk4(X1,X4,X3,X2),X2,X3,X4),true) = true,
inference(orient,[status(thm)],[t62]) ).
cnf(t13,plain,
ifeq(not(X1),true,X1,false) = false,
introduced(definition) ).
cnf(t268,plain,
ifeq(not(X1),true,X1,false) = false,
inference(orient,[status(thm)],[t13]) ).
cnf(f48,axiom,
( B != D
| ~ between_c(A,B,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',between_c_defn_1) ).
fof(f48_nnf,plain,
! [A,B,C,D] :
( B != D
| ~ between_c(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f48]) ).
fof(f48_sk,plain,
! [A,B,C,D] :
( B != D
| ~ between_c(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f48_nnf]) ).
cnf(c48,plain,
( X1 != X3
| ~ between_c(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f48_sk]) ).
cnf(t33,plain,
or(not(between_c(X1,X2,X3,X4)),not(eq(X2,X4))) = true,
inference(equality_encoding,[status(esa)],[c48]) ).
cnf(t195,plain,
or(not(between_c(X1,X2,X3,X4)),not(eq(X2,X4))) = true,
inference(orient,[status(thm)],[t33]) ).
cnf(t2,plain,
eq(X1,X1) = true,
introduced(definition) ).
cnf(t232,plain,
eq(X1,X1) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(t233,plain,
true = or(not(between_c(X1,X2,X3,X2)),not(true)),
inference(cp,[status(thm)],[t195,t232]) ).
cnf(t1,plain,
not(true) = false,
introduced(definition) ).
cnf(t272,plain,
not(true) = false,
inference(orient,[status(thm)],[t1]) ).
cnf(t6334,plain,
true = or(not(between_c(X1,X2,X3,X2)),false),
inference(step,[status(thm)],[t233,t272]) ).
cnf(t4,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t105,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t4]) ).
cnf(t6335,plain,
true = not(between_c(X1,X2,X3,X2)),
inference(step,[status(thm)],[t6334,t105]) ).
cnf(t2678,plain,
not(between_c(X1,X2,X3,X2)) = true,
inference(orient,[status(thm)],[t6335]) ).
cnf(t2679,plain,
false = ifeq(true,true,between_c(X1,X2,X3,X2),false),
inference(cp,[status(thm)],[t268,t2678]) ).
cnf(t12,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t101,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t12]) ).
cnf(t6336,plain,
false = between_c(X1,X2,X3,X2),
inference(step,[status(thm)],[t2679,t101]) ).
cnf(t2680,plain,
between_c(X1,X2,X3,X2) = false,
inference(orient,[status(thm)],[t6336]) ).
cnf(t2685,plain,
true = ifeq(between_o(X1,X2,X3,X2),true,false,true),
inference(cp,[status(thm)],[t163,t2680]) ).
cnf(t3373,plain,
ifeq(between_o(X1,X2,X3,X2),true,false,true) = true,
inference(orient,[status(thm)],[t2685]) ).
cnf(f58,axiom,
( between_o(A,B,C,D)
| ~ ordered_by(A,C,D)
| ~ ordered_by(A,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',between_o_defn_5) ).
fof(f58_nnf,plain,
! [A,B,C,D] :
( between_o(A,B,C,D)
| ~ ordered_by(A,C,D)
| ~ ordered_by(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f58]) ).
fof(f58_sk,plain,
! [A,B,C,D] :
( between_o(A,B,C,D)
| ~ ordered_by(A,C,D)
| ~ ordered_by(A,B,C) ),
inference(skolemisation,[status(esa)],[f58_nnf]) ).
cnf(c58,plain,
( between_o(X0,X1,X2,X3)
| ~ ordered_by(X0,X2,X3)
| ~ ordered_by(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f58_sk]) ).
cnf(t74,plain,
ifeq(ordered_by(X1,X2,X3),true,ifeq(ordered_by(X1,X3,X4),true,between_o(X1,X2,X3,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c58]) ).
cnf(t146,plain,
ifeq(ordered_by(X1,X2,X3),true,ifeq(ordered_by(X1,X3,X4),true,between_o(X1,X2,X3,X4),true),true) = true,
inference(orient,[status(thm)],[t74]) ).
cnf(f96,negated_conjecture,
ordered_by(sk25,sk26,sk27),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theorem_4_5_133) ).
fof(f96_nnf,plain,
ordered_by(sk25,sk26,sk27),
inference(nnf_transformation,[status(thm)],[f96]) ).
cnf(c96,plain,
ordered_by(sk25,sk26,sk27),
inference(cnf_transformation,[status(esa)],[f96_nnf]) ).
cnf(t9,plain,
ordered_by(sk25,sk26,sk27) = true,
inference(equality_encoding,[status(esa)],[c96]) ).
cnf(t198,plain,
ordered_by(sk25,sk26,sk27) = true,
inference(orient,[status(thm)],[t9]) ).
cnf(t209,plain,
true = ifeq(true,true,ifeq(ordered_by(sk25,sk27,X1),true,between_o(sk25,sk26,sk27,X1),true),true),
inference(cp,[status(thm)],[t146,t198]) ).
cnf(t6475,plain,
true = ifeq(ordered_by(sk25,sk27,X1),true,between_o(sk25,sk26,sk27,X1),true),
inference(step,[status(thm)],[t209,t101]) ).
cnf(t6223,plain,
ifeq(ordered_by(sk25,sk27,X1),true,between_o(sk25,sk26,sk27,X1),true) = true,
inference(orient,[status(thm)],[t6475]) ).
cnf(f97,negated_conjecture,
ordered_by(sk25,sk27,sk26),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theorem_4_5_134) ).
fof(f97_nnf,plain,
ordered_by(sk25,sk27,sk26),
inference(nnf_transformation,[status(thm)],[f97]) ).
cnf(c97,plain,
ordered_by(sk25,sk27,sk26),
inference(cnf_transformation,[status(esa)],[f97_nnf]) ).
cnf(t10,plain,
ordered_by(sk25,sk27,sk26) = true,
inference(equality_encoding,[status(esa)],[c97]) ).
cnf(t215,plain,
ordered_by(sk25,sk27,sk26) = true,
inference(orient,[status(thm)],[t10]) ).
cnf(t6224,plain,
true = ifeq(true,true,between_o(sk25,sk26,sk27,sk26),true),
inference(cp,[status(thm)],[t6223,t215]) ).
cnf(t6476,plain,
true = between_o(sk25,sk26,sk27,sk26),
inference(step,[status(thm)],[t6224,t101]) ).
cnf(t6225,plain,
between_o(sk25,sk26,sk27,sk26) = true,
inference(orient,[status(thm)],[t6476]) ).
cnf(t6226,plain,
true = ifeq(true,true,false,true),
inference(cp,[status(thm)],[t3373,t6225]) ).
cnf(t6477,plain,
true = false,
inference(step,[status(thm)],[t6226,t101]) ).
cnf(t6230,plain,
false = true,
inference(orient,[status(thm)],[t6477]) ).
cnf(f21,axiom,
( ~ end_point(A,B)
| ~ inner_point(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inner_point_defn_22) ).
fof(f21_nnf,plain,
! [A,B] :
( ~ end_point(A,B)
| ~ inner_point(A,B) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [A,B] :
( ~ end_point(A,B)
| ~ inner_point(A,B) ),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c21,plain,
( ~ end_point(X0,X1)
| ~ inner_point(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(f30,axiom,
( ~ end_point(B,A)
| ~ closed(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closed_defn_31) ).
fof(f30_nnf,plain,
! [A,B] :
( ~ end_point(B,A)
| ~ closed(A) ),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
! [A,B] :
( ~ end_point(B,A)
| ~ closed(A) ),
inference(skolemisation,[status(esa)],[f30_nnf]) ).
cnf(c30,plain,
( ~ end_point(X1,X0)
| ~ closed(X0) ),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
cnf(f41,axiom,
( A != ax0_sk11(A,B)
| ~ end_point(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c6_42) ).
fof(f41_nnf,plain,
! [A,B] :
( A != ax0_sk11(A,B)
| ~ end_point(A,B) ),
inference(nnf_transformation,[status(thm)],[f41]) ).
fof(f41_sk,plain,
! [A,B] :
( A != ax0_sk11(A,B)
| ~ end_point(A,B) ),
inference(skolemisation,[status(esa)],[f41_nnf]) ).
cnf(c41,plain,
( X0 != ax0_sk11(X0,X1)
| ~ end_point(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f41_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c21,c30,c41,c48]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t6230]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO118-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n016.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 11:03:10 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 14.47/2.28 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.47/2.28 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------