%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO552+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 : n015.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 01:18:08 PM UTC 2026
% Result : Theorem 249.98s 32.46s
% Output : Proof 249.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 70
% Number of leaves : 32
% Syntax : Number of formulae : 315 ( 191 unt; 0 def)
% Number of atoms : 526 ( 186 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 355 ( 144 ~; 138 |; 41 &)
% ( 0 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-8 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-5 aty)
% Number of variables : 974 ( 54 sgn 442 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f94,conjecture,
! [A,B,C,O,D,E,F,NWPNT1] :
( ( midp(F,B,A)
& coll(E,B,D)
& coll(E,A,C)
& circle(O,A,D,NWPNT1)
& perp(A,C,B,D)
& circle(O,A,B,C) )
=> perp(F,E,C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exemplo6GDDFULL012012) ).
fof(f94_neg,negated_conjecture,
~ ! [A,B,C,O,D,E,F,NWPNT1] :
( ( midp(F,B,A)
& coll(E,B,D)
& coll(E,A,C)
& circle(O,A,D,NWPNT1)
& perp(A,C,B,D)
& circle(O,A,B,C) )
=> perp(F,E,C,D) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,B,C,O,D,E,F,NWPNT1] :
( ~ perp(F,E,C,D)
& midp(F,B,A)
& coll(E,B,D)
& coll(E,A,C)
& circle(O,A,D,NWPNT1)
& perp(A,C,B,D)
& circle(O,A,B,C) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ perp(sk26,sk25,sk22,sk24)
& midp(sk26,sk21,sk20)
& coll(sk25,sk21,sk24)
& coll(sk25,sk20,sk22)
& circle(sk23,sk20,sk24,sk27)
& perp(sk20,sk22,sk21,sk24)
& circle(sk23,sk20,sk21,sk22) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24,sk25,sk26,sk27])],[f94_nnf]) ).
cnf(c119,plain,
~ perp(sk26,sk25,sk22,sk24),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(t66,plain,
perp(sk26,sk25,sk22,sk24) = false,
inference(equality_encoding,[status(esa)],[c119]) ).
cnf(t3178,plain,
perp(sk26,sk25,sk22,sk24) = false,
inference(orient,[status(thm)],[t66]) ).
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(t112,plain,
ifeq(perp(X1,X2,X3,X4),true,perp(X3,X4,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t274,plain,
ifeq(perp(X1,X2,X3,X4),true,perp(X3,X4,X1,X2),true) = true,
inference(orient,[status(thm)],[t112]) ).
cnf(t3182,plain,
true = ifeq(perp(sk22,sk24,sk26,sk25),true,false,true),
inference(cp,[status(thm)],[t274,t3178]) ).
cnf(t8673,plain,
ifeq(perp(sk22,sk24,sk26,sk25),true,false,true) = true,
inference(orient,[status(thm)],[t3182]) ).
fof(f74,axiom,
! [A,B,C,D,P,Q,U,V] :
( ( perp(P,Q,U,V)
& eqangle(A,B,C,D,P,Q,U,V) )
=> perp(A,B,C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD74) ).
fof(f74_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( perp(A,B,C,D)
| ~ perp(P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f74]) ).
fof(f74_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( perp(A,B,C,D)
| ~ perp(P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f74_nnf]) ).
cnf(c74,plain,
( perp(X0,X1,X2,X3)
| ~ perp(X4,X5,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f74_sk]) ).
cnf(t211,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,ifeq(perp(X5,X6,X7,X8),true,perp(X1,X2,X3,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c74]) ).
cnf(t301,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,ifeq(perp(X5,X6,X7,X8),true,perp(X1,X2,X3,X4),true),true) = true,
inference(orient,[status(thm)],[t211]) ).
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]) ).
cnf(c118,plain,
midp(sk26,sk21,sk20),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi118,negated_conjecture,
midp(sk26,sk21,sk20) = true,
inference(equality_encoding,[status(esa)],[c118]) ).
cnf(h14,plain,
coll(sk26,sk21,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi69,hi118]) ).
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(h44,plain,
coll(sk20,sk20,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi2,h14,h14]) ).
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(c116,plain,
coll(sk25,sk20,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi116,negated_conjecture,
coll(sk25,sk20,sk22) = true,
inference(equality_encoding,[status(esa)],[c116]) ).
cnf(h6,plain,
coll(sk25,sk22,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi116]) ).
cnf(h32,plain,
coll(sk20,sk20,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi2,h6,h6]) ).
cnf(h141,plain,
coll(sk25,sk26,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi2,h32,h44]) ).
cnf(h1038,plain,
coll(sk25,sk20,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi0,h141]) ).
cnf(h129,plain,
coll(sk20,sk25,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi0,h32]) ).
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(h438,plain,
coll(sk25,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi1,h129]) ).
cnf(h3404,plain,
coll(sk20,sk26,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi2,h438,h1038]) ).
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(h15,plain,
cong(sk26,sk21,sk26,sk20) = 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(h71,plain,
circle(sk26,sk21,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi11,h15,h15]) ).
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(h427,plain,
perp(sk21,sk20,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi53,h71,h14]) ).
fof(f90,axiom,
! [A,B,C,E,F] :
? [P] :
( ( coll(B,E,F)
& perp(A,C,C,B) )
=> ( perp(P,A,E,F)
& coll(P,E,F) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleX15) ).
fof(f90_nnf,plain,
! [A,B,C,E,F] :
? [P] :
( ( perp(P,A,E,F)
& coll(P,E,F) )
| ~ coll(B,E,F)
| ~ perp(A,C,C,B) ),
inference(nnf_transformation,[status(thm)],[f90]) ).
fof(f90_sk,plain,
! [A,C,B,E,F] :
( ( perp(sk16(A,B,C,E,F),A,E,F)
& coll(sk16(A,B,C,E,F),E,F) )
| ~ coll(B,E,F)
| ~ perp(A,C,C,B) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk16])],[f90_nnf]) ).
cnf(c107,plain,
( perp(sk16(X0,X1,X2,X3,X4),X0,X3,X4)
| ~ coll(X1,X3,X4)
| ~ perp(X0,X2,X2,X1) ),
inference(cnf_transformation,[status(esa)],[f90_sk]) ).
cnf(hi107,axiom,
ifeq(perp(X0,X1,X1,X2),true,ifeq(coll(X2,X3,X4),true,perp(sk16(X0,X2,X1,X3,X4),X0,X3,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c107]) ).
cnf(t87,plain,
perp(sk16(sk21,sk20,sk20,sk26,sk25),sk21,sk26,sk25) = true,
inference(hyper_resolution,[status(thm)],[hi107,h427,h3404]) ).
cnf(t1092,plain,
perp(sk16(sk21,sk20,sk20,sk26,sk25),sk21,sk26,sk25) = true,
inference(orient,[status(thm)],[t87]) ).
cnf(t1102,plain,
true = ifeq(eqangle(X1,X2,X3,X4,sk16(sk21,sk20,sk20,sk26,sk25),sk21,sk26,sk25),true,ifeq(true,true,perp(X1,X2,X3,X4),true),true),
inference(cp,[status(thm)],[t301,t1092]) ).
cnf(t57,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t57]) ).
cnf(t40355,plain,
true = ifeq(eqangle(X1,X2,X3,X4,sk16(sk21,sk20,sk20,sk26,sk25),sk21,sk26,sk25),true,perp(X1,X2,X3,X4),true),
inference(step,[status(thm)],[t1102,t256]) ).
cnf(t37033,plain,
ifeq(eqangle(X1,X2,X3,X4,sk16(sk21,sk20,sk20,sk26,sk25),sk21,sk26,sk25),true,perp(X1,X2,X3,X4),true) = true,
inference(orient,[status(thm)],[t40355]) ).
fof(f39,axiom,
! [A,B,C,D,P,Q] :
( para(A,B,C,D)
=> eqangle(A,B,P,Q,C,D,P,Q) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD40) ).
fof(f39_nnf,plain,
! [A,B,C,D,P,Q] :
( eqangle(A,B,P,Q,C,D,P,Q)
| ~ para(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f39]) ).
fof(f39_sk,plain,
! [A,B,C,D,P,Q] :
( eqangle(A,B,P,Q,C,D,P,Q)
| ~ para(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f39_nnf]) ).
cnf(c39,plain,
( eqangle(X0,X1,X4,X5,X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
cnf(t149,plain,
ifeq(para(X1,X2,X3,X4),true,eqangle(X1,X2,X5,X6,X3,X4,X5,X6),true) = true,
inference(equality_encoding,[status(esa)],[c39]) ).
cnf(t330,plain,
ifeq(para(X1,X2,X3,X4),true,eqangle(X1,X2,X5,X6,X3,X4,X5,X6),true) = true,
inference(orient,[status(thm)],[t149]) ).
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(t180,plain,
ifeq(perp(X1,X2,X3,X4),true,ifeq(perp(X3,X4,X5,X6),true,para(X1,X2,X5,X6),true),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t265,plain,
ifeq(perp(X1,X2,X3,X4),true,ifeq(perp(X3,X4,X5,X6),true,para(X1,X2,X5,X6),true),true) = true,
inference(orient,[status(thm)],[t180]) ).
fof(f56,axiom,
! [A,B,P,Q] :
( ( cong(A,Q,B,Q)
& cong(A,P,B,P) )
=> perp(A,B,P,Q) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD56) ).
fof(f56_nnf,plain,
! [A,B,P,Q] :
( perp(A,B,P,Q)
| ~ cong(A,Q,B,Q)
| ~ cong(A,P,B,P) ),
inference(nnf_transformation,[status(thm)],[f56]) ).
fof(f56_sk,plain,
! [A,P,B,Q] :
( perp(A,B,P,Q)
| ~ cong(A,Q,B,Q)
| ~ cong(A,P,B,P) ),
inference(skolemisation,[status(esa)],[f56_nnf]) ).
cnf(c56,plain,
( perp(X0,X1,X2,X3)
| ~ cong(X0,X3,X1,X3)
| ~ cong(X0,X2,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f56_sk]) ).
cnf(t167,plain,
ifeq(cong(X1,X2,X3,X2),true,ifeq(cong(X1,X4,X3,X4),true,perp(X1,X3,X2,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c56]) ).
cnf(t289,plain,
ifeq(cong(X1,X2,X3,X2),true,ifeq(cong(X1,X4,X3,X4),true,perp(X1,X3,X2,X4),true),true) = true,
inference(orient,[status(thm)],[t167]) ).
cnf(t100,plain,
ifeq(midp(X1,X2,X3),true,cong(X1,X2,X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c68]) ).
cnf(t351,plain,
ifeq(midp(X1,X2,X3),true,cong(X1,X2,X1,X3),true) = true,
inference(orient,[status(thm)],[t100]) ).
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(t226,plain,
ifeq(midp(X1,X2,X3),true,ifeq(para(X2,X4,X3,X5),true,ifeq(para(X2,X5,X3,X4),true,midp(X1,X4,X5),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c64]) ).
cnf(t341,plain,
ifeq(midp(X1,X2,X3),true,ifeq(para(X2,X4,X3,X5),true,ifeq(para(X2,X5,X3,X4),true,midp(X1,X4,X5),true),true),true) = true,
inference(orient,[status(thm)],[t226]) ).
fof(f38,axiom,
! [A,B,C,D,P,Q] :
( eqangle(A,B,P,Q,C,D,P,Q)
=> para(A,B,C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD39) ).
fof(f38_nnf,plain,
! [A,B,C,D,P,Q] :
( para(A,B,C,D)
| ~ eqangle(A,B,P,Q,C,D,P,Q) ),
inference(nnf_transformation,[status(thm)],[f38]) ).
fof(f38_sk,plain,
! [A,B,P,Q,C,D] :
( para(A,B,C,D)
| ~ eqangle(A,B,P,Q,C,D,P,Q) ),
inference(skolemisation,[status(esa)],[f38_nnf]) ).
cnf(c38,plain,
( para(X0,X1,X2,X3)
| ~ eqangle(X0,X1,X4,X5,X2,X3,X4,X5) ),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
cnf(t148,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X3,X4),true,para(X1,X2,X5,X6),true) = true,
inference(equality_encoding,[status(esa)],[c38]) ).
cnf(t314,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X3,X4),true,para(X1,X2,X5,X6),true) = true,
inference(orient,[status(thm)],[t148]) ).
fof(f18,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(C,D,A,B,U,V,P,Q) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD19) ).
fof(f18_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(C,D,A,B,U,V,P,Q)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(C,D,A,B,U,V,P,Q)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
( eqangle(X2,X3,X0,X1,X6,X7,X4,X5)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(t172,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,eqangle(X3,X4,X1,X2,X7,X8,X5,X6),true) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t308,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,eqangle(X3,X4,X1,X2,X7,X8,X5,X6),true) = true,
inference(orient,[status(thm)],[t172]) ).
fof(f40,axiom,
! [A,B,P,Q] :
( cyclic(A,B,P,Q)
=> eqangle(P,A,P,B,Q,A,Q,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD41) ).
fof(f40_nnf,plain,
! [A,B,P,Q] :
( eqangle(P,A,P,B,Q,A,Q,B)
| ~ cyclic(A,B,P,Q) ),
inference(nnf_transformation,[status(thm)],[f40]) ).
fof(f40_sk,plain,
! [A,B,P,Q] :
( eqangle(P,A,P,B,Q,A,Q,B)
| ~ cyclic(A,B,P,Q) ),
inference(skolemisation,[status(esa)],[f40_nnf]) ).
cnf(c40,plain,
( eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f40_sk]) ).
cnf(t147,plain,
ifeq(cyclic(X1,X2,X3,X4),true,eqangle(X3,X1,X3,X2,X4,X1,X4,X2),true) = true,
inference(equality_encoding,[status(esa)],[c40]) ).
cnf(t359,plain,
ifeq(cyclic(X1,X2,X3,X4),true,eqangle(X3,X1,X3,X2,X4,X1,X4,X2),true) = true,
inference(orient,[status(thm)],[t147]) ).
cnf(h45,plain,
coll(sk21,sk26,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi1,h14]) ).
cnf(h156,plain,
coll(sk20,sk20,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi2,h45,h45]) ).
cnf(h1091,plain,
coll(sk21,sk21,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi2,h156,h156]) ).
cnf(hi7,axiom,
ifeq(perp(X0,X1,X2,X3),true,perp(X2,X3,X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(c114,plain,
perp(sk20,sk22,sk21,sk24),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi114,negated_conjecture,
perp(sk20,sk22,sk21,sk24) = true,
inference(equality_encoding,[status(esa)],[c114]) ).
cnf(h1,plain,
perp(sk21,sk24,sk20,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi114]) ).
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(h24,plain,
para(sk21,sk24,sk21,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi8,h1,hi114]) ).
cnf(hi39,axiom,
ifeq(para(X0,X1,X2,X3),true,eqangle(X0,X1,X4,X5,X2,X3,X4,X5),true) = true,
inference(equality_encoding,[status(esa)],[c39]) ).
cnf(h114,plain,
eqangle(sk21,sk24,V0,V1,sk21,sk24,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h24]) ).
fof(f42,axiom,
! [A,B,P,Q] :
( ( coll(P,Q,B)
& eqangle(P,A,P,B,Q,A,Q,B) )
=> cyclic(A,B,P,Q) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD42b) ).
fof(f42_nnf,plain,
! [A,B,P,Q] :
( cyclic(A,B,P,Q)
| ~ coll(P,Q,B)
| ~ eqangle(P,A,P,B,Q,A,Q,B) ),
inference(nnf_transformation,[status(thm)],[f42]) ).
fof(f42_sk,plain,
! [P,A,B,Q] :
( cyclic(A,B,P,Q)
| ~ coll(P,Q,B)
| ~ eqangle(P,A,P,B,Q,A,Q,B) ),
inference(skolemisation,[status(esa)],[f42_nnf]) ).
cnf(c42,plain,
( cyclic(X0,X1,X2,X3)
| ~ coll(X2,X3,X1)
| ~ eqangle(X2,X0,X2,X1,X3,X0,X3,X1) ),
inference(cnf_transformation,[status(esa)],[f42_sk]) ).
cnf(hi42,axiom,
ifeq(eqangle(X0,X1,X0,X2,X3,X1,X3,X2),true,ifeq(coll(X0,X3,X2),true,cyclic(X1,X2,X0,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c42]) ).
cnf(t51,plain,
cyclic(sk24,sk20,sk21,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi42,h114,h1091]) ).
cnf(t2580,plain,
cyclic(sk24,sk20,sk21,sk21) = true,
inference(orient,[status(thm)],[t51]) ).
cnf(t2585,plain,
true = ifeq(true,true,eqangle(sk21,sk24,sk21,sk20,sk21,sk24,sk21,sk20),true),
inference(cp,[status(thm)],[t359,t2580]) ).
cnf(t37341,plain,
true = eqangle(sk21,sk24,sk21,sk20,sk21,sk24,sk21,sk20),
inference(step,[status(thm)],[t2585,t256]) ).
cnf(t6260,plain,
eqangle(sk21,sk24,sk21,sk20,sk21,sk24,sk21,sk20) = true,
inference(orient,[status(thm)],[t37341]) ).
cnf(t6261,plain,
true = ifeq(true,true,para(sk21,sk24,sk21,sk24),true),
inference(cp,[status(thm)],[t314,t6260]) ).
cnf(t37342,plain,
true = para(sk21,sk24,sk21,sk24),
inference(step,[status(thm)],[t6261,t256]) ).
cnf(t6276,plain,
para(sk21,sk24,sk21,sk24) = true,
inference(orient,[status(thm)],[t37342]) ).
cnf(t6280,plain,
true = ifeq(true,true,eqangle(sk21,sk24,X1,X2,sk21,sk24,X1,X2),true),
inference(cp,[status(thm)],[t330,t6276]) ).
cnf(t37812,plain,
true = eqangle(sk21,sk24,X1,X2,sk21,sk24,X1,X2),
inference(step,[status(thm)],[t6280,t256]) ).
cnf(t12775,plain,
eqangle(sk21,sk24,X1,X2,sk21,sk24,X1,X2) = true,
inference(orient,[status(thm)],[t37812]) ).
cnf(t12780,plain,
true = ifeq(true,true,eqangle(X1,X2,sk21,sk24,X1,X2,sk21,sk24),true),
inference(cp,[status(thm)],[t308,t12775]) ).
cnf(t38501,plain,
true = eqangle(X1,X2,sk21,sk24,X1,X2,sk21,sk24),
inference(step,[status(thm)],[t12780,t256]) ).
cnf(t19983,plain,
eqangle(X1,X2,sk21,sk24,X1,X2,sk21,sk24) = true,
inference(orient,[status(thm)],[t38501]) ).
cnf(t19985,plain,
true = ifeq(true,true,para(X1,X2,X1,X2),true),
inference(cp,[status(thm)],[t314,t19983]) ).
cnf(t38502,plain,
true = para(X1,X2,X1,X2),
inference(step,[status(thm)],[t19985,t256]) ).
cnf(t20007,plain,
para(X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t38502]) ).
cnf(t20023,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(true,true,ifeq(para(X2,X3,X2,X3),true,midp(X1,X3,X3),true),true),true),
inference(cp,[status(thm)],[t341,t20007]) ).
cnf(t40122,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(para(X2,X3,X2,X3),true,midp(X1,X3,X3),true),true),
inference(step,[status(thm)],[t20023,t256]) ).
cnf(t40123,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(true,true,midp(X1,X3,X3),true),true),
inference(step,[status(thm)],[t40122,t20007]) ).
cnf(t40124,plain,
true = ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true),
inference(step,[status(thm)],[t40123,t256]) ).
cnf(t34412,plain,
ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true) = true,
inference(orient,[status(thm)],[t40124]) ).
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(t158,plain,
ifeq(cong(X1,X2,X1,X3),true,ifeq(coll(X1,X2,X3),true,midp(X1,X2,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c67]) ).
cnf(t290,plain,
ifeq(cong(X1,X2,X1,X3),true,ifeq(coll(X1,X2,X3),true,midp(X1,X2,X3),true),true) = true,
inference(orient,[status(thm)],[t158]) ).
fof(f66,axiom,
! [A,B,C] :
( para(A,B,A,C)
=> coll(A,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD66) ).
fof(f66_nnf,plain,
! [A,B,C] :
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(nnf_transformation,[status(thm)],[f66]) ).
fof(f66_sk,plain,
! [A,B,C] :
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(skolemisation,[status(esa)],[f66_nnf]) ).
cnf(c66,plain,
( coll(X0,X1,X2)
| ~ para(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(esa)],[f66_sk]) ).
cnf(t101,plain,
ifeq(para(X1,X2,X1,X3),true,coll(X1,X2,X3),true) = true,
inference(equality_encoding,[status(esa)],[c66]) ).
cnf(t337,plain,
ifeq(para(X1,X2,X1,X3),true,coll(X1,X2,X3),true) = true,
inference(orient,[status(thm)],[t101]) ).
fof(f3,axiom,
! [A,B,C,D] :
( para(A,B,C,D)
=> para(A,B,D,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD4) ).
fof(f3_nnf,plain,
! [A,B,C,D] :
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B,C,D] :
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( para(X0,X1,X3,X2)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t109,plain,
ifeq(para(X1,X2,X3,X4),true,para(X1,X2,X4,X3),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t334,plain,
ifeq(para(X1,X2,X3,X4),true,para(X1,X2,X4,X3),true) = true,
inference(orient,[status(thm)],[t109]) ).
fof(f4,axiom,
! [A,B,C,D] :
( para(A,B,C,D)
=> para(C,D,A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD5) ).
fof(f4_nnf,plain,
! [A,B,C,D] :
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B,C,D] :
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( para(X2,X3,X0,X1)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t110,plain,
ifeq(para(X1,X2,X3,X4),true,para(X3,X4,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t331,plain,
ifeq(para(X1,X2,X3,X4),true,para(X3,X4,X1,X2),true) = true,
inference(orient,[status(thm)],[t110]) ).
fof(f15,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(B,A,C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD16) ).
fof(f15_nnf,plain,
! [A,B,C,D] :
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [A,B,C,D] :
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
( cyclic(X1,X0,X2,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(t108,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X2,X1,X3,X4),true) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t360,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X2,X1,X3,X4),true) = true,
inference(orient,[status(thm)],[t108]) ).
cnf(h23,plain,
para(sk20,sk22,sk20,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi114,h1]) ).
cnf(h109,plain,
eqangle(sk20,sk22,V0,V1,sk20,sk22,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h23]) ).
cnf(t49,plain,
cyclic(sk22,sk25,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi42,h109,h32]) ).
cnf(t2798,plain,
cyclic(sk22,sk25,sk20,sk20) = true,
inference(orient,[status(thm)],[t49]) ).
cnf(t2801,plain,
true = ifeq(true,true,cyclic(sk25,sk22,sk20,sk20),true),
inference(cp,[status(thm)],[t360,t2798]) ).
cnf(t37244,plain,
true = cyclic(sk25,sk22,sk20,sk20),
inference(step,[status(thm)],[t2801,t256]) ).
cnf(t4537,plain,
cyclic(sk25,sk22,sk20,sk20) = true,
inference(orient,[status(thm)],[t37244]) ).
cnf(t4540,plain,
true = ifeq(true,true,eqangle(sk20,sk25,sk20,sk22,sk20,sk25,sk20,sk22),true),
inference(cp,[status(thm)],[t359,t4537]) ).
cnf(t37602,plain,
true = eqangle(sk20,sk25,sk20,sk22,sk20,sk25,sk20,sk22),
inference(step,[status(thm)],[t4540,t256]) ).
cnf(t10909,plain,
eqangle(sk20,sk25,sk20,sk22,sk20,sk25,sk20,sk22) = true,
inference(orient,[status(thm)],[t37602]) ).
cnf(t10910,plain,
true = ifeq(true,true,para(sk20,sk25,sk20,sk25),true),
inference(cp,[status(thm)],[t314,t10909]) ).
cnf(t37603,plain,
true = para(sk20,sk25,sk20,sk25),
inference(step,[status(thm)],[t10910,t256]) ).
cnf(t10922,plain,
para(sk20,sk25,sk20,sk25) = true,
inference(orient,[status(thm)],[t37603]) ).
cnf(t10924,plain,
true = ifeq(true,true,para(sk20,sk25,sk25,sk20),true),
inference(cp,[status(thm)],[t334,t10922]) ).
cnf(t37610,plain,
true = para(sk20,sk25,sk25,sk20),
inference(step,[status(thm)],[t10924,t256]) ).
cnf(t11065,plain,
para(sk20,sk25,sk25,sk20) = true,
inference(orient,[status(thm)],[t37610]) ).
cnf(t11066,plain,
true = ifeq(true,true,para(sk25,sk20,sk20,sk25),true),
inference(cp,[status(thm)],[t331,t11065]) ).
cnf(t37611,plain,
true = para(sk25,sk20,sk20,sk25),
inference(step,[status(thm)],[t11066,t256]) ).
cnf(t11089,plain,
para(sk25,sk20,sk20,sk25) = true,
inference(orient,[status(thm)],[t37611]) ).
cnf(t11090,plain,
true = ifeq(true,true,para(sk25,sk20,sk25,sk20),true),
inference(cp,[status(thm)],[t334,t11089]) ).
cnf(t37612,plain,
true = para(sk25,sk20,sk25,sk20),
inference(step,[status(thm)],[t11090,t256]) ).
cnf(t11112,plain,
para(sk25,sk20,sk25,sk20) = true,
inference(orient,[status(thm)],[t37612]) ).
cnf(t11113,plain,
true = ifeq(true,true,coll(sk25,sk20,sk20),true),
inference(cp,[status(thm)],[t337,t11112]) ).
cnf(t37613,plain,
true = coll(sk25,sk20,sk20),
inference(step,[status(thm)],[t11113,t256]) ).
cnf(t11136,plain,
coll(sk25,sk20,sk20) = true,
inference(orient,[status(thm)],[t37613]) ).
cnf(t11145,plain,
true = ifeq(cong(sk25,sk20,sk25,sk20),true,ifeq(true,true,midp(sk25,sk20,sk20),true),true),
inference(cp,[status(thm)],[t290,t11136]) ).
fof(f75,axiom,
! [A,B,C,D,P,Q,U,V] :
( ( cong(P,Q,U,V)
& eqratio(A,B,C,D,P,Q,U,V) )
=> cong(A,B,C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD75) ).
fof(f75_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( cong(A,B,C,D)
| ~ cong(P,Q,U,V)
| ~ eqratio(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f75]) ).
fof(f75_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( cong(A,B,C,D)
| ~ cong(P,Q,U,V)
| ~ eqratio(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f75_nnf]) ).
cnf(c75,plain,
( cong(X0,X1,X2,X3)
| ~ cong(X4,X5,X6,X7)
| ~ eqratio(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f75_sk]) ).
cnf(t212,plain,
ifeq(eqratio(X1,X2,X3,X4,X5,X6,X7,X8),true,ifeq(cong(X5,X6,X7,X8),true,cong(X1,X2,X3,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c75]) ).
cnf(t366,plain,
ifeq(eqratio(X1,X2,X3,X4,X5,X6,X7,X8),true,ifeq(cong(X5,X6,X7,X8),true,cong(X1,X2,X3,X4),true),true) = true,
inference(orient,[status(thm)],[t212]) ).
fof(f28,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqratio(A,B,C,D,P,Q,U,V)
=> eqratio(A,B,P,Q,C,D,U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD29) ).
fof(f28_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( eqratio(A,B,P,Q,C,D,U,V)
| ~ eqratio(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( eqratio(A,B,P,Q,C,D,U,V)
| ~ eqratio(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f28_nnf]) ).
cnf(c28,plain,
( eqratio(X0,X1,X4,X5,X2,X3,X6,X7)
| ~ eqratio(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(t174,plain,
ifeq(eqratio(X1,X2,X3,X4,X5,X6,X7,X8),true,eqratio(X1,X2,X5,X6,X3,X4,X7,X8),true) = true,
inference(equality_encoding,[status(esa)],[c28]) ).
cnf(t376,plain,
ifeq(eqratio(X1,X2,X3,X4,X5,X6,X7,X8),true,eqratio(X1,X2,X5,X6,X3,X4,X7,X8),true) = true,
inference(orient,[status(thm)],[t174]) ).
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(h17,plain,
para(sk26,sk26,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi44,hi118,hi118]) ).
cnf(hi4,axiom,
ifeq(para(X0,X1,X2,X3),true,para(X2,X3,X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(h98,plain,
para(sk20,sk20,sk26,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi4,h17]) ).
fof(f65,axiom,
! [A,B,C,D,O] :
( ( coll(O,B,D)
& coll(O,A,C)
& para(A,B,C,D) )
=> eqratio(O,A,A,C,O,B,B,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD65) ).
fof(f65_nnf,plain,
! [A,B,C,D,O] :
( eqratio(O,A,A,C,O,B,B,D)
| ~ coll(O,B,D)
| ~ coll(O,A,C)
| ~ para(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f65]) ).
fof(f65_sk,plain,
! [A,B,C,D,O] :
( eqratio(O,A,A,C,O,B,B,D)
| ~ coll(O,B,D)
| ~ coll(O,A,C)
| ~ para(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f65_nnf]) ).
cnf(c65,plain,
( eqratio(X4,X0,X0,X2,X4,X1,X1,X3)
| ~ coll(X4,X1,X3)
| ~ coll(X4,X0,X2)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f65_sk]) ).
cnf(hi65,axiom,
ifeq(para(X0,X1,X2,X3),true,ifeq(coll(X4,X0,X2),true,ifeq(coll(X4,X1,X3),true,eqratio(X4,X0,X0,X2,X4,X1,X1,X3),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c65]) ).
cnf(t74,plain,
eqratio(sk25,sk20,sk20,sk26,sk25,sk20,sk20,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi65,h98,h1038,h1038]) ).
cnf(t2908,plain,
eqratio(sk25,sk20,sk20,sk26,sk25,sk20,sk20,sk26) = true,
inference(orient,[status(thm)],[t74]) ).
cnf(t2909,plain,
true = ifeq(true,true,eqratio(sk25,sk20,sk25,sk20,sk20,sk26,sk20,sk26),true),
inference(cp,[status(thm)],[t376,t2908]) ).
cnf(t37451,plain,
true = eqratio(sk25,sk20,sk25,sk20,sk20,sk26,sk20,sk26),
inference(step,[status(thm)],[t2909,t256]) ).
cnf(t7677,plain,
eqratio(sk25,sk20,sk25,sk20,sk20,sk26,sk20,sk26) = true,
inference(orient,[status(thm)],[t37451]) ).
cnf(t7686,plain,
true = ifeq(true,true,ifeq(cong(sk20,sk26,sk20,sk26),true,cong(sk25,sk20,sk25,sk20),true),true),
inference(cp,[status(thm)],[t366,t7677]) ).
cnf(t37452,plain,
true = ifeq(cong(sk20,sk26,sk20,sk26),true,cong(sk25,sk20,sk25,sk20),true),
inference(step,[status(thm)],[t7686,t256]) ).
fof(f22,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(A,B,D,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD23) ).
fof(f22_nnf,plain,
! [A,B,C,D] :
( cong(A,B,D,C)
| ~ cong(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
! [A,B,C,D] :
( cong(A,B,D,C)
| ~ cong(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c22,plain,
( cong(X0,X1,X3,X2)
| ~ cong(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(hi22,axiom,
ifeq(cong(X0,X1,X2,X3),true,cong(X0,X1,X3,X2),true) = true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(h69,plain,
cong(sk26,sk21,sk20,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi22,h15]) ).
fof(f23,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(C,D,A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD24) ).
fof(f23_nnf,plain,
! [A,B,C,D] :
( cong(C,D,A,B)
| ~ cong(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [A,B,C,D] :
( cong(C,D,A,B)
| ~ cong(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c23,plain,
( cong(X2,X3,X0,X1)
| ~ cong(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(hi23,axiom,
ifeq(cong(X0,X1,X2,X3),true,cong(X2,X3,X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(h414,plain,
cong(sk20,sk26,sk26,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi23,h69]) ).
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(t33,plain,
cong(sk20,sk26,sk20,sk26) = true,
inference(hyper_resolution,[status(thm)],[hi24,h414,h69]) ).
cnf(t1260,plain,
cong(sk20,sk26,sk20,sk26) = true,
inference(orient,[status(thm)],[t33]) ).
cnf(t37453,plain,
true = ifeq(true,true,cong(sk25,sk20,sk25,sk20),true),
inference(step,[status(thm)],[t37452,t1260]) ).
cnf(t37454,plain,
true = cong(sk25,sk20,sk25,sk20),
inference(step,[status(thm)],[t37453,t256]) ).
cnf(t7688,plain,
cong(sk25,sk20,sk25,sk20) = true,
inference(orient,[status(thm)],[t37454]) ).
cnf(t37615,plain,
true = ifeq(true,true,ifeq(true,true,midp(sk25,sk20,sk20),true),true),
inference(step,[status(thm)],[t11145,t7688]) ).
cnf(t37616,plain,
true = ifeq(true,true,midp(sk25,sk20,sk20),true),
inference(step,[status(thm)],[t37615,t256]) ).
cnf(t37617,plain,
true = midp(sk25,sk20,sk20),
inference(step,[status(thm)],[t37616,t256]) ).
cnf(t11196,plain,
midp(sk25,sk20,sk20) = true,
inference(orient,[status(thm)],[t37617]) ).
cnf(t34413,plain,
true = ifeq(true,true,midp(sk25,X1,X1),true),
inference(cp,[status(thm)],[t34412,t11196]) ).
cnf(t40125,plain,
true = midp(sk25,X1,X1),
inference(step,[status(thm)],[t34413,t256]) ).
cnf(t34439,plain,
midp(sk25,X1,X1) = true,
inference(orient,[status(thm)],[t40125]) ).
cnf(t34440,plain,
true = ifeq(true,true,cong(sk25,X1,sk25,X1),true),
inference(cp,[status(thm)],[t351,t34439]) ).
cnf(t40131,plain,
true = cong(sk25,X1,sk25,X1),
inference(step,[status(thm)],[t34440,t256]) ).
cnf(t34559,plain,
cong(sk25,X1,sk25,X1) = true,
inference(orient,[status(thm)],[t40131]) ).
cnf(t34570,plain,
true = ifeq(true,true,ifeq(cong(sk25,X1,sk25,X1),true,perp(sk25,sk25,X2,X1),true),true),
inference(cp,[status(thm)],[t289,t34559]) ).
cnf(t40139,plain,
true = ifeq(cong(sk25,X1,sk25,X1),true,perp(sk25,sk25,X2,X1),true),
inference(step,[status(thm)],[t34570,t256]) ).
cnf(t40140,plain,
true = ifeq(true,true,perp(sk25,sk25,X2,X1),true),
inference(step,[status(thm)],[t40139,t34559]) ).
cnf(t40141,plain,
true = perp(sk25,sk25,X2,X1),
inference(step,[status(thm)],[t40140,t256]) ).
cnf(t34769,plain,
perp(sk25,sk25,X1,X2) = true,
inference(orient,[status(thm)],[t40141]) ).
cnf(t34776,plain,
true = ifeq(true,true,perp(X1,X2,sk25,sk25),true),
inference(cp,[status(thm)],[t274,t34769]) ).
cnf(t40166,plain,
true = perp(X1,X2,sk25,sk25),
inference(step,[status(thm)],[t34776,t256]) ).
cnf(t35166,plain,
perp(X1,X2,sk25,sk25) = true,
inference(orient,[status(thm)],[t40166]) ).
cnf(t35183,plain,
true = ifeq(true,true,ifeq(perp(sk25,sk25,X1,X2),true,para(X3,X4,X1,X2),true),true),
inference(cp,[status(thm)],[t265,t35166]) ).
cnf(t40197,plain,
true = ifeq(perp(sk25,sk25,X1,X2),true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t35183,t256]) ).
cnf(t40198,plain,
true = ifeq(true,true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t40197,t34769]) ).
cnf(t40199,plain,
true = para(X3,X4,X1,X2),
inference(step,[status(thm)],[t40198,t256]) ).
cnf(t35783,plain,
para(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t40199]) ).
cnf(t40212,plain,
ifeq(true,true,eqangle(X1,X2,X5,X6,X3,X4,X5,X6),true) = true,
inference(step,[status(thm)],[t330,t35783]) ).
cnf(t40213,plain,
eqangle(X1,X2,X5,X6,X3,X4,X5,X6) = true,
inference(step,[status(thm)],[t40212,t256]) ).
cnf(t35793,plain,
eqangle(X1,X2,X5,X6,X3,X4,X5,X6) = true,
inference(rw,[status(thm)],[t40213]) ).
cnf(t36716,plain,
eqangle(X1,X2,X3,X4,X5,X6,X3,X4) = true,
inference(orient,[status(thm)],[t35793]) ).
cnf(t37034,plain,
true = ifeq(true,true,perp(X1,X2,sk26,sk25),true),
inference(cp,[status(thm)],[t37033,t36716]) ).
cnf(t40356,plain,
true = perp(X1,X2,sk26,sk25),
inference(step,[status(thm)],[t37034,t256]) ).
cnf(t37150,plain,
perp(X1,X2,sk26,sk25) = true,
inference(orient,[status(thm)],[t40356]) ).
cnf(t40357,plain,
ifeq(true,true,false,true) = true,
inference(step,[status(thm)],[t8673,t37150]) ).
cnf(t40358,plain,
false = true,
inference(step,[status(thm)],[t40357,t256]) ).
cnf(t37183,plain,
false = true,
inference(rw,[status(thm)],[t40358]) ).
cnf(t37185,plain,
false = true,
inference(orient,[status(thm)],[t37183]) ).
cnf(t40360,plain,
perp(sk26,sk25,sk22,sk24) = true,
inference(step,[status(thm)],[t3178,t37185]) ).
cnf(t37186,plain,
perp(sk26,sk25,sk22,sk24) = true,
inference(orient,[status(thm)],[t40360]) ).
cnf(goal_0,negated_conjecture,
perp(sk26,sk25,sk22,sk24) != true,
inference(equality_encoding,[status(esa)],[c119]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t37186]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO552+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.57 % Computer : n015.cluster.edu
% 0.10/0.57 % Model : x86_64 x86_64
% 0.10/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.57 % Memory : 8046.5625MB
% 0.10/0.57 % OS : Linux 6.8.0-71-generic
% 0.10/0.57 % CPULimit : 300
% 0.10/0.57 % WCLimit : 300
% 0.10/0.57 % DateTime : Wed Sep 23 12:25:55 UTC 2026
% 0.10/0.57 % CPUTime :
% 0.10/0.57 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 249.98/32.46 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 249.98/32.46 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------