%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC123-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n019.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 03:07:59 PM UTC 2026
% Result : Unsatisfiable 51.90s 17.91s
% Output : CNFRefutation 51.90s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f240ERROR: Could not build tree for root c_93692ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause8) ).
fof(f11,axiom,
~ singletonP(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause11) ).
fof(f51,axiom,
! [X0,X1] : ssList(skaf45(X0,X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause51) ).
fof(f56,axiom,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause56) ).
fof(f57,axiom,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause57) ).
fof(f60,axiom,
! [X0] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause60) ).
fof(f64,axiom,
! [X0] :
( equalelemsP(cons(X0,nil))
| ~ ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause64) ).
fof(f74,axiom,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause74) ).
fof(f77,axiom,
! [X0] :
( nil = X0
| ssList(tl(X0))
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause77) ).
fof(f78,axiom,
! [X0] :
( nil = X0
| ssItem(hd(X0))
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause78) ).
fof(f79,axiom,
! [X0] :
( segmentP(nil,X0)
| ~ ssList(X0)
| nil != X0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause79) ).
fof(f83,axiom,
! [X0] :
( frontsegP(nil,X0)
| ~ ssList(X0)
| nil != X0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause83) ).
fof(f84,axiom,
! [X0] :
( nil = X0
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause84) ).
fof(f85,axiom,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause85) ).
fof(f86,axiom,
! [X0,X1] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause86) ).
fof(f101,axiom,
! [X0,X1] :
( X1 = X0
| neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause100) ).
fof(f102,plain,
! [X0,X1] :
( X0 = X1
| neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(reorient_equations,[],[f101]) ).
fof(f107,axiom,
! [X0] :
( nil = X0
| cons(hd(X0),tl(X0)) = X0
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause104) ).
fof(f119,axiom,
! [X0,X1] :
( singletonP(X1)
| ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,nil) != X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause116) ).
fof(f129,axiom,
! [X0,X1] :
( hd(app(X1,X0)) = hd(X1)
| nil = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause123) ).
fof(f134,axiom,
! [X0,X1] :
( X1 = X0
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause127) ).
fof(f135,plain,
! [X0,X1] :
( X0 = X1
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1) ),
inference(reorient_equations,[],[f134]) ).
fof(f143,axiom,
! [X0,X1] :
( app(X1,skaf45(X0,X1)) = X0
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause132) ).
fof(f155,axiom,
! [X2,X0,X1] :
( frontsegP(X2,X0)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause144) ).
fof(f164,axiom,
! [X2,X0,X1] :
( segmentP(X0,X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause152) ).
fof(f166,axiom,
! [X2,X0,X1] :
( frontsegP(X0,X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause154) ).
fof(f186,axiom,
! [X2,X3,X0,X1] :
( segmentP(app(app(X3,X0),X2),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ segmentP(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause172) ).
fof(f202,negated_conjecture,
ssList(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_3) ).
fof(f203,negated_conjecture,
ssList(sk4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_4) ).
fof(f204,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
fof(f205,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
fof(f206,negated_conjecture,
neq(sk2,nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
fof(f207,negated_conjecture,
frontsegP(sk4,sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
fof(f208,negated_conjecture,
equalelemsP(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
fof(f209,negated_conjecture,
! [X0] :
( ~ equalelemsP(X0)
| ~ segmentP(X0,sk3)
| ~ frontsegP(sk4,X0)
| ~ neq(sk3,X0)
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
fof(f210,negated_conjecture,
( ~ segmentP(sk2,sk1)
| ~ neq(sk1,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
fof(f213,plain,
neq(sk4,nil),
inference(definition_unfolding,[],[f206,f204]) ).
fof(f214,plain,
( ~ segmentP(sk4,sk3)
| ~ neq(sk3,nil) ),
inference(definition_unfolding,[],[f210,f205,f204,f205]) ).
fof(f215,plain,
( segmentP(nil,nil)
| ~ ssList(nil) ),
inference(equality_resolution,[],[f79]) ).
fof(f217,plain,
( frontsegP(nil,nil)
| ~ ssList(nil) ),
inference(equality_resolution,[],[f83]) ).
fof(f222,plain,
! [X0] :
( singletonP(cons(X0,nil))
| ~ ssList(cons(X0,nil))
| ~ ssItem(X0) ),
inference(equality_resolution,[],[f119]) ).
fof(f226,plain,
! [X0,X1] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(app(X0,X1))
| ~ ssList(X0)
| ~ ssList(X1) ),
inference(equality_resolution,[],[f155]) ).
tcf(c_252,plain,
ssList(nil),
inference(cnf_transformation,[],[f8]) ).
tcf(c_255,plain,
~ singletonP(nil),
inference(cnf_transformation,[],[f11]) ).
tcf(c_295,plain,
! [X0: $i,X1: $i] : ssList(skaf45(X0,X1)),
inference(cnf_transformation,[],[f51]) ).
tcf(c_300,plain,
! [X0: $i] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_301,plain,
! [X0: $i] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_304,plain,
! [X0: $i] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_308,plain,
! [X0: $i] :
( equalelemsP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_318,plain,
! [X0: $i] :
( ( app(nil,X0) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_321,plain,
! [X0: $i] :
( ssList(tl(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f77]) ).
tcf(c_322,plain,
! [X0: $i] :
( ssItem(hd(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_323,plain,
( segmentP(nil,nil)
| ~ ssList(nil) ),
inference(cnf_transformation,[],[f215]) ).
tcf(c_327,plain,
( frontsegP(nil,nil)
| ~ ssList(nil) ),
inference(cnf_transformation,[],[f217]) ).
tcf(c_328,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ),
inference(cnf_transformation,[],[f84]) ).
tcf(c_329,plain,
! [X0: $i,X1: $i] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f85]) ).
tcf(c_330,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f86]) ).
tcf(c_344,plain,
! [X0: $i,X1: $i] :
( neq(X1,X0)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f102]) ).
tcf(c_348,plain,
! [X0: $i] :
( ( X0 = nil )
| ( cons(hd(X0),tl(X0)) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f107]) ).
tcf(c_359,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ neq(X0,X0) ),
inference(cnf_transformation,[],[f240]) ).
tcf(c_360,plain,
! [X0: $i] :
( singletonP(cons(X0,nil))
| ~ ssItem(X0)
| ~ ssList(cons(X0,nil)) ),
inference(cnf_transformation,[],[f222]) ).
tcf(c_367,plain,
! [X0: $i,X1: $i] :
( ( X1 = nil )
| ( hd(app(X1,X0)) = hd(X1) )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f129]) ).
tcf(c_371,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1) ),
inference(cnf_transformation,[],[f135]) ).
tcf(c_376,plain,
! [X0: $i,X1: $i] :
( ( app(X1,skaf45(X0,X1)) = X0 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[],[f143]) ).
tcf(c_388,plain,
! [X0: $i,X1: $i] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f226]) ).
tcf(c_396,plain,
! [X0: $i,X1: $i,X2: $i] :
( segmentP(X0,X2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1) ),
inference(cnf_transformation,[],[f164]) ).
tcf(c_398,plain,
! [X0: $i,X1: $i,X2: $i] :
( frontsegP(X0,X2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[],[f166]) ).
tcf(c_416,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( segmentP(app(app(X3,X0),X2),X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X0,X1) ),
inference(cnf_transformation,[],[f186]) ).
tcf(c_422,plain,
! [X0: $i,X1: $i,X2: $i] :
( frontsegP(cons(X2,X0),cons(X2,X1))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[],[f244]) ).
tcf(c_432,negated_conjecture,
ssList(sk3),
inference(cnf_transformation,[],[f202]) ).
tcf(c_433,negated_conjecture,
ssList(sk4),
inference(cnf_transformation,[],[f203]) ).
tcf(c_434,negated_conjecture,
neq(sk4,nil),
inference(cnf_transformation,[],[f213]) ).
tcf(c_435,negated_conjecture,
frontsegP(sk4,sk3),
inference(cnf_transformation,[],[f207]) ).
tcf(c_436,negated_conjecture,
equalelemsP(sk3),
inference(cnf_transformation,[],[f208]) ).
tcf(c_437,negated_conjecture,
! [X0: $i] :
( ~ equalelemsP(X0)
| ~ ssList(X0)
| ~ segmentP(X0,sk3)
| ~ frontsegP(sk4,X0)
| ~ neq(sk3,X0) ),
inference(cnf_transformation,[],[f209]) ).
tcf(c_438,negated_conjecture,
( ~ segmentP(sk4,sk3)
| ~ neq(sk3,nil) ),
inference(cnf_transformation,[],[f214]) ).
tcf(c_499,plain,
( ( nil = nil )
| ~ ssList(nil)
| ~ frontsegP(nil,nil) ),
inference(instantiation,[status(thm)],[c_328]) ).
tcf(c_798,plain,
! [X0: $i,X1: $i] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_388,c_329]) ).
tcf(c_2865,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ equalelemsP(X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X0,sk3)
| ~ frontsegP(sk4,X0)
| ( X2 != sk3 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_437,c_344]) ).
tcf(c_2866,plain,
! [X0: $i] :
( ( X0 = sk3 )
| ~ ssList(sk3)
| ~ equalelemsP(X0)
| ~ ssList(X0)
| ~ segmentP(X0,sk3)
| ~ frontsegP(sk4,X0) ),
inference(unflattening,[status(thm)],[c_2865]) ).
tcf(c_2868,plain,
! [X0: $i] :
( ( X0 = sk3 )
| ~ frontsegP(sk4,X0)
| ~ segmentP(X0,sk3)
| ~ ssList(X0)
| ~ equalelemsP(X0) ),
inference(global_subsumption_just,[status(thm)],[c_2866,c_432,c_2866]) ).
tcf(c_2869,plain,
! [X0: $i] :
( ( X0 = sk3 )
| ~ equalelemsP(X0)
| ~ ssList(X0)
| ~ segmentP(X0,sk3)
| ~ frontsegP(sk4,X0) ),
inference(renaming,[status(thm)],[c_2868]) ).
tcf(c_2921,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(sk4,sk3)
| ( X1 != sk3 )
| ( X0 != nil ) ),
inference(resolution_lifted,[status(thm)],[c_344,c_438]) ).
tcf(c_2922,plain,
( ( nil = sk3 )
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ segmentP(sk4,sk3) ),
inference(unflattening,[status(thm)],[c_2921]) ).
tcf(c_2923,plain,
( ( nil = sk3 )
| ~ segmentP(sk4,sk3) ),
inference(global_subsumption_just,[status(thm)],[c_2922,c_432,c_252,c_2922]) ).
tcf(c_2939,plain,
! [X0: $i] :
( ~ ssList(X0)
| ( X0 != nil )
| ( X0 != sk4 ) ),
inference(resolution_lifted,[status(thm)],[c_359,c_434]) ).
tcf(c_2940,plain,
( ~ ssList(sk4)
| ( sk4 != nil ) ),
inference(unflattening,[status(thm)],[c_2939]) ).
tcf(c_2941,plain,
sk4 != nil,
inference(global_subsumption_just,[status(thm)],[c_2940,c_433,c_2940]) ).
tcf(c_6855,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_6859,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( segmentP(X0,X2)
| ~ segmentP(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_6867,plain,
! [X0: $i,X1: $i] :
( singletonP(X0)
| ~ singletonP(X1)
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_9385,plain,
( segmentP(sk3,sk3)
| ~ ssList(sk3) ),
inference(instantiation,[status(thm)],[c_301]) ).
tcf(c_9387,plain,
( ssList(tl(sk4))
| ( sk4 = nil )
| ~ ssList(sk4) ),
inference(instantiation,[status(thm)],[c_321]) ).
tcf(c_9388,plain,
( ssItem(hd(sk4))
| ( sk4 = nil )
| ~ ssList(sk4) ),
inference(instantiation,[status(thm)],[c_322]) ).
tcf(c_9541,plain,
! [X0: $i,X1: $i] :
( singletonP(X0)
| ~ singletonP(cons(X1,nil))
| ( X0 != cons(X1,nil) ) ),
inference(instantiation,[status(thm)],[c_6867]) ).
tcf(c_10436,plain,
! [X0: $i,X1: $i] :
( ( X1 = cons(X0,nil) )
| ~ ssList(X1)
| ~ ssList(cons(X0,nil))
| ~ segmentP(X1,cons(X0,nil))
| ~ segmentP(cons(X0,nil),X1) ),
inference(instantiation,[status(thm)],[c_371]) ).
tcf(c_12020,plain,
! [X0: $i] :
( segmentP(cons(X0,nil),nil)
| ~ ssList(cons(X0,nil)) ),
inference(instantiation,[status(thm)],[c_300]) ).
tcf(c_13291,plain,
! [X0: $i,X1: $i] :
( ( cons(X0,X1) = sk3 )
| ~ equalelemsP(cons(X0,X1))
| ~ ssList(cons(X0,X1))
| ~ segmentP(cons(X0,X1),sk3)
| ~ frontsegP(sk4,cons(X0,X1)) ),
inference(instantiation,[status(thm)],[c_2869]) ).
tcf(c_13638,plain,
! [X0: $i] :
( ssList(app(sk4,X0))
| ~ ssList(sk4)
| ~ ssList(X0) ),
inference(instantiation,[status(thm)],[c_329]) ).
tcf(c_13705,plain,
! [X0: $i] :
( ssList(cons(hd(sk4),X0))
| ~ ssList(X0)
| ~ ssItem(hd(sk4)) ),
inference(instantiation,[status(thm)],[c_330]) ).
tcf(c_13706,plain,
( ssList(cons(hd(sk4),nil))
| ~ ssList(nil)
| ~ ssItem(hd(sk4)) ),
inference(instantiation,[status(thm)],[c_13705]) ).
tcf(c_19170,plain,
! [X0: $i] :
( frontsegP(X0,sk3)
| ~ ssList(sk4)
| ~ ssList(sk3)
| ~ ssList(X0)
| ~ frontsegP(X0,sk4) ),
inference(superposition,[status(thm)],[c_435,c_398]) ).
tcf(c_19185,plain,
! [X0: $i] :
( frontsegP(X0,sk3)
| ~ ssList(X0)
| ~ frontsegP(X0,sk4) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19170,c_433,c_432]) ).
tcf(c_19204,plain,
! [X0: $i] :
( frontsegP(app(sk4,X0),sk3)
| ~ ssList(sk4)
| ~ ssList(X0)
| ~ ssList(app(sk4,X0)) ),
inference(superposition,[status(thm)],[c_798,c_19185]) ).
tcf(c_19206,plain,
! [X0: $i] :
( frontsegP(app(sk4,X0),sk3)
| ~ ssList(X0)
| ~ ssList(app(sk4,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19204,c_433]) ).
tcf(c_21610,plain,
! [X0: $i,X1: $i,X2: $i] :
( segmentP(X0,X2)
| ~ equalelemsP(X2)
| ~ ssList(X2)
| ~ segmentP(X2,sk3)
| ~ segmentP(X1,sk3)
| ~ frontsegP(sk4,X2)
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_6859,c_2869]) ).
tcf(c_21983,plain,
! [X0: $i] :
( frontsegP(app(sk4,X0),sk3)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_19206,c_433,c_13638,c_19206]) ).
tcf(c_21991,plain,
! [X0: $i] :
( ( app(sk3,skaf45(app(sk4,X0),sk3)) = app(sk4,X0) )
| ~ ssList(sk3)
| ~ ssList(X0)
| ~ ssList(app(sk4,X0)) ),
inference(superposition,[status(thm)],[c_21983,c_376]) ).
tcf(c_21994,plain,
! [X0: $i] :
( ( app(sk3,skaf45(app(sk4,X0),sk3)) = app(sk4,X0) )
| ~ ssList(X0)
| ~ ssList(app(sk4,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21991,c_432]) ).
tcf(c_22659,plain,
! [X0: $i] :
( ( X0 = cons(hd(sk4),nil) )
| ~ ssList(X0)
| ~ ssList(cons(hd(sk4),nil))
| ~ segmentP(X0,cons(hd(sk4),nil))
| ~ segmentP(cons(hd(sk4),nil),X0) ),
inference(instantiation,[status(thm)],[c_10436]) ).
tcf(c_22666,plain,
( singletonP(cons(hd(sk4),nil))
| ~ ssItem(hd(sk4))
| ~ ssList(cons(hd(sk4),nil)) ),
inference(instantiation,[status(thm)],[c_360]) ).
tcf(c_22671,plain,
( segmentP(cons(hd(sk4),nil),nil)
| ~ ssList(cons(hd(sk4),nil)) ),
inference(instantiation,[status(thm)],[c_12020]) ).
tcf(c_22675,plain,
( ( nil = cons(hd(sk4),nil) )
| ~ ssList(nil)
| ~ ssList(cons(hd(sk4),nil))
| ~ segmentP(nil,cons(hd(sk4),nil))
| ~ segmentP(cons(hd(sk4),nil),nil) ),
inference(instantiation,[status(thm)],[c_22659]) ).
tcf(c_22680,plain,
! [X0: $i] :
( ( cons(hd(sk4),X0) = sk3 )
| ~ equalelemsP(cons(hd(sk4),X0))
| ~ ssList(cons(hd(sk4),X0))
| ~ segmentP(cons(hd(sk4),X0),sk3)
| ~ frontsegP(sk4,cons(hd(sk4),X0)) ),
inference(instantiation,[status(thm)],[c_13291]) ).
tcf(c_22720,plain,
( ( cons(hd(sk4),nil) = sk3 )
| ~ equalelemsP(cons(hd(sk4),nil))
| ~ ssList(cons(hd(sk4),nil))
| ~ segmentP(cons(hd(sk4),nil),sk3)
| ~ frontsegP(sk4,cons(hd(sk4),nil)) ),
inference(instantiation,[status(thm)],[c_22680]) ).
tcf(c_22995,plain,
! [X0: $i] :
( segmentP(nil,X0)
| ~ equalelemsP(X0)
| ~ ssList(X0)
| ~ segmentP(sk4,sk3)
| ~ segmentP(sk3,sk3)
| ~ segmentP(X0,sk3)
| ~ frontsegP(sk4,X0) ),
inference(resolution,[status(thm)],[c_21610,c_2923]) ).
tcf(c_23149,plain,
! [X0: $i] :
( segmentP(nil,X0)
| ~ equalelemsP(X0)
| ~ ssList(X0)
| ~ segmentP(sk4,sk3)
| ~ frontsegP(sk4,X0)
| ~ segmentP(X0,sk3) ),
inference(global_subsumption_just,[status(thm)],[c_22995,c_432,c_9385,c_22995]) ).
tcf(c_23150,plain,
! [X0: $i] :
( segmentP(nil,X0)
| ~ equalelemsP(X0)
| ~ ssList(X0)
| ~ segmentP(sk4,sk3)
| ~ segmentP(X0,sk3)
| ~ frontsegP(sk4,X0) ),
inference(renaming,[status(thm)],[c_23149]) ).
tcf(c_29110,plain,
( segmentP(nil,sk3)
| ~ equalelemsP(sk3)
| ~ ssList(sk3)
| ~ segmentP(sk4,sk3)
| ~ frontsegP(sk4,sk3) ),
inference(resolution,[status(thm)],[c_23150,c_301]) ).
tcf(c_32853,plain,
( equalelemsP(cons(hd(sk4),nil))
| ~ ssItem(hd(sk4)) ),
inference(instantiation,[status(thm)],[c_308]) ).
tcf(c_34758,plain,
( segmentP(nil,sk3)
| ~ segmentP(sk4,sk3) ),
inference(global_subsumption_just,[status(thm)],[c_29110,c_436,c_432,c_435,c_29110]) ).
tcf(c_40656,plain,
app(nil,sk3) = sk3,
inference(superposition,[status(thm)],[c_432,c_318]) ).
tcf(c_41079,plain,
( ( sk4 = nil )
| ( cons(hd(sk4),tl(sk4)) = sk4 ) ),
inference(superposition,[status(thm)],[c_433,c_348]) ).
tcf(c_41111,plain,
cons(hd(sk4),tl(sk4)) = sk4,
inference(forward_subsumption_resolution,[status(thm)],[c_41079,c_2941]) ).
tcf(c_41388,plain,
! [X0: $i] :
( ( X0 = nil )
| ( hd(app(X0,sk4)) = hd(X0) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_433,c_367]) ).
tcf(c_41492,plain,
( ( sk4 = nil )
| ( hd(app(sk4,sk4)) = hd(sk4) ) ),
inference(superposition,[status(thm)],[c_433,c_41388]) ).
tcf(c_41524,plain,
hd(app(sk4,sk4)) = hd(sk4),
inference(forward_subsumption_resolution,[status(thm)],[c_41492,c_2941]) ).
tcf(c_41626,plain,
( ( app(sk3,skaf45(sk4,sk3)) = sk4 )
| ~ ssList(sk4)
| ~ ssList(sk3) ),
inference(superposition,[status(thm)],[c_435,c_376]) ).
tcf(c_41641,plain,
app(sk3,skaf45(sk4,sk3)) = sk4,
inference(forward_subsumption_resolution,[status(thm)],[c_41626,c_433,c_432]) ).
tcf(c_42156,plain,
( ssItem(hd(sk4))
| ( app(sk4,sk4) = nil )
| ~ ssList(app(sk4,sk4)) ),
inference(superposition,[status(thm)],[c_41524,c_322]) ).
tcf(c_42288,plain,
! [X0: $i] :
( frontsegP(X0,sk3)
| ~ ssList(sk4)
| ~ ssList(sk3)
| ~ ssList(X0)
| ~ frontsegP(X0,sk4) ),
inference(superposition,[status(thm)],[c_435,c_398]) ).
tcf(c_42302,plain,
! [X0: $i] :
( frontsegP(X0,sk3)
| ~ ssList(X0)
| ~ frontsegP(X0,sk4) ),
inference(forward_subsumption_resolution,[status(thm)],[c_42288,c_433,c_432]) ).
tcf(c_42330,plain,
! [X0: $i] :
( frontsegP(app(sk4,X0),sk3)
| ~ ssList(sk4)
| ~ ssList(X0)
| ~ ssList(app(sk4,X0)) ),
inference(superposition,[status(thm)],[c_798,c_42302]) ).
tcf(c_42332,plain,
! [X0: $i] :
( frontsegP(app(sk4,X0),sk3)
| ~ ssList(X0)
| ~ ssList(app(sk4,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_42330,c_433]) ).
tcf(c_42372,plain,
! [X0: $i] :
( frontsegP(sk4,cons(hd(sk4),X0))
| ~ ssList(X0)
| ~ ssItem(hd(sk4))
| ~ ssList(tl(sk4))
| ~ frontsegP(tl(sk4),X0) ),
inference(superposition,[status(thm)],[c_41111,c_422]) ).
tcf(c_42586,plain,
! [X0: $i] :
( frontsegP(app(sk4,X0),sk3)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_42332,c_21983]) ).
tcf(c_42593,plain,
! [X0: $i] :
( ( app(sk3,skaf45(app(sk4,X0),sk3)) = app(sk4,X0) )
| ~ ssList(sk3)
| ~ ssList(X0)
| ~ ssList(app(sk4,X0)) ),
inference(superposition,[status(thm)],[c_42586,c_376]) ).
tcf(c_42596,plain,
! [X0: $i] :
( ( app(sk3,skaf45(app(sk4,X0),sk3)) = app(sk4,X0) )
| ~ ssList(X0)
| ~ ssList(app(sk4,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_42593,c_432]) ).
tcf(c_43621,plain,
! [X0: $i,X1: $i] :
( segmentP(app(sk3,X1),X0)
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(sk3,X0) ),
inference(superposition,[status(thm)],[c_40656,c_416]) ).
tcf(c_43651,plain,
! [X0: $i,X1: $i] :
( segmentP(app(sk3,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(sk3,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_43621,c_252,c_432]) ).
tcf(c_44426,plain,
! [X0: $i] :
( segmentP(sk4,X0)
| ~ ssList(X0)
| ~ segmentP(sk3,X0)
| ~ ssList(skaf45(sk4,sk3)) ),
inference(superposition,[status(thm)],[c_41641,c_43651]) ).
tcf(c_44431,plain,
! [X0: $i] :
( segmentP(sk4,X0)
| ~ ssList(X0)
| ~ segmentP(sk3,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_44426,c_295]) ).
tcf(c_44558,plain,
( segmentP(sk4,sk3)
| ~ ssList(sk3) ),
inference(superposition,[status(thm)],[c_301,c_44431]) ).
tcf(c_44559,plain,
segmentP(sk4,sk3),
inference(forward_subsumption_resolution,[status(thm)],[c_44558,c_432]) ).
tcf(c_44564,plain,
sk3 = nil,
inference(backward_subsumption_resolution,[status(thm)],[c_2923,c_44559]) ).
tcf(c_46500,plain,
! [X0: $i] :
( ( app(sk3,skaf45(app(sk4,X0),sk3)) = app(sk4,X0) )
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_42596,c_433,c_13638,c_21994]) ).
tcf(c_46503,plain,
! [X0: $i] :
( ( app(nil,skaf45(app(sk4,X0),nil)) = app(sk4,X0) )
| ~ ssList(X0) ),
inference(light_normalisation,[status(thm)],[c_46500,c_44564]) ).
tcf(c_46508,plain,
app(nil,skaf45(app(sk4,sk4),nil)) = app(sk4,sk4),
inference(superposition,[status(thm)],[c_433,c_46503]) ).
tcf(c_46572,plain,
( ssList(app(sk4,sk4))
| ~ ssList(nil)
| ~ ssList(skaf45(app(sk4,sk4),nil)) ),
inference(superposition,[status(thm)],[c_46508,c_329]) ).
tcf(c_46588,plain,
ssList(app(sk4,sk4)),
inference(forward_subsumption_resolution,[status(thm)],[c_46572,c_252,c_295]) ).
tcf(c_46726,plain,
( ssItem(hd(sk4))
| ( app(sk4,sk4) = nil ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_42156,c_46588]) ).
tcf(c_67009,plain,
ssItem(hd(sk4)),
inference(global_subsumption_just,[status(thm)],[c_46726,c_433,c_2940,c_9388]) ).
tcf(c_67043,plain,
! [X0: $i] :
( frontsegP(sk4,cons(hd(sk4),X0))
| ~ ssList(X0)
| ~ ssList(tl(sk4))
| ~ frontsegP(tl(sk4),X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_42372,c_67009]) ).
tcf(c_67052,plain,
( frontsegP(sk4,cons(hd(sk4),nil))
| ~ ssList(nil)
| ~ ssList(tl(sk4))
| ~ frontsegP(tl(sk4),nil) ),
inference(instantiation,[status(thm)],[c_67043]) ).
tcf(c_67394,plain,
! [X0: $i,X1: $i,X2: $i] :
( segmentP(X1,cons(hd(sk4),nil))
| ~ segmentP(X2,X0)
| ( X1 != X2 )
| ( cons(hd(sk4),nil) != X0 ) ),
inference(instantiation,[status(thm)],[c_6859]) ).
tcf(c_67395,plain,
( segmentP(nil,cons(hd(sk4),nil))
| ~ segmentP(nil,nil)
| ( nil != nil )
| ( cons(hd(sk4),nil) != nil ) ),
inference(instantiation,[status(thm)],[c_67394]) ).
tcf(c_68073,plain,
( frontsegP(tl(sk4),nil)
| ~ ssList(tl(sk4)) ),
inference(instantiation,[status(thm)],[c_304]) ).
tcf(c_68432,plain,
! [X0: $i] :
( singletonP(X0)
| ~ singletonP(cons(hd(sk4),nil))
| ( X0 != cons(hd(sk4),nil) ) ),
inference(instantiation,[status(thm)],[c_9541]) ).
tcf(c_68433,plain,
( singletonP(nil)
| ~ singletonP(cons(hd(sk4),nil))
| ( nil != cons(hd(sk4),nil) ) ),
inference(instantiation,[status(thm)],[c_68432]) ).
tcf(c_81896,plain,
! [X0: $i,X1: $i] :
( ( cons(hd(sk4),X0) = nil )
| ( nil != X1 )
| ( cons(hd(sk4),X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_6855]) ).
tcf(c_91229,plain,
! [X0: $i] :
( ( cons(hd(sk4),X0) = nil )
| ( nil != sk3 )
| ( cons(hd(sk4),X0) != sk3 ) ),
inference(instantiation,[status(thm)],[c_81896]) ).
tcf(c_91231,plain,
( ( cons(hd(sk4),nil) = nil )
| ( nil != sk3 )
| ( cons(hd(sk4),nil) != sk3 ) ),
inference(instantiation,[status(thm)],[c_91229]) ).
tcf(c_93688,plain,
! [X0: $i,X1: $i] :
( segmentP(cons(hd(sk4),X0),sk3)
| ~ ssList(sk3)
| ~ ssList(X1)
| ~ segmentP(X1,sk3)
| ~ ssList(cons(hd(sk4),X0))
| ~ segmentP(cons(hd(sk4),X0),X1) ),
inference(instantiation,[status(thm)],[c_396]) ).
tcf(c_93691,plain,
( segmentP(cons(hd(sk4),nil),sk3)
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ segmentP(nil,sk3)
| ~ ssList(cons(hd(sk4),nil))
| ~ segmentP(cons(hd(sk4),nil),nil) ),
inference(instantiation,[status(thm)],[c_93688]) ).
tcf(c_93692,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_93691,c_91231,c_68433,c_68073,c_67395,c_67052,c_44559,c_34758,c_32853,c_22720,c_22675,c_22666,c_22671,c_13706,c_9388,c_9387,c_2940,c_2923,c_499,c_323,c_327,c_255,c_252,c_432,c_433]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC123-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/5.39 % Computer : n019.cluster.edu
% 0.12/5.39 % Model : x86_64 x86_64
% 0.12/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.39 % Memory : 8046.5625MB
% 0.12/5.39 % OS : Linux 6.8.0-71-generic
% 0.12/5.39 % CPULimit : 300
% 0.12/5.39 % WCLimit : 300
% 0.12/5.39 % DateTime : Thu Sep 24 16:31:27 UTC 2026
% 0.12/5.39 % CPUTime :
% 0.12/5.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/5.43 Running first-order theorem proving
% 0.15/5.43 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/5.44
% 0.15/5.44 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.44
% 0.15/5.44 % Detected problem language: tptp
% 0.15/5.45 % Proving...
% 51.90/17.91 % SZS status Started for theBenchmark.p
% 51.90/17.91 % SZS status Unsatisfiable for theBenchmark.p
% 51.90/17.91
% 51.90/17.91 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 51.90/17.91
% 51.90/17.91 % ------ iProver source info
% 51.90/17.91
% 51.90/17.91 % git: date: 2026-07-19 20:42:38 +0200
% 51.90/17.91 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 51.90/17.91 % git: non_committed_changes: false
% 51.90/17.91
% 51.90/17.91 % ------ Parsing...% successful
% 51.90/17.91
% 51.90/17.91
% 51.90/17.91 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 51.90/17.91
% 51.90/17.91 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 51.90/17.91
% 51.90/17.91 % ------ Preprocessing... gs_s sp: 2 0s gs_e snvd_s sp: 0 0s snvd_e %
% 51.90/17.91
% 51.90/17.91 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 51.90/17.91 % ------ Proving...
% 51.90/17.91 % ------ Problem Properties
% 51.90/17.91
% 51.90/17.91 %
% 51.90/17.91 % clauses 186
% 51.90/17.91 % conjectures 4
% 51.90/17.91 % EPR 61
% 51.90/17.91 % Horn 158
% 51.90/17.91 % unary 63
% 51.90/17.91 % binary 23
% 51.90/17.91 % lits 558
% 51.90/17.91 % lits eq 74
% 51.90/17.91 % fd_pure 0
% 51.90/17.91 % fd_pseudo 0
% 51.90/17.91 % fd_cond 16
% 51.90/17.91 % fd_pseudo_cond 14
% 51.90/17.91 % AC symbols 0
% 51.90/17.91
% 51.90/17.91 % ------ Input Options Time Limit: Unbounded
% 51.90/17.91
% 51.90/17.91
% 51.90/17.91 % ------
% 51.90/17.91 % Current options:
% 51.90/17.91 % ------
% 51.90/17.91
% 51.90/17.91
% 51.90/17.91 %
% 51.90/17.91
% 51.90/17.91 % ------ Proving...
% 51.90/17.91 %
% 51.90/17.91
% 51.90/17.91 % SZS status Unsatisfiable for theBenchmark.p
% 51.90/17.91
% 51.90/17.91 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 51.90/17.91
% 51.90/17.91
%------------------------------------------------------------------------------