0.06/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.06/0.12 % Command : run_vampire %s %d THM 0.12/0.33 % Computer : n010.cluster.edu 0.12/0.33 % Model : x86_64 x86_64 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.33 % Memory : 8042.1875MB 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.33 % CPULimit : 1920 0.12/0.33 % WCLimit : 240 0.12/0.33 % DateTime : Wed Jul 30 01:59:34 EDT 2025 0.12/0.33 % CPUTime : 0.12/0.35 This is a FOF_ problem 0.12/0.36 Running first-order theorem proving 0.12/0.36 Running /export/starexec/sandbox/solver/bin/vampire --mode casc -m 16384 --cores 7 -t 240 /export/starexec/sandbox/benchmark/theBenchmark.p 0.21/0.41 % (31540)Running in auto input_syntax mode. Trying TPTP 0.21/0.41 % (31548)dis+1011_1_slsqr=8,1:sil=2000:spb=units:fd=off:kmz=on:flr=on:sac=on:slsq=on:random_seed=2226370127:st=2:i=121:sd=30:afp=100000:aac=none:ep=RS:ss=axioms:sgt=10_2399 on theBenchmark for (2399ds/121Mi) 0.21/0.41 % (31548)First to succeed. 0.21/0.41 % (31548)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-31540" 0.21/0.41 % (31540)Running in auto input_syntax mode. Trying TPTP 0.21/0.41 % (31548)Refutation found. Thanks to Tanya! 0.21/0.41 % SZS status Theorem for theBenchmark 0.21/0.41 % SZS output start Proof for theBenchmark 0.21/0.41 fof(f327,plain,( 0.21/0.41 $false), 0.21/0.41 inference(subsumption_resolution,[],[f326,f101])). 0.21/0.41 fof(f101,plain,( 0.21/0.41 contains_slb(sK1,sK3)), 0.21/0.41 inference(cnf_transformation,[],[f90])). 0.21/0.41 fof(f90,plain,( 0.21/0.41 ~pair_in_list(update_slb(sK1,findmin_pqp_res(sK0)),sK3,findmin_pqp_res(sK0)) & ! [X4] : (~pair_in_list(update_slb(sK1,findmin_pqp_res(sK0)),sK3,X4) | ~less_than(findmin_pqp_res(sK0),X4)) & contains_slb(sK1,sK3) & strictly_less_than(sK3,findmin_cpq_res(triple(sK0,sK1,sK2)))), 0.21/0.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f56,f89])). 0.21/0.41 fof(f89,plain,( 0.21/0.41 ? [X0,X1,X2,X3] : (~pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,findmin_pqp_res(X0)) & ! [X4] : (~pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,X4) | ~less_than(findmin_pqp_res(X0),X4)) & contains_slb(X1,X3) & strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2)))) => (~pair_in_list(update_slb(sK1,findmin_pqp_res(sK0)),sK3,findmin_pqp_res(sK0)) & ! [X4] : (~pair_in_list(update_slb(sK1,findmin_pqp_res(sK0)),sK3,X4) | ~less_than(findmin_pqp_res(sK0),X4)) & contains_slb(sK1,sK3) & strictly_less_than(sK3,findmin_cpq_res(triple(sK0,sK1,sK2))))), 0.21/0.41 introduced(definition,[],[choice_axiom])). 0.21/0.41 fof(f56,plain,( 0.21/0.41 ? [X0,X1,X2,X3] : (~pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,findmin_pqp_res(X0)) & ! [X4] : (~pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,X4) | ~less_than(findmin_pqp_res(X0),X4)) & contains_slb(X1,X3) & strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2))))), 0.21/0.41 inference(flattening,[],[f55])). 0.21/0.41 fof(f55,plain,( 0.21/0.41 ? [X0,X1,X2,X3] : ((~pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,findmin_pqp_res(X0)) & ! [X4] : (~pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,X4) | ~less_than(findmin_pqp_res(X0),X4))) & (contains_slb(X1,X3) & strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2)))))), 0.21/0.41 inference(ennf_transformation,[],[f43])). 0.21/0.41 fof(f43,negated_conjecture,( 0.21/0.41 ~! [X0,X1,X2,X3] : ((contains_slb(X1,X3) & strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2)))) => (pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,findmin_pqp_res(X0)) | ? [X4] : (pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,X4) & less_than(findmin_pqp_res(X0),X4))))), 0.21/0.41 inference(negated_conjecture,[status(cth)],[f42])). 0.21/0.41 fof(f42,conjecture,( 0.21/0.41 ! [X0,X1,X2,X3] : ((contains_slb(X1,X3) & strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2)))) => (pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,findmin_pqp_res(X0)) | ? [X4] : (pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,X4) & less_than(findmin_pqp_res(X0),X4))))), 0.21/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown)). 0.21/0.41 fof(f326,plain,( 0.21/0.41 ~contains_slb(sK1,sK3)), 0.21/0.41 inference(resolution,[],[f325,f104])). 0.21/0.41 fof(f104,plain,( 0.21/0.41 ( ! [X0,X1] : (pair_in_list(X0,X1,sK4(X0,X1)) | ~contains_slb(X0,X1)) )), 0.21/0.41 inference(cnf_transformation,[],[f92])). 0.21/0.41 fof(f92,plain,( 0.21/0.41 ! [X0,X1] : (pair_in_list(X0,X1,sK4(X0,X1)) | ~contains_slb(X0,X1))), 0.21/0.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f57,f91])). 0.21/0.41 fof(f91,plain,( 0.21/0.41 ! [X0,X1] : (? [X2] : pair_in_list(X0,X1,X2) => pair_in_list(X0,X1,sK4(X0,X1)))), 0.21/0.41 introduced(definition,[],[choice_axiom])). 0.21/0.41 fof(f57,plain,( 0.21/0.41 ! [X0,X1] : (? [X2] : pair_in_list(X0,X1,X2) | ~contains_slb(X0,X1))), 0.21/0.41 inference(ennf_transformation,[],[f44])). 0.21/0.41 fof(f44,axiom,( 0.21/0.41 ! [X0,X1] : (contains_slb(X0,X1) => ? [X2] : pair_in_list(X0,X1,X2))), 0.21/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown)). 0.21/0.41 fof(f325,plain,( 0.21/0.41 ( ! [X0] : (~pair_in_list(sK1,sK3,X0)) )), 0.21/0.41 inference(subsumption_resolution,[],[f324,f108])). 0.21/0.41 fof(f108,plain,( 0.21/0.41 ( ! [X0] : (less_than(X0,X0)) )), 0.21/0.41 inference(cnf_transformation,[],[f5])). 0.21/0.41 fof(f5,axiom,( 0.21/0.41 ! [X0] : less_than(X0,X0)), 0.21/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown)). 0.21/0.41 fof(f324,plain,( 0.21/0.41 ( ! [X0] : (~pair_in_list(sK1,sK3,X0) | ~less_than(findmin_pqp_res(sK0),findmin_pqp_res(sK0))) )), 0.21/0.41 inference(subsumption_resolution,[],[f323,f222])). 0.21/0.41 fof(f222,plain,( 0.21/0.41 ( ! [X0,X1] : (~pair_in_list(sK1,sK3,X1) | ~less_than(findmin_pqp_res(sK0),X0) | ~less_than(X0,X1)) )), 0.21/0.41 inference(subsumption_resolution,[],[f221,f109])). 0.21/0.41 fof(f109,plain,( 0.21/0.41 ( ! [X2,X0,X1] : (less_than(X0,X2) | ~less_than(X1,X2) | ~less_than(X0,X1)) )), 0.21/0.41 inference(cnf_transformation,[],[f64])). 0.21/0.41 fof(f64,plain,( 0.21/0.41 ! [X0,X1,X2] : (less_than(X0,X2) | ~less_than(X1,X2) | ~less_than(X0,X1))), 0.21/0.41 inference(flattening,[],[f63])). 0.21/0.41 fof(f63,plain,( 0.21/0.41 ! [X0,X1,X2] : (less_than(X0,X2) | (~less_than(X1,X2) | ~less_than(X0,X1)))), 0.21/0.41 inference(ennf_transformation,[],[f4])). 0.21/0.41 fof(f4,axiom,( 0.21/0.41 ! [X0,X1,X2] : ((less_than(X1,X2) & less_than(X0,X1)) => less_than(X0,X2))), 0.21/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown)). 0.21/0.41 fof(f221,plain,( 0.21/0.41 ( ! [X0,X1] : (~less_than(findmin_pqp_res(sK0),X0) | ~pair_in_list(sK1,sK3,X1) | ~less_than(X0,X1) | ~less_than(findmin_pqp_res(sK0),X1)) )), 0.21/0.41 inference(resolution,[],[f214,f102])). 0.21/0.41 fof(f102,plain,( 0.21/0.41 ( ! [X4] : (~pair_in_list(update_slb(sK1,findmin_pqp_res(sK0)),sK3,X4) | ~less_than(findmin_pqp_res(sK0),X4)) )), 0.21/0.41 inference(cnf_transformation,[],[f90])). 0.21/0.41 fof(f214,plain,( 0.21/0.41 ( ! [X2,X3,X0,X1,X4] : (pair_in_list(update_slb(X3,X2),X4,X1) | ~less_than(X2,X0) | ~pair_in_list(X3,X4,X1) | ~less_than(X0,X1)) )), 0.21/0.41 inference(resolution,[],[f109,f105])). 0.21/0.41 fof(f105,plain,( 0.21/0.41 ( ! [X2,X3,X0,X1] : (~less_than(X3,X2) | ~pair_in_list(X0,X1,X2) | pair_in_list(update_slb(X0,X3),X1,X2)) )), 0.21/0.41 inference(cnf_transformation,[],[f59])). 0.21/0.41 fof(f59,plain,( 0.21/0.41 ! [X0,X1,X2,X3] : (pair_in_list(update_slb(X0,X3),X1,X2) | ~pair_in_list(X0,X1,X2) | ~less_than(X3,X2))), 0.21/0.41 inference(flattening,[],[f58])). 0.21/0.41 fof(f58,plain,( 0.21/0.41 ! [X0,X1,X2,X3] : (pair_in_list(update_slb(X0,X3),X1,X2) | (~pair_in_list(X0,X1,X2) | ~less_than(X3,X2)))), 0.21/0.41 inference(ennf_transformation,[],[f45])). 0.21/0.41 fof(f45,axiom,( 0.21/0.41 ! [X0,X1,X2,X3] : ((pair_in_list(X0,X1,X2) & less_than(X3,X2)) => pair_in_list(update_slb(X0,X3),X1,X2))), 0.21/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown)). 0.21/0.41 fof(f323,plain,( 0.21/0.41 ( ! [X0] : (~pair_in_list(sK1,sK3,X0) | less_than(findmin_pqp_res(sK0),X0) | ~less_than(findmin_pqp_res(sK0),findmin_pqp_res(sK0))) )), 0.21/0.41 inference(resolution,[],[f315,f102])). 0.21/0.41 fof(f315,plain,( 0.21/0.41 ( ! [X2,X3,X0,X1] : (pair_in_list(update_slb(X2,X0),X3,X0) | ~pair_in_list(X2,X3,X1) | less_than(X0,X1)) )), 0.21/0.41 inference(resolution,[],[f256,f106])). 0.21/0.41 fof(f106,plain,( 0.21/0.41 ( ! [X2,X3,X0,X1] : (~strictly_less_than(X2,X3) | ~pair_in_list(X0,X1,X2) | pair_in_list(update_slb(X0,X3),X1,X3)) )), 0.21/0.41 inference(cnf_transformation,[],[f61])). 0.21/0.41 fof(f61,plain,( 0.21/0.41 ! [X0,X1,X2,X3] : (pair_in_list(update_slb(X0,X3),X1,X3) | ~pair_in_list(X0,X1,X2) | ~strictly_less_than(X2,X3))), 0.21/0.41 inference(flattening,[],[f60])). 0.21/0.41 fof(f60,plain,( 0.21/0.41 ! [X0,X1,X2,X3] : (pair_in_list(update_slb(X0,X3),X1,X3) | (~pair_in_list(X0,X1,X2) | ~strictly_less_than(X2,X3)))), 0.21/0.41 inference(ennf_transformation,[],[f46])). 0.21/0.41 fof(f46,axiom,( 0.21/0.41 ! [X0,X1,X2,X3] : ((pair_in_list(X0,X1,X2) & strictly_less_than(X2,X3)) => pair_in_list(update_slb(X0,X3),X1,X3))), 0.21/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown)). 0.21/0.41 fof(f256,plain,( 0.21/0.41 ( ! [X0,X1] : (strictly_less_than(X0,X1) | less_than(X1,X0)) )), 0.21/0.41 inference(subsumption_resolution,[],[f112,f113])). 0.21/0.41 fof(f113,plain,( 0.21/0.41 ( ! [X0,X1] : (less_than(X1,X0) | less_than(X0,X1)) )), 0.21/0.41 inference(cnf_transformation,[],[f2])). 0.21/0.41 fof(f2,axiom,( 0.21/0.41 ! [X0,X1] : (less_than(X1,X0) | less_than(X0,X1))), 0.21/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown)). 0.21/0.41 fof(f112,plain,( 0.21/0.41 ( ! [X0,X1] : (strictly_less_than(X0,X1) | ~less_than(X0,X1) | less_than(X1,X0)) )), 0.21/0.41 inference(cnf_transformation,[],[f94])). 0.21/0.41 fof(f94,plain,( 0.21/0.41 ! [X0,X1] : ((strictly_less_than(X0,X1) | ~less_than(X0,X1) | less_than(X1,X0)) & ((less_than(X0,X1) & ~less_than(X1,X0)) | ~strictly_less_than(X0,X1)))), 0.21/0.41 inference(flattening,[],[f93])). 0.21/0.41 fof(f93,plain,( 0.21/0.41 ! [X0,X1] : ((strictly_less_than(X0,X1) | (~less_than(X0,X1) | less_than(X1,X0))) & ((less_than(X0,X1) & ~less_than(X1,X0)) | ~strictly_less_than(X0,X1)))), 0.21/0.41 inference(nnf_transformation,[],[f3])). 0.21/0.41 fof(f3,axiom,( 0.21/0.41 ! [X0,X1] : (strictly_less_than(X0,X1) <=> (less_than(X0,X1) & ~less_than(X1,X0)))), 0.21/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown)). 0.21/0.41 % SZS output end Proof for theBenchmark 0.21/0.41 % (31548)------------------------------ 0.21/0.41 % (31548)Version: Vampire 5.0.0 (Release build, commit 3ce9b74f2 on 2025-07-14 12:22:21 +0200) 0.21/0.41 % (31548)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c 0.21/0.41 % (31548)Termination reason: Refutation 0.21/0.41 0.21/0.41 % (31548)Time elapsed: 0.004 s 0.21/0.41 % (31548)Peak memory usage: 8 MB 0.21/0.41 % (31548)Instructions burned: 10 (million) 0.21/0.41 % (31548)------------------------------ 0.21/0.41 % (31548)------------------------------ 0.21/0.41 % (31540)Success in time 0.053 s 0.21/0.42 EOF