%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO309^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n001.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 : Wed Sep 30 08:49:42 AM UTC 2026
% Result : Theorem 2.38s 0.59s
% Output : Refutation 2.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO309^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.18 % Computer : n001.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 16:50:36 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.21 Running first-order model finding
% 0.07/0.21 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.38/0.58 % (1491522)Will run a generic schedule for satisfiability detection.
% 2.38/0.58 % (1491529)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1692350447:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.38/0.58 % (1491528)% WARNING: option uhcvi not known.
% 2.38/0.58 % (1491527)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1264376316_2999 on theBenchmark for (2999ds/0Mi)
% 2.38/0.58 % (1491528)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=287900851:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.38/0.58 % (1491530)dis+10_1_sil=32000:sp=arity:random_seed=311440867:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.38/0.58 % (1491531)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4067389351:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.38/0.58 % (1491528)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.38/0.58 % Exception at run slice level
% 2.38/0.58 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.38/0.58 % (1491531)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.38/0.58 % (1491528)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.38/0.58 % (1491533)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2945424519:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.38/0.58 % (1491532)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2164176101:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.38/0.58 % (1491539)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=562730868:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 2.38/0.58 % Exception at run slice level
% 2.38/0.58 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.38/0.58 % (1491543)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=4017350262:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 2.38/0.58 % (1491530)Instruction limit reached!
% 2.38/0.58 % (1491530)------------------------------
% 2.38/0.58 % (1491530)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.38/0.58 % (1491530)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.38/0.58 % (1491530)CaDiCaL version: 2.1.3
% 2.38/0.58 % (1491530)Termination reason: Instruction limit
% 2.38/0.58 % (1491530)Termination phase: Saturation
% 2.38/0.58 % (1491530)Time elapsed: 0.050 s
% 2.38/0.58 % (1491530)Peak memory usage: 12 MB
% 2.38/0.58 % (1491530)Instructions burned: 105 (million)
% 2.38/0.58 % (1491531)Instruction limit reached!
% 2.38/0.58 % (1491531)------------------------------
% 2.38/0.58 % (1491531)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.38/0.58 % (1491531)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.38/0.58 % (1491531)CaDiCaL version: 2.1.3
% 2.38/0.58 % (1491531)Termination reason: Instruction limit
% 2.38/0.58 % (1491531)Termination phase: Saturation
% 2.38/0.58 % (1491531)Time elapsed: 0.054 s
% 2.38/0.58 % (1491531)Peak memory usage: 12 MB
% 2.38/0.58 % (1491531)Instructions burned: 116 (million)
% 2.38/0.58 % (1491545)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=3750028385:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 2.38/0.58 % (1491545)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.38/0.58 % (1491545)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.38/0.58 % (1491546)ott-21_1_sil=16000:fs=off:random_seed=3635555851:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 2.38/0.58 % (1491532)Instruction limit reached!
% 2.38/0.58 % (1491532)------------------------------
% 2.38/0.58 % (1491532)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.38/0.58 % (1491532)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.38/0.58 % (1491532)CaDiCaL version: 2.1.3
% 2.38/0.58 % (1491532)Termination reason: Instruction limit
% 2.38/0.58 % (1491532)Termination phase: Saturation
% 2.38/0.58 % (1491532)Time elapsed: 0.061 s
% 2.38/0.58 % (1491532)Peak memory usage: 12 MB
% 2.38/0.58 % (1491532)Instructions burned: 131 (million)
% 2.38/0.58 % (1491549)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2236325181:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 2.38/0.58 % (1491543)Instruction limit reached!
% 2.38/0.58 % (1491543)------------------------------
% 2.38/0.58 % (1491543)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.38/0.58 % (1491543)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.38/0.58 % (1491543)CaDiCaL version: 2.1.3
% 2.38/0.58 % (1491543)Termination reason: Instruction limit
% 2.38/0.58 % (1491543)Termination phase: Saturation
% 2.38/0.58 % (1491543)Time elapsed: 0.065 s
% 2.38/0.58 % (1491543)Peak memory usage: 12 MB
% 2.38/0.58 % (1491543)Instructions burned: 131 (million)
% 2.38/0.58 % (1491533)Instruction limit reached!
% 2.38/0.58 % (1491533)------------------------------
% 2.38/0.58 % (1491533)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.38/0.58 % (1491533)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.38/0.58 % (1491533)CaDiCaL version: 2.1.3
% 2.38/0.58 % (1491533)Termination reason: Instruction limit
% 2.38/0.58 % (1491533)Termination phase: Saturation
% 2.38/0.58 % (1491533)Time elapsed: 0.091 s
% 2.38/0.58 % (1491533)Peak memory usage: 12 MB
% 2.38/0.58 % (1491533)Instructions burned: 159 (million)
% 2.38/0.58 % (1491551)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=278609764:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 2.38/0.58 % Exception at run slice level
% 2.38/0.58 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.38/0.58 % (1491552)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3130801323:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 2.38/0.58 % (1491554)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=2105991085:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 2.38/0.58 % Exception at run slice level
% 2.38/0.58 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.38/0.58 % (1491546)Instruction limit reached!
% 2.38/0.58 % (1491546)------------------------------
% 2.38/0.58 % (1491546)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.38/0.58 % (1491546)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.38/0.58 % (1491546)CaDiCaL version: 2.1.3
% 2.38/0.58 % (1491546)Termination reason: Instruction limit
% 2.38/0.58 % (1491546)Termination phase: Saturation
% 2.38/0.58 % (1491546)Time elapsed: 0.084 s
% 2.38/0.58 % (1491546)Peak memory usage: 12 MB
% 2.38/0.58 % (1491546)Instructions burned: 180 (million)
% 2.38/0.58 % (1491557)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=1004200867:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 2.38/0.58 % (1491557)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.38/0.58 % (1491558)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=1587336664:i=879:kws=inv_precedence:fsr=off_2998 on theBenchmark for (2998ds/879Mi)
% 2.38/0.58 % (1491558)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.38/0.58 % (1491552) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1491522-1491552"...
% 2.38/0.59 % (1491552)...printing done.
% 2.38/0.59 % (1491552)Refutation found. Thanks to Tanya!
% 2.38/0.59 % SZS status Theorem for theBenchmark
% 2.38/0.59 % SZS output start Proof for theBenchmark
% 2.38/0.59 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 2.38/0.59 thf(func_def_0, type, cS: ($i > $i)).
% 2.38/0.59 thf(func_def_1, type, cQ: ($i > $i)).
% 2.38/0.59 thf(func_def_2, type, cR: ($i > $i > $o)).
% 2.38/0.59 thf(func_def_6, type, sK0: (($i > $o) > $i)).
% 2.38/0.59 thf(func_def_7, type, sK1: ($i > $i)).
% 2.38/0.59 thf(func_def_8, type, sK2: ($i > $i)).
% 2.38/0.59 thf(func_def_9, type, sF3: (($i > $o) > $i)).
% 2.38/0.59 thf(func_def_10, type, sF4: (($i > $o) > $i)).
% 2.38/0.59 thf(func_def_11, type, sF5: (($i > $o) > $o)).
% 2.38/0.59 thf(func_def_12, type, sF6: (($i > $o) > $o)).
% 2.38/0.59 thf(func_def_13, type, sF7: ($i > $i)).
% 2.38/0.59 thf(func_def_14, type, sF8: ($i > $i)).
% 2.38/0.59 thf(func_def_15, type, sF9: ($i > $o)).
% 2.38/0.59 thf(func_def_16, type, sF10: ($i > $i)).
% 2.38/0.59 thf(func_def_17, type, sF11: ($i > $i)).
% 2.38/0.59 thf(func_def_18, type, sF12: ($i > $i)).
% 2.38/0.59 thf(func_def_19, type, sF13: ($i > $o)).
% 2.38/0.59 thf(func_def_20, type, sF14: ($i > $i)).
% 2.38/0.59 thf(func_def_21, type, sF15: ($i > $i > $o)).
% 2.38/0.59 thf(func_def_22, type, sF16: ($i > $i > $o)).
% 2.38/0.59 thf(func_def_23, type, vNOT: ($o > $o)).
% 2.38/0.59 thf(func_def_24, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 2.38/0.59 thf(func_def_25, type, db0: !>[X0: $tType]:(X0)).
% 2.38/0.59 thf(func_def_26, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 2.38/0.59 thf(f1,conjecture,(
% 2.38/0.59 ! [X0 : $i] : (? [X1 : $i] : (cR @ X0 @ (cQ @ X1)) <=> ~ ? [X2 : $i] : (cR @ (cS @ X0) @ (cQ @ X2))) => ? [X3 : ($i > $o)] : ! [X0 : $i] : ((X3 @ X0) <=> ~(X3 @ (cS @ X0)))),
% 2.38/0.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cEO1)).
% 2.38/0.59 thf(f2,negated_conjecture,(
% 2.38/0.59 ~(! [X0 : $i] : (? [X1 : $i] : (cR @ X0 @ (cQ @ X1)) <=> ~ ? [X2 : $i] : (cR @ (cS @ X0) @ (cQ @ X2))) => ? [X3 : ($i > $o)] : ! [X0 : $i] : ((X3 @ X0) <=> ~(X3 @ (cS @ X0))))),
% 2.38/0.59 inference(negated_conjecture,[status(cth)],[f1])).
% 2.38/0.59 thf(f3,plain,(
% 2.38/0.59 ~(! [X0 : $i] : (? [X1 : $i] : (cR @ X0 @ (cQ @ X1)) <=> ~ ? [X2 : $i] : (cR @ (cS @ X0) @ (cQ @ X2))) => ? [X3 : ($i > $o)] : ! [X4 : $i] : ((X3 @ X4) <=> ~(X3 @ (cS @ X4))))),
% 2.38/0.59 inference(rectify,[],[f2])).
% 2.38/0.59 thf(f4,plain,(
% 2.38/0.59 ~(! [X0 : $i] : (? [X1 : $i] : (((cR @ X0 @ (cQ @ X1))) = $true) <=> ~ ? [X2 : $i] : (((cR @ (cS @ X0) @ (cQ @ X2))) = $true)) => ? [X3 : ($i > $o)] : ! [X4 : $i] : ((((X3 @ X4)) = $true) <=> ~ (((X3 @ (cS @ X4))) = $true)))),
% 2.38/0.59 inference(fool_elimination,[],[f3])).
% 2.38/0.59 thf(f5,plain,(
% 2.38/0.59 ~(! [X0 : $i] : (? [X1 : $i] : (((cR @ X0 @ (cQ @ X1))) = $true) <=> ~ ? [X2 : $i] : (((cR @ (cS @ X0) @ (cQ @ X2))) = $true)) => ? [X3 : ($i > $o)] : ! [X4 : $i] : ((((X3 @ X4)) = $true) <=> (((X3 @ (cS @ X4))) != $true)))),
% 2.38/0.59 inference(flattening,[],[f4])).
% 2.38/0.59 thf(f6,plain,(
% 2.38/0.59 ! [X3 : ($i > $o)] : ? [X4 : $i] : ((((X3 @ X4)) = $true) <~> (((X3 @ (cS @ X4))) != $true)) & ! [X0 : $i] : (? [X1 : $i] : (((cR @ X0 @ (cQ @ X1))) = $true) <=> ! [X2 : $i] : (((cR @ (cS @ X0) @ (cQ @ X2))) != $true))),
% 2.38/0.59 inference(ennf_transformation,[],[f5])).
% 2.38/0.59 thf(f7,plain,(
% 2.38/0.59 ! [X3 : ($i > $o)] : ? [X4 : $i] : (((((X3 @ (cS @ X4))) = $true) | (((X3 @ X4)) != $true)) & ((((X3 @ (cS @ X4))) != $true) | (((X3 @ X4)) = $true))) & ! [X0 : $i] : ((? [X1 : $i] : (((cR @ X0 @ (cQ @ X1))) = $true) | ? [X2 : $i] : (((cR @ (cS @ X0) @ (cQ @ X2))) = $true)) & (! [X2 : $i] : (((cR @ (cS @ X0) @ (cQ @ X2))) != $true) | ! [X1 : $i] : (((cR @ X0 @ (cQ @ X1))) != $true)))),
% 2.38/0.59 inference(nnf_transformation,[],[f6])).
% 2.38/0.59 thf(f8,plain,(
% 2.38/0.59 ! [X0 : ($i > $o)] : ? [X1 : $i] : ((($true = ((X0 @ (cS @ X1)))) | ($true != ((X0 @ X1)))) & (($true != ((X0 @ (cS @ X1)))) | ($true = ((X0 @ X1))))) & ! [X2 : $i] : ((? [X3 : $i] : ($true = ((cR @ X2 @ (cQ @ X3)))) | ? [X4 : $i] : ($true = ((cR @ (cS @ X2) @ (cQ @ X4))))) & (! [X5 : $i] : ($true != ((cR @ (cS @ X2) @ (cQ @ X5)))) | ! [X6 : $i] : ($true != ((cR @ X2 @ (cQ @ X6))))))),
% 2.38/0.59 inference(rectify,[],[f7])).
% 2.38/0.59 thf(f9,plain,(
% 2.38/0.59 ! [X0 : ($i > $o)] : ((($true = ((X0 @ (cS @ (sK0 @ X0))))) | ($true != ((X0 @ (sK0 @ X0))))) & (($true != ((X0 @ (cS @ (sK0 @ X0))))) | ($true = ((X0 @ (sK0 @ X0)))))) & ! [X2 : $i] : ((($true = ((cR @ X2 @ (cQ @ (sK1 @ X2))))) | ($true = ((cR @ (cS @ X2) @ (cQ @ (sK2 @ X2)))))) & (! [X5 : $i] : ($true != ((cR @ (cS @ X2) @ (cQ @ X5)))) | ! [X6 : $i] : ($true != ((cR @ X2 @ (cQ @ X6))))))),
% 2.38/0.59 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,vAPP]),skolemize(X4,sK2 @ X2),skolemize(X4,sK2 @ X2),skolemize(X4,sK2 @ X2)],[f8])).
% 2.38/0.59 thf(f10,plain,(
% 2.38/0.59 ( ! [X2 : $i,X6 : $i,X5 : $i] : (($true != ((cR @ (cS @ X2) @ (cQ @ X5)))) | ($true != ((cR @ X2 @ (cQ @ X6))))) )),
% 2.38/0.59 inference(cnf_transformation,[],[f9])).
% 2.38/0.59 thf(f11,plain,(
% 2.38/0.59 ( ! [X2 : $i] : (($true = ((cR @ X2 @ (cQ @ (sK1 @ X2))))) | ($true = ((cR @ (cS @ X2) @ (cQ @ (sK2 @ X2)))))) )),
% 2.38/0.59 inference(cnf_transformation,[],[f9])).
% 2.38/0.59 thf(f12,plain,(
% 2.38/0.59 ( ! [X0 : ($i > $o)] : (($true != ((X0 @ (cS @ (sK0 @ X0))))) | ($true = ((X0 @ (sK0 @ X0))))) )),
% 2.38/0.59 inference(cnf_transformation,[],[f9])).
% 2.38/0.59 thf(f13,plain,(
% 2.38/0.59 ( ! [X0 : ($i > $o)] : (($true = ((X0 @ (cS @ (sK0 @ X0))))) | ($true != ((X0 @ (sK0 @ X0))))) )),
% 2.38/0.59 inference(cnf_transformation,[],[f9])).
% 2.38/0.59 thf(f15,definition,(
% 2.38/0.59 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 2.38/0.59 introduced(theory,[fool_exhaustiveness_axiom])).
% 2.38/0.59 thf(f16,definition,(
% 2.38/0.59 ( ! [X0 : ($i > $o)] : ((((sF3 @ X0)) = ((sK0 @ X0)))) )),
% 2.38/0.59 introduced(definition,[new_symbols(definition,[sF3])],[function_definition])).
% 2.38/0.59 thf(f17,plain,(
% 2.38/0.59 ( ! [X0 : ($i > $o)] : ((((sK0 @ X0)) = ((sF3 @ X0)))) )),
% 2.38/0.59 inference(reorient_equations,[],[f16])).
% 2.38/0.59 thf(f18,definition,(
% 2.38/0.59 ( ! [X0 : ($i > $o)] : ((((sF4 @ X0)) = ((cS @ (sF3 @ X0))))) )),
% 2.38/0.59 introduced(definition,[new_symbols(definition,[sF4])],[function_definition])).
% 2.38/0.59 thf(f19,plain,(
% 2.38/0.59 ( ! [X0 : ($i > $o)] : ((((cS @ (sF3 @ X0))) = ((sF4 @ X0)))) )),
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% 2.38/0.59 thf(f1635,plain,(
% 2.38/0.59 ( ! [X0 : $i,X1 : $i] : (($true = $false) | ($false = ((sF13 @ X0))) | ($false = ((sF16 @ X1 @ X0)))) )),
% 2.38/0.59 inference(constrained_superposition,[],[f54,f686])).
% 2.38/0.59 thf(f1665,plain,(
% 2.38/0.59 ( ! [X0 : $i,X1 : $i] : (($false = ((sF16 @ X1 @ X0))) | ($false = ((sF13 @ X0)))) )),
% 2.38/0.59 inference(trivial_inequality_removal,[],[f1635])).
% 2.38/0.59 thf(f1688,plain,(
% 2.38/0.59 ( ! [X0 : $i,X1 : $i] : (($true = $false) | ($false = ((cR @ X1 @ (sF12 @ X0)))) | ($false = ((sF13 @ X1)))) )),
% 2.38/0.59 inference(constrained_superposition,[],[f448,f1665])).
% 2.38/0.59 thf(f1699,plain,(
% 2.38/0.59 ( ! [X0 : $i,X1 : $i] : (($false = ((cR @ X1 @ (sF12 @ X0)))) | ($false = ((sF13 @ X1)))) )),
% 2.38/0.59 inference(trivial_inequality_removal,[],[f1688])).
% 2.38/0.59 thf(f1843,plain,(
% 2.38/0.59 ( ! [X0 : $i] : (($true = $false) | ($false = ((sF13 @ X0))) | ($false = ((sF13 @ (sF10 @ X0))))) )),
% 2.38/0.59 inference(constrained_superposition,[],[f54,f1699])).
% 2.38/0.59 thf(f1856,plain,(
% 2.38/0.59 ( ! [X0 : $i] : (($false = ((sF13 @ (sF10 @ X0)))) | ($false = ((sF13 @ X0)))) )),
% 2.38/0.59 inference(trivial_inequality_removal,[],[f1843])).
% 2.38/0.59 thf(f1911,plain,(
% 2.38/0.59 ( ! [X0 : $i] : (($true = $false) | ($true = ((sF9 @ (sF10 @ X0)))) | ($false = ((sF13 @ X0)))) )),
% 2.38/0.59 inference(constrained_superposition,[],[f40,f1856])).
% 2.38/0.59 thf(f1928,plain,(
% 2.38/0.59 ( ! [X0 : $i] : (($false = ((sF13 @ X0))) | ($true = ((sF9 @ (sF10 @ X0))))) )),
% 2.38/0.59 inference(trivial_inequality_removal,[],[f1911])).
% 2.38/0.59 thf(f2228,plain,(
% 2.38/0.59 ( ! [X0 : $i] : (($true = $false) | ($true = ((sF9 @ X0))) | ($true = ((sF9 @ (sF10 @ X0))))) )),
% 2.38/0.59 inference(constrained_superposition,[],[f40,f1928])).
% 2.38/0.59 thf(f2237,plain,(
% 2.38/0.59 ( ! [X0 : $i] : (($true = ((sF9 @ (sF10 @ X0)))) | ($true = ((sF9 @ X0)))) )),
% 2.38/0.59 inference(trivial_inequality_removal,[],[f2228])).
% 2.38/0.59 thf(f2315,plain,(
% 2.38/0.59 ( ! [X0 : $i] : (($true = $false) | ($true = (((^[Y0 : $i]: (sF9 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ (sF3 @ (^[Y0 : $i]: (sF9 @ ((^[Y1 : $i]: (Y1)) @ Y0))))))) | ($true = ((sF9 @ X0))) | (((sF3 @ sF9)) != X0)) )),
% 2.38/0.59 inference(constrained_superposition,[],[f155,f2237])).
% 2.38/0.59 thf(f2321,plain,(
% 2.38/0.59 ( ! [X0 : $i] : (($true = (((^[Y0 : $i]: (sF9 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ (sF3 @ (^[Y0 : $i]: (sF9 @ ((^[Y1 : $i]: (Y1)) @ Y0))))))) | ($true = ((sF9 @ X0))) | (((sF3 @ sF9)) != X0)) )),
% 2.38/0.59 inference(trivial_inequality_removal,[],[f2315])).
% 2.38/0.59 thf(f2322,plain,(
% 2.38/0.59 ( ! [X0 : $i] : (($true = ((sF9 @ (sF3 @ sF9)))) | ($true = ((sF9 @ X0))) | (((sF3 @ sF9)) != X0)) )),
% 2.38/0.59 inference(beta-eta_normalization,[],[f2321])).
% 2.38/0.59 thf(f2334,plain,(
% 2.38/0.59 ( ! [X0 : $i] : (($true = $false) | ($true = ((sF9 @ X0))) | (((sF3 @ sF9)) != X0)) ) | ~spl17_2),
% 2.38/0.59 inference(forward_demodulation,[],[f2322,f1275])).
% 2.38/0.59 thf(f2335,plain,(
% 2.38/0.59 ( ! [X0 : $i] : ((((sF3 @ sF9)) != X0) | ($true = ((sF9 @ X0)))) ) | ~spl17_2),
% 2.38/0.59 inference(trivial_inequality_removal,[],[f2334])).
% 2.38/0.59 thf(f2406,plain,(
% 2.38/0.59 ($true = ((sF9 @ (sF3 @ sF9)))) | ~spl17_2),
% 2.38/0.59 inference(equality_resolution,[],[f2335])).
% 2.38/0.59 thf(f2407,plain,(
% 2.38/0.59 ($true = $false) | ~spl17_2),
% 2.38/0.59 inference(forward_demodulation,[],[f2406,f1275])).
% 2.38/0.59 thf(f2408,plain,(
% 2.38/0.59 $false | ~spl17_2),
% 2.38/0.59 inference(trivial_inequality_removal,[],[f2407])).
% 2.38/0.59 thf(f2409,plain,(
% 2.38/0.59 ~spl17_2),
% 2.38/0.59 inference(avatar_contradiction_clause,[],[f2408])).
% 2.38/0.59 thf(f2529,plain,(
% 2.38/0.59 ($false = ((sF9 @ (sF3 @ sF9)))) | ~spl17_1),
% 2.38/0.59 inference(equality_resolution,[],[f1271])).
% 2.38/0.59 thf(f2530,plain,(
% 2.38/0.59 $false | (~spl17_1 | spl17_2)),
% 2.38/0.59 inference(forward_subsumption_resolution,[],[f2529,f1274])).
% 2.38/0.59 thf(f2531,plain,(
% 2.38/0.59 ~spl17_1 | spl17_2),
% 2.38/0.59 inference(avatar_contradiction_clause,[],[f2530])).
% 2.38/0.59 cnf(s3, plain, spl17_1 | spl17_2, inference(sat_conversion,[],[f1278])).
% 2.38/0.59 cnf(s8, plain, ~spl17_2, inference(sat_conversion,[],[f2409])).
% 2.38/0.59 cnf(s12, plain, ~spl17_1 | spl17_2, inference(sat_conversion,[],[f2531])).
% 2.38/0.59 cnf(s13, plain, ~spl17_1, inference(rat,[],[s12,s8])).
% 2.38/0.59 cnf(s14, plain, $false, inference(rat,[],[s3,s8,s13])).
% 2.38/0.59 thf(f2532,plain,(
% 2.38/0.59 $false),
% 2.38/0.59 inference(avatar_sat_refutation,[],[s14])).
% 2.38/0.59 % SZS output end Proof for theBenchmark
% 2.38/0.59 % (1491552)------------------------------
% 2.38/0.59 % (1491552)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.38/0.59 % (1491552)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.38/0.59 % (1491552)CaDiCaL version: 2.1.3
% 2.38/0.59 % (1491552)Termination reason: Refutation
% 2.38/0.59 % (1491552)Time elapsed: 0.190 s
% 2.38/0.59 % (1491552)Peak memory usage: 13 MB
% 2.38/0.59 % (1491552)Instructions burned: 261 (million)
% 2.38/0.59 % (1491522)Success in time 0.362 s
% 2.38/0.59 % Vampire exiting
%------------------------------------------------------------------------------