%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO541+1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n007.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 01:18:06 PM UTC 2026
% Result : Theorem 14.73s 7.40s
% Output : Proof 14.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 17
% Syntax : Number of formulae : 139 ( 71 unt; 0 def)
% Number of atoms : 271 ( 64 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 219 ( 87 ~; 81 |; 33 &)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-4 aty)
% Number of variables : 356 ( 0 sgn 215 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f69,axiom,
! [A,B,C] :
( midp(A,B,C)
=> coll(A,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD69) ).
fof(f69_nnf,plain,
! [A,B,C] :
( coll(A,B,C)
| ~ midp(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f69]) ).
fof(f69_sk,plain,
! [A,B,C] :
( coll(A,B,C)
| ~ midp(A,B,C) ),
inference(skolemisation,[status(esa)],[f69_nnf]) ).
cnf(c69,plain,
( coll(X0,X1,X2)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f69_sk]) ).
cnf(hi69,axiom,
ifeq(midp(X0,X1,X2),true,coll(X0,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c69]) ).
fof(f94,conjecture,
! [A,B,C,D,E,F,G] :
( ( midp(G,D,E)
& midp(F,C,B)
& coll(E,A,C)
& perp(E,B,A,C)
& coll(D,A,B)
& perp(D,C,A,B) )
=> perp(F,G,D,E) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exemplo6GDDFULL012001) ).
fof(f94_neg,negated_conjecture,
~ ! [A,B,C,D,E,F,G] :
( ( midp(G,D,E)
& midp(F,C,B)
& coll(E,A,C)
& perp(E,B,A,C)
& coll(D,A,B)
& perp(D,C,A,B) )
=> perp(F,G,D,E) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,B,C,D,E,F,G] :
( ~ perp(F,G,D,E)
& midp(G,D,E)
& midp(F,C,B)
& coll(E,A,C)
& perp(E,B,A,C)
& coll(D,A,B)
& perp(D,C,A,B) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ perp(sk25,sk26,sk23,sk24)
& midp(sk26,sk23,sk24)
& midp(sk25,sk22,sk21)
& coll(sk24,sk20,sk22)
& perp(sk24,sk21,sk20,sk22)
& coll(sk23,sk20,sk21)
& perp(sk23,sk22,sk20,sk21) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24,sk25,sk26])],[f94_nnf]) ).
cnf(c118,plain,
midp(sk26,sk23,sk24),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi118,negated_conjecture,
midp(sk26,sk23,sk24) = true,
inference(equality_encoding,[status(esa)],[c118]) ).
cnf(h11,plain,
coll(sk26,sk23,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi69,hi118]) ).
fof(f68,axiom,
! [A,B,C] :
( midp(A,B,C)
=> cong(A,B,A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD68) ).
fof(f68_nnf,plain,
! [A,B,C] :
( cong(A,B,A,C)
| ~ midp(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f68]) ).
fof(f68_sk,plain,
! [A,B,C] :
( cong(A,B,A,C)
| ~ midp(A,B,C) ),
inference(skolemisation,[status(esa)],[f68_nnf]) ).
cnf(c68,plain,
( cong(X0,X1,X0,X2)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f68_sk]) ).
cnf(hi68,axiom,
ifeq(midp(X0,X1,X2),true,cong(X0,X1,X0,X2),true) = true,
inference(equality_encoding,[status(esa)],[c68]) ).
cnf(h12,plain,
cong(sk26,sk23,sk26,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi68,hi118]) ).
fof(f11,axiom,
! [A,B,C,O] :
( ( cong(O,A,O,C)
& cong(O,A,O,B) )
=> circle(O,A,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD12) ).
fof(f11_nnf,plain,
! [A,B,C,O] :
( circle(O,A,B,C)
| ~ cong(O,A,O,C)
| ~ cong(O,A,O,B) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [O,A,B,C] :
( circle(O,A,B,C)
| ~ cong(O,A,O,C)
| ~ cong(O,A,O,B) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( circle(X3,X0,X1,X2)
| ~ cong(X3,X0,X3,X2)
| ~ cong(X3,X0,X3,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi11,axiom,
ifeq(cong(X0,X1,X0,X2),true,ifeq(cong(X0,X1,X0,X3),true,circle(X0,X1,X2,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(h369,plain,
circle(sk26,sk23,sk24,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi11,h12,h12]) ).
fof(f53,axiom,
! [A,B,C,O] :
( ( coll(O,A,C)
& circle(O,A,B,C) )
=> perp(A,B,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD53) ).
fof(f53_nnf,plain,
! [A,B,C,O] :
( perp(A,B,B,C)
| ~ coll(O,A,C)
| ~ circle(O,A,B,C) ),
inference(nnf_transformation,[status(thm)],[f53]) ).
fof(f53_sk,plain,
! [O,A,B,C] :
( perp(A,B,B,C)
| ~ coll(O,A,C)
| ~ circle(O,A,B,C) ),
inference(skolemisation,[status(esa)],[f53_nnf]) ).
cnf(c53,plain,
( perp(X0,X1,X1,X2)
| ~ coll(X3,X0,X2)
| ~ circle(X3,X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f53_sk]) ).
cnf(hi53,axiom,
ifeq(circle(X0,X1,X2,X3),true,ifeq(coll(X0,X1,X3),true,perp(X1,X2,X2,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c53]) ).
cnf(h411,plain,
perp(sk23,sk24,sk24,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi53,h369,h11]) ).
fof(f7,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(C,D,A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD8) ).
fof(f7_nnf,plain,
! [A,B,C,D] :
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A,B,C,D] :
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( perp(X2,X3,X0,X1)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi7,axiom,
ifeq(perp(X0,X1,X2,X3),true,perp(X2,X3,X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(h536,plain,
perp(sk24,sk24,sk23,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi7,h411]) ).
fof(f2,axiom,
! [A,B,C,D] :
( ( coll(A,B,D)
& coll(A,B,C) )
=> coll(C,D,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD3) ).
fof(f2_nnf,plain,
! [A,B,C,D] :
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B,C,D] :
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( coll(X2,X3,X0)
| ~ coll(X0,X1,X3)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
ifeq(coll(X0,X1,X2),true,ifeq(coll(X0,X1,X3),true,coll(X2,X3,X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h36,plain,
coll(sk24,sk24,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi2,h11,h11]) ).
fof(f0,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(A,C,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD1) ).
fof(f0_nnf,plain,
! [A,B,C] :
( coll(A,C,B)
| ~ coll(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B,C] :
( coll(A,C,B)
| ~ coll(A,B,C) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( coll(X0,X2,X1)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
ifeq(coll(X0,X1,X2),true,coll(X0,X2,X1),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h77,plain,
coll(sk24,sk26,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi0,h36]) ).
fof(f1,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(B,A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD2) ).
fof(f1_nnf,plain,
! [A,B,C] :
( coll(B,A,C)
| ~ coll(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B,C] :
( coll(B,A,C)
| ~ coll(A,B,C) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( coll(X1,X0,X2)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
ifeq(coll(X0,X1,X2),true,coll(X1,X0,X2),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h131,plain,
coll(sk26,sk24,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi1,h77]) ).
fof(f10,axiom,
! [A,B,M] :
( midp(M,B,A)
=> midp(M,A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD11) ).
fof(f10_nnf,plain,
! [A,B,M] :
( midp(M,A,B)
| ~ midp(M,B,A) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [M,B,A] :
( midp(M,A,B)
| ~ midp(M,B,A) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( midp(X2,X0,X1)
| ~ midp(X2,X1,X0) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(hi10,axiom,
ifeq(midp(X0,X1,X2),true,midp(X0,X2,X1),true) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(h15,plain,
midp(sk26,sk24,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi10,hi118]) ).
cnf(h39,plain,
cong(sk26,sk24,sk26,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi68,h15]) ).
fof(f24,axiom,
! [A,B,C,D,E,F] :
( ( cong(C,D,E,F)
& cong(A,B,C,D) )
=> cong(A,B,E,F) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD25) ).
fof(f24_nnf,plain,
! [A,B,C,D,E,F] :
( cong(A,B,E,F)
| ~ cong(C,D,E,F)
| ~ cong(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [A,B,C,D,E,F] :
( cong(A,B,E,F)
| ~ cong(C,D,E,F)
| ~ cong(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c24,plain,
( cong(X0,X1,X4,X5)
| ~ cong(X2,X3,X4,X5)
| ~ cong(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(hi24,axiom,
ifeq(cong(X0,X1,X2,X3),true,ifeq(cong(X2,X3,X4,X5),true,cong(X0,X1,X4,X5),true),true) = true,
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(h382,plain,
cong(sk26,sk24,sk26,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi24,h39,h12]) ).
fof(f67,axiom,
! [A,B,C] :
( ( coll(A,B,C)
& cong(A,B,A,C) )
=> midp(A,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD67) ).
fof(f67_nnf,plain,
! [A,B,C] :
( midp(A,B,C)
| ~ coll(A,B,C)
| ~ cong(A,B,A,C) ),
inference(nnf_transformation,[status(thm)],[f67]) ).
fof(f67_sk,plain,
! [A,B,C] :
( midp(A,B,C)
| ~ coll(A,B,C)
| ~ cong(A,B,A,C) ),
inference(skolemisation,[status(esa)],[f67_nnf]) ).
cnf(c67,plain,
( midp(X0,X1,X2)
| ~ coll(X0,X1,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(esa)],[f67_sk]) ).
cnf(hi67,axiom,
ifeq(cong(X0,X1,X0,X2),true,ifeq(coll(X0,X1,X2),true,midp(X0,X1,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c67]) ).
cnf(h469,plain,
midp(sk26,sk24,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi67,h382,h131]) ).
cnf(c113,plain,
perp(sk23,sk22,sk20,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi113,negated_conjecture,
perp(sk23,sk22,sk20,sk21) = true,
inference(equality_encoding,[status(esa)],[c113]) ).
cnf(h359,plain,
perp(sk20,sk21,sk23,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi113]) ).
fof(f8,axiom,
! [A,B,C,D,E,F] :
( ( perp(C,D,E,F)
& perp(A,B,C,D) )
=> para(A,B,E,F) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD9) ).
fof(f8_nnf,plain,
! [A,B,C,D,E,F] :
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [A,B,C,D,E,F] :
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( para(X0,X1,X4,X5)
| ~ perp(X2,X3,X4,X5)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi8,axiom,
ifeq(perp(X0,X1,X2,X3),true,ifeq(perp(X2,X3,X4,X5),true,para(X0,X1,X4,X5),true),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(h391,plain,
para(sk23,sk22,sk23,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi113,h359]) ).
cnf(c114,plain,
coll(sk23,sk20,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi114,negated_conjecture,
coll(sk23,sk20,sk21) = true,
inference(equality_encoding,[status(esa)],[c114]) ).
cnf(h0,plain,
coll(sk21,sk21,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi114,hi114]) ).
cnf(h16,plain,
coll(sk23,sk23,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi2,h0,h0]) ).
cnf(h44,plain,
coll(sk23,sk21,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi0,h16]) ).
cnf(h82,plain,
coll(sk23,sk23,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi2,h44,h44]) ).
cnf(h38,plain,
coll(sk26,sk24,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi0,h11]) ).
cnf(h80,plain,
coll(sk23,sk23,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi2,h38,h38]) ).
cnf(h145,plain,
coll(sk26,sk23,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi2,h80,h82]) ).
cnf(h381,plain,
cong(sk26,sk23,sk26,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi24,h12,h39]) ).
cnf(h450,plain,
midp(sk26,sk23,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi67,h381,h145]) ).
fof(f64,axiom,
! [A,B,C,D,M] :
( ( para(A,D,B,C)
& para(A,C,B,D)
& midp(M,A,B) )
=> midp(M,C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD64) ).
fof(f64_nnf,plain,
! [A,B,C,D,M] :
( midp(M,C,D)
| ~ para(A,D,B,C)
| ~ para(A,C,B,D)
| ~ midp(M,A,B) ),
inference(nnf_transformation,[status(thm)],[f64]) ).
fof(f64_sk,plain,
! [M,A,B,C,D] :
( midp(M,C,D)
| ~ para(A,D,B,C)
| ~ para(A,C,B,D)
| ~ midp(M,A,B) ),
inference(skolemisation,[status(esa)],[f64_nnf]) ).
cnf(c64,plain,
( midp(X4,X2,X3)
| ~ para(X0,X3,X1,X2)
| ~ para(X0,X2,X1,X3)
| ~ midp(X4,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f64_sk]) ).
cnf(hi64,axiom,
ifeq(midp(X0,X1,X2),true,ifeq(para(X1,X3,X2,X4),true,ifeq(para(X1,X4,X2,X3),true,midp(X0,X3,X4),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c64]) ).
cnf(h487,plain,
midp(sk26,sk22,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi64,h450,h391,h391]) ).
fof(f63,axiom,
! [A,B,C,D,M] :
( ( midp(M,C,D)
& midp(M,A,B) )
=> para(A,C,B,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD63) ).
fof(f63_nnf,plain,
! [A,B,C,D,M] :
( para(A,C,B,D)
| ~ midp(M,C,D)
| ~ midp(M,A,B) ),
inference(nnf_transformation,[status(thm)],[f63]) ).
fof(f63_sk,plain,
! [M,A,B,C,D] :
( para(A,C,B,D)
| ~ midp(M,C,D)
| ~ midp(M,A,B) ),
inference(skolemisation,[status(esa)],[f63_nnf]) ).
cnf(c63,plain,
( para(X0,X2,X1,X3)
| ~ midp(X4,X2,X3)
| ~ midp(X4,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f63_sk]) ).
cnf(hi63,axiom,
ifeq(midp(X0,X1,X2),true,ifeq(midp(X0,X3,X4),true,para(X1,X3,X2,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c63]) ).
cnf(h494,plain,
para(sk22,sk24,sk22,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi63,h487,h469]) ).
cnf(c116,plain,
coll(sk24,sk20,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi116,negated_conjecture,
coll(sk24,sk20,sk22) = true,
inference(equality_encoding,[status(esa)],[c116]) ).
cnf(h3,plain,
coll(sk22,sk22,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi116,hi116]) ).
cnf(h23,plain,
coll(sk22,sk24,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi0,h3]) ).
cnf(h54,plain,
coll(sk22,sk22,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi2,h23,h23]) ).
cnf(c117,plain,
midp(sk25,sk22,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi117,negated_conjecture,
midp(sk25,sk22,sk21) = true,
inference(equality_encoding,[status(esa)],[c117]) ).
cnf(h6,plain,
coll(sk25,sk22,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi69,hi117]) ).
cnf(h30,plain,
coll(sk25,sk21,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi0,h6]) ).
cnf(h72,plain,
coll(sk22,sk22,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi2,h30,h30]) ).
cnf(h125,plain,
coll(sk25,sk22,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi2,h72,h54]) ).
cnf(h10,plain,
midp(sk25,sk21,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi10,hi117]) ).
cnf(h31,plain,
cong(sk25,sk21,sk25,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi68,h10]) ).
cnf(h7,plain,
cong(sk25,sk22,sk25,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi68,hi117]) ).
cnf(h371,plain,
cong(sk25,sk22,sk25,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi24,h7,h31]) ).
cnf(h413,plain,
midp(sk25,sk22,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi67,h371,h125]) ).
cnf(h610,plain,
midp(sk25,sk24,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi64,h413,h494,h494]) ).
fof(f44,axiom,
! [A,B,C,E,F] :
( ( midp(F,A,C)
& midp(E,A,B) )
=> para(E,F,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD44) ).
fof(f44_nnf,plain,
! [A,B,C,E,F] :
( para(E,F,B,C)
| ~ midp(F,A,C)
| ~ midp(E,A,B) ),
inference(nnf_transformation,[status(thm)],[f44]) ).
fof(f44_sk,plain,
! [E,A,B,F,C] :
( para(E,F,B,C)
| ~ midp(F,A,C)
| ~ midp(E,A,B) ),
inference(skolemisation,[status(esa)],[f44_nnf]) ).
cnf(c44,plain,
( para(X3,X4,X1,X2)
| ~ midp(X4,X0,X2)
| ~ midp(X3,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f44_sk]) ).
cnf(hi44,axiom,
ifeq(midp(X0,X1,X2),true,ifeq(midp(X3,X1,X4),true,para(X0,X3,X2,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c44]) ).
cnf(h619,plain,
para(sk25,sk26,sk24,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi44,h610,h469]) ).
fof(f9,axiom,
! [A,B,C,D,E,F] :
( ( perp(C,D,E,F)
& para(A,B,C,D) )
=> perp(A,B,E,F) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD10) ).
fof(f9_nnf,plain,
! [A,B,C,D,E,F] :
( perp(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ para(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [A,B,C,D,E,F] :
( perp(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ para(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( perp(X0,X1,X4,X5)
| ~ perp(X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(hi9,axiom,
ifeq(para(X0,X1,X2,X3),true,ifeq(perp(X2,X3,X4,X5),true,perp(X0,X1,X4,X5),true),true) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t131,plain,
perp(sk25,sk26,sk23,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi9,h619,h536]) ).
cnf(t1545,plain,
perp(sk25,sk26,sk23,sk24) = true,
inference(orient,[status(thm)],[t131]) ).
cnf(c119,plain,
~ perp(sk25,sk26,sk23,sk24),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(goal_0,negated_conjecture,
perp(sk25,sk26,sk23,sk24) != true,
inference(equality_encoding,[status(esa)],[c119]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t1545]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO541+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/5.46 % Computer : n007.cluster.edu
% 0.18/5.46 % Model : x86_64 x86_64
% 0.18/5.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.46 % Memory : 8046.5625MB
% 0.18/5.46 % OS : Linux 6.8.0-71-generic
% 0.18/5.46 % CPULimit : 300
% 0.18/5.46 % WCLimit : 300
% 0.18/5.46 % DateTime : Wed Sep 23 12:19:27 UTC 2026
% 0.18/5.47 % CPUTime :
% 0.18/5.47 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 14.73/7.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.73/7.40 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------